Mathematical models of natural gas consumption
International Nuclear Information System (INIS)
Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana
2011-01-01
In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.
Mathematical analysis of intermittent gas injection model in oil production
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
Energy Technology Data Exchange (ETDEWEB)
Gomes, Leonardo Vinicius; Mendes, Pedro Paulo C. [Escola Federal de Engenharia de Itajuba, MG (Brazil). Dept. de Eletrotecnica; Ferreira, Claudio [Agencia Nacional de Energia Eletrica (ANEEL), Brasilia, DF (Brazil)
1999-07-01
This paper presents the development and analysis of various mathematical models for gas turbine which can be incorporated to dynamic stability or to electric power systems. The work provides answers for questions such as: the dynamic behaviour of gas turbine driven generator unities, the influence of those equipment in the other elements and the best operational conditions for the equipment.
Mathematical modelling of mixing in gas stirred ladles
International Nuclear Information System (INIS)
Ramirez-Argaez, M. A.; Tapia, J.; Espinoza, J.; Alcantar, E.
2006-01-01
In this work injection of air into a water physical model of an industrial steel ladle was mathematically simulated. Calculations were developed based on a multiphase Eulerian fluid flow model involving principles of conservation of mass, momentum and chemical species on both phases in order to predict turbulent flow patterns and mixing times in both centric and eccentric injections. Mixing phenomena was addressed by injecting a tracer centric and eccentric injections. Mixing phenomena was addressed by injecting a tracer and it was analyzed the effect of the gas flow rate, injector position, number of injectors and geometry of the ladle on the mixing time. It was concluded that the optimum injection conditions is using a single injector at 2/3 of the radius with high gas flow rates. It is shown that incrementing the number of injectors is detrimental on mixing. Finally, quantitative correlations of mixing time as a function of gas flow rate, position of the injectors, geometry of the ladle and mass of liquid were obtained. (Author)
Study and mathematical model of ultra-low gas burner
International Nuclear Information System (INIS)
Gueorguieva, A.
2001-01-01
The main objective of this project is prediction and reduction of NOx and CO 2 emissions under levels recommended from European standards for gas combustion processes. A mathematical model of burner and combustion chamber is developed based on interacting fluid dynamics processes: turbulent flow, gas phase chemical reactions, heat and radiation transfer The NOx prediction model for prompt and thermal NOx is developed. The validation of CFD (Computer fluid-dynamics) simulations corresponds to 5 MWI burner type - TEA, installed on CASPER boiler. This burner is three-stream air distribution burner with swirl effect, designed by ENEL to meet future NOx emission standards. For performing combustion computer modelling, FLUENT CFD code is preferred, because of its capabilities to provide accurately description of large number of rapid interacting processes: turbulent flow, phase chemical reactions and heat transfer and for its possibilities to present wide range of calculation and graphical output reporting data The computational tool used in this study is FLUENT version 5.4.1, installed on fs 8200 UNIX systems The work includes: study the effectiveness of low-NOx concepts and understand the impact of combustion and swirl air distribution and flue gas recirculation on peak flame temperatures, flame structure and fuel/air mixing. A finite rate combustion model: Eddy-Dissipation (Magnussen-Hjertager) Chemical Model for 1, 2 step Chemical reactions of bi-dimensional (2D) grid is developed along with NOx and CO 2 predictions. The experimental part of the project consists of participation at combustion tests on experimental facilities located in Livorno. The results of the experiments are used, to obtain better vision for combustion process on small-scaled design and to collect the necessary input data for further Fluent simulations
Mathematical model of gas plasma applied to chronic wounds
Energy Technology Data Exchange (ETDEWEB)
Wang, J. G.; Liu, X. Y.; Liu, D. W.; Lu, X. P. [State Key Lab of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, WuHan, HuBei 430074 (China); Zhang, Y. T. [Shandong Provincial Key Lab of UHV Technology and Gas Discharge Physics, School of Electrical Engineering, Shandong University, Jinan, Shandong Province 250061 (China)
2013-11-15
Chronic wounds are a major burden for worldwide health care systems, and patients suffer pain and discomfort from this type of wound. Recently gas plasmas have been shown to safely speed chronic wounds healing. In this paper, we develop a deterministic mathematical model formulated by eight-species reaction-diffusion equations, and use it to analyze the plasma treatment process. The model follows spatial and temporal concentration within the wound of oxygen, chemoattractants, capillary sprouts, blood vessels, fibroblasts, extracellular matrix material, nitric oxide (NO), and inflammatory cell. Two effects of plasma, increasing NO concentration and reducing bacteria load, are considered in this model. The plasma treatment decreases the complete healing time from 25 days (normal wound healing) to 17 days, and the contributions of increasing NO concentration and reducing bacteria load are about 1/4 and 3/4, respectively. Increasing plasma treatment frequency from twice to three times per day accelerates healing process. Finally, the response of chronic wounds of different etiologies to treatment with gas plasmas is analyzed.
Lam, R. B.; And Others
1983-01-01
Investigated application of binomial statistics to equilibrium distribution of ester systems by employing gas chromatography to verify the mathematical model used. Discusses model development and experimental techniques, indicating the model enables a straightforward extension to symmetrical polyfunctional esters and presents a mathematical basis…
Mathematical models for gas transportation simulation and interactive graphics
Energy Technology Data Exchange (ETDEWEB)
Giannini, L.; Marinetti, A.
1988-01-01
This paper describes a simulation system particularly suitable for a wide range of applications: 1. short, medium and long term planning: 2. pipeline design; 3. modelling research; 4. dispatching planning; 5. training. The system may furthermore be used for the same purpose by both skilled and non-skilled personnel, operating in different ways. In view of this variety of outlooks regarding the system, an integrated software package was found to be necessary, in order to manage multiple simulations of different networks for varying applications. The mathematical model, which forms the basis of the system, uses the complete formulation of gasdynamics 1-D equations: the continuity equation, the momentum conservation equation and the energy conservation equation. These three equations form a system of quasi-linear partial differential equations which are resolved numerically. Multi-windowing techniques are used together with cooperative process techniques (organized as detached processes or hierarchical trees), in order to reduce response times.
Rodrigues, M.A.M.; Cone, J.W.; Ferreira, L.M.M.; Blok, M.C.; Guedes, C.
2009-01-01
In vitro and in situ studies were conducted to evaluate the influence of different mathematical models, used to fit gas production profiles of 15 feedstuffs, on estimates of nylon bag organic matter (OM) degradation kinetics. The gas production data were fitted to Exponential, Logistic, Gompertz and
MATHEMATIC MODELING IN ANALYSIS OF BIO-GAS PURIFICATION FROM CARBON DIOXIDE
Directory of Open Access Journals (Sweden)
Y. A. Losiouk
2009-01-01
Full Text Available The paper considers a possibility to involve bio-gas generated at testing grounds of hard domestic garbage in power supply system in the Republic of Belarus. An example of optimization using mathematical modeling of plant operation which is used for bio-gas enrichment is given in the paper.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive......Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...
The High Level Mathematical Models in Calculating Aircraft Gas Turbine Engine Parameters
Directory of Open Access Journals (Sweden)
Yu. A. Ezrokhi
2017-01-01
Full Text Available The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
М. В. Грязев; Н. М. Качурин; С. А. Воробьев
2017-01-01
New trends have been traced and the existing ones refined regarding filtration and diffusive motion of gases in coal beds and surrounding rock, spontaneous heating of coal and transport of gas traces by ventilation currents in operating coal mines. Mathematical models of gas-dynamic and thermophysical processes inside underworked territories after mine abandonment have been justified. Mathematical models are given for feasible air feeding of production and development areas, as well as for th...
Mathematical model for liquid-gas equilibrium in acetic acid fermentations
Romero; Cantero
1998-08-05
An experimental study was conducted to propose an adequate mathematical model for liquid-gas equilibrium in acetic acid fermentations. Three operation scales (laboratory, pilot plant, and industrial plant) were employed to obtain the sets of experimental data. The proposed model, based in the UNIFAC method for the estimation of activity coefficients of a solution consisting of several components, takes into account the effect of temperature. However, in the set of equations, it has been necessary to put in the degree of equilibrium (epsilon). This coefficient adequately reflects the physical conditions of fermentation equipment. The experimental and numerical results help to define the fundamental mechanisms for liquid-gas equilibrium in these systems and demonstrate the model validity in the three tested scales. It was also found that in an industrial setting, closed systems are those with lowest evaporation losses. Copyright 1998 John Wiley & Sons, Inc.
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Contribution to complex gas-liquid flows: Development and validation of a mathematical model
Selma, Brahim
This study describes the development and validation of Computational Fluid Dynamics (CFD) model for the simulation of dispersed two-phase flows taking in the account the population balance of particles size distribution. A two-fluid (Euler-Euler) methodology previously developed for complex flows is adapted to the present project. The continuous phase turbulence is represented using a two-equation k --- epsilon turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence and the effects of the gas-liquid interface. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift, virtual mass and drift velocity. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture a good accuracy for gas hold-up, liquid velocity profiles and turbulence parameters. Furthermore, a correlation for the effect of the drift velocity on the turbulence behaviour is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely [61]. Finally, assessment of the model is made with reference to experimental data for gas-liquid bubbly flow in a rectangular bubble column [133; 134; 135; 18], in a double-turbine stirred tank reactor [126; 127] and in an air-lift bioreacator [101]. Key words: mathematical modelling, complex flow gas-liquid, turbulence, population balance, computational fluids dynamics CFD, OpenFOAM, moments method, method of classes, QMOM, DQMOM.
Energy Technology Data Exchange (ETDEWEB)
Ramirez-Argaez, M. A.; Tapia, J.; Espinoza, J.; Alcantar, E.
2006-07-01
In this work injection of air into a water physical model of an industrial steel ladle was mathematically simulated. Calculations were developed based on a multiphase Eulerian fluid flow model involving principles of conservation of mass, momentum and chemical species on both phases in order to predict turbulent flow patterns and mixing times in both centric and eccentric injections. Mixing phenomena was addressed by injecting a tracer centric and eccentric injections. Mixing phenomena was addressed by injecting a tracer and it was analyzed the effect of the gas flow rate, injector position, number of injectors and geometry of the ladle on the mixing time. It was concluded that the optimum injection conditions is using a single injector at 2/3 of the radius with high gas flow rates. It is shown that incrementing the number of injectors is detrimental on mixing. Finally, quantitative correlations of mixing time as a function of gas flow rate, position of the injectors, geometry of the ladle and mass of liquid were obtained. (Author)
Mathematical modeling of non-stationary gas flow in gas pipeline
Fetisov, V. G.; Nikolaev, A. K.; Lykov, Y. V.; Duchnevich, L. N.
2018-03-01
An analysis of the operation of the gas transportation system shows that for a considerable part of time pipelines operate in an unsettled regime of gas movement. Its pressure and flow rate vary along the length of pipeline and over time as a result of uneven consumption and selection, switching on and off compressor units, shutting off stop valves, emergence of emergency leaks. The operational management of such regimes is associated with difficulty of reconciling the operating modes of individual sections of gas pipeline with each other, as well as with compressor stations. Determining the grounds that cause change in the operating mode of the pipeline system and revealing patterns of these changes determine the choice of its parameters. Therefore, knowledge of the laws of changing the main technological parameters of gas pumping through pipelines in conditions of non-stationary motion is of great importance for practice.
Mathematical modelling of flue gas tempered flames produced from pulverised coal fired with oxygen
Energy Technology Data Exchange (ETDEWEB)
Breussin, A.; Weber, R.; Kamp, W.L. van de
1997-10-01
The combustion of pulverised coal in conventional utility boilers contributes significantly to global CO{sub 2} emissions. Because atmospheric air is used as the combustion medium, the exhaust gases of conventional pulverised coal fired utility boilers contain approximately 15 % CO{sub 2}. This relatively low concentration makes separating and recovering CO{sub 2} a very energy-intensive process. This process can be simplified if N{sub 2} is eliminated from the comburent before combustion by firing the pulverised coal with pure oxygen. However, this concept will result in very high flames temperatures. Flue gas recirculation can be used to moderate the flame temperature, whilst generating a flue gas with a CO{sub 2} concentration of 95 %. In this presentation, both experimental and modelling work will be described. The former deals with identifying the issues related to the combustion of pulverised coal in simulated turbine exhaust gas, particularly with respect to stability, burnout and pollutant emissions. The second part of this presentation describes mathematical modelling of type 2 as well as type 1 swirling pulverised coal flames. Future work will concentrate on high CO{sub 2} levels environments. (orig.)
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Study on Fluid-solid Coupling Mathematical Models and Numerical Simulation of Coal Containing Gas
Xu, Gang; Hao, Meng; Jin, Hongwei
2018-02-01
Based on coal seam gas migration theory under multi-physics field coupling effect, fluid-solid coupling model of coal seam gas was build using elastic mechanics, fluid mechanics in porous medium and effective stress principle. Gas seepage behavior under different original gas pressure was simulated. Results indicated that residual gas pressure, gas pressure gradient and gas low were bigger when original gas pressure was higher. Coal permeability distribution decreased exponentially when original gas pressure was lower than critical pressure. Coal permeability decreased rapidly first and then increased slowly when original pressure was higher than critical pressure.
Oil, Gas and Conflict: A Mathematical Model for the Resource Curse.
Cai, Yiyong; Newth, David
2013-01-01
Oil and natural gas are highly valuable natural resources, but many countries with large untapped reserves suffer from poor economic and social-welfare performance. This conundrum is known as the resource curse. The resource curse is a result of poor governance and wealth distribution structures that allow the elite to monopolize resources for self-gain. When rival social groups compete for natural resources, civil unrest soon follows. While conceptually easy to follow, there have been few formal attempts to study this phenomenon. Thus, we develop a mathematical model that captures the basic elements and dynamics of this dilemma. We show that when resources are monopolized by the elite, increased exportation leads to decreased domestic production. This is due to under-provision of the resource-embedded energy and industrial infrastructure. Decreased domestic production then lowers the marginal return on productive activities, and insurgency emerges. The resultant conflict further displaces human, built, and natural capital. It forces the economy into a vicious downward spiral. Our numerical results highlight the importance of governance reform and productivity growth in reducing oil-and-gas-related conflicts, and thus identify potential points of intervention to break the downward spiral.
Oil, Gas and Conflict: A Mathematical Model for the Resource Curse.
Directory of Open Access Journals (Sweden)
Yiyong Cai
Full Text Available Oil and natural gas are highly valuable natural resources, but many countries with large untapped reserves suffer from poor economic and social-welfare performance. This conundrum is known as the resource curse. The resource curse is a result of poor governance and wealth distribution structures that allow the elite to monopolize resources for self-gain. When rival social groups compete for natural resources, civil unrest soon follows. While conceptually easy to follow, there have been few formal attempts to study this phenomenon. Thus, we develop a mathematical model that captures the basic elements and dynamics of this dilemma. We show that when resources are monopolized by the elite, increased exportation leads to decreased domestic production. This is due to under-provision of the resource-embedded energy and industrial infrastructure. Decreased domestic production then lowers the marginal return on productive activities, and insurgency emerges. The resultant conflict further displaces human, built, and natural capital. It forces the economy into a vicious downward spiral. Our numerical results highlight the importance of governance reform and productivity growth in reducing oil-and-gas-related conflicts, and thus identify potential points of intervention to break the downward spiral.
Mathematical Model Based on Newton’s Laws and in First Thermodynamic Law of a Gas Turbine
Ottmar Rafael Uriza Gosebruch; Carlos Alexander Nuñez Martin; Eloy Edmundo Rodríguez Vázquez; Eduardo Campos Mercado
2017-01-01
The present article explains the modeling of a Gas Turbine system; the mathematical modeling is based on fluid mechanics applying the principal energy laws such as Euler’s Law, Newton’s second Law and the first thermodynamic law to obtain the equations for mass, momentum and energy conservation; expressed as the continuity equation, the Navier-Stokes equation and the energy conservation using Fourier’s Law. The purpose of this article is to establish a precise mathematical model to be applied...
Mathematical Model Based on Newton’s Laws and in First Thermodynamic Law of a Gas Turbine
Directory of Open Access Journals (Sweden)
Ottmar Rafael Uriza Gosebruch
2017-09-01
Full Text Available The present article explains the modeling of a Gas Turbine system; the mathematical modeling is based on fluid mechanics applying the principal energy laws such as Euler’s Law, Newton’s second Law and the first thermodynamic law to obtain the equations for mass, momentum and energy conservation; expressed as the continuity equation, the Navier-Stokes equation and the energy conservation using Fourier’s Law. The purpose of this article is to establish a precise mathematical model to be applied in control applications, for future works, within industry applications.
Energy Technology Data Exchange (ETDEWEB)
Freire, Marcelo; Mendes, Pedro Paulo de C.; Ferreira, Claudio; Passaro, Mauricio Campos; Gomes, Leonardo Vinicius [Escola Federal de Engenharia de Itajuba, MG (Brazil). Dept. de Eletronica]. E-mails: freire_marcelo@hotmail.com; ppaulo@iee.efei.br; claudio@iee.efei.br; mcpassaro@uol.com.br; leonardo@iee.efei.br
2002-07-01
This paper develops, implements and simulates simplified mathematical models of multiple shafts, aero derivatives and heavy-duty gas turbines, aiming the subsides for studies of power systems dynamic behaviour. These components are fundamental to an approximated evaluation of the National Integrated System after the new thermoelectric plants are incorporated.
Directory of Open Access Journals (Sweden)
М. В. Грязев
2017-03-01
Full Text Available New trends have been traced and the existing ones refined regarding filtration and diffusive motion of gases in coal beds and surrounding rock, spontaneous heating of coal and transport of gas traces by ventilation currents in operating coal mines. Mathematical models of gas-dynamic and thermophysical processes inside underworked territories after mine abandonment have been justified. Mathematical models are given for feasible air feeding of production and development areas, as well as for the development of geotechnical solutions to ensure gas-dynamic safety at every stage of coal mine operation. It is demonstrated that the use of high-performance equipment in the production and development areas requires more precise filtration equations used when assessing coal mine methane hazard. A mathematical model of pressure field of non-associated methane in the edge area of the coal seam has been justified. The model is based on one-dimensional hyperbolic equation and takes into consideration final rate of pressure distribution in the seam. Trends in gas exchange between mined-out spaces of high methane- and CO2-concentration mines with the earth surface have been refined in order to ensure environmental safety of underworked territories.
Directory of Open Access Journals (Sweden)
Lenuta Suciu
2006-10-01
Full Text Available The works presents the mathematical model of electrical arc welding, simulation of the electrical arc as a moving source with help programs software Ansys, passing through three stage of simulation: pre- processing, processing (solution and post-processing.
Directory of Open Access Journals (Sweden)
Szwast Maciej
2015-06-01
Full Text Available The paper presents the mathematical modelling of selected isothermal separation processes of gaseous mixtures, taking place in plants using membranes, in particular nonporous polymer membranes. The modelling concerns membrane modules consisting of two channels - the feeding and the permeate channels. Different shapes of the channels cross-section were taken into account. Consideration was given to co-current and counter-current flows, for feeding and permeate streams, respectively, flowing together with the inert gas receiving permeate. In the proposed mathematical model it was considered that pressure of gas changes along the length of flow channels was the result of both - the drop of pressure connected with flow resistance, and energy transfer by molecules of gas flowing in a given channel to molecules which penetrate this channel from the adjacent channel. The literature on membrane technology takes into account only the drop of pressure connected with flow resistance. Consideration given to energy transfer by molecules of gas flowing in a given channel to molecules which penetrate this channel from the adjacent channel constitute the essential novelty in the current study. The paper also presents results of calculations obtained by means of a computer program which used equations of the derived model. Physicochemical data concerning separation of the CO2/CH4 mixture with He as the sweep gas and data concerning properties of the membrane made of PDMS were assumed for calculations.
Boroujeni, Mahdi K.; Goodarzi, F.
2011-09-01
In present study, a special mathematical model for membrane separation processes was studied. Mathematical model was developed for propylene/propane system and was solved using finite difference solution approach. In this study, membrane length is shared into a number of nodes and required equations are written for each node, separately. Also, golden section method was used for suitable step size selection. It is prescience that the results accuracy and calculation time, depend on number of meshes. Therefore 20 meshes were obtained as an optimum number. The effect of pressure drop equation on solution procedure of the model was also investigated and it was found that the pressure drop equation has a negligible effect on it.
International Nuclear Information System (INIS)
Ramirez-Argaez, M. A.; Conteras, F.; Gonzalez, C.
2006-01-01
In this work a fundamental Eulerian mathematical model was developed to study fluid flow and mixing phenomena in aluminium ladles equipped with impeller for deshidrogenization treatment. The effect of critical process parameters such as rotor speed, depth of immersion, gas flow rate, and type of rotor on the mixing behavior and vortex formation was analyzed with this model. The model simulates operation with and without gas injection and it was developed on the commercial CFD code PHOENICS 3.4 in order to solve all conservation equations governing the process, i. e. continuity, 3D turbulent Navier-Stockers and the kε turbulence model for a two-phase fluid flow problem using the Inter Phase Slip Algorithm (IPSA). (Author). 20 refs
Directory of Open Access Journals (Sweden)
Yan Zeng
2018-01-01
Full Text Available Multistage fractured horizontal wells (MFHWs have become the main technology for shale gas exploration. However, the existing models have neglected the percolation mechanism in nanopores of organic matter and failed to consider the differences among the reservoir properties in different areas. On that account, in this study, a modified apparent permeability model was proposed describing gas flow in shale gas reservoirs by integrating bulk gas flow in nanopores and gas desorption from nanopores. The apparent permeability was introduced into the macroseepage model to establish a dynamic pressure analysis model for MFHWs dual-porosity formations. The Laplace transformation and the regular perturbation method were used to obtain an analytical solution. The influences of fracture half-length, fracture permeability, Langmuir volume, matrix radius, matrix permeability, and induced fracture permeability on pressure and production were discussed. Results show that fracture half-length, fracture permeability, and induced fracture permeability exert a significant influence on production. A larger Langmuir volume results in a smaller pressure and pressure derivative. An increase in matrix permeability increases the production rate. Besides, this model fits the actual field data relatively well. It has a reliable theoretical foundation and can preferably describe the dynamic changes of pressure in the exploration process.
Hankin, R K; Britter, R E
1999-05-14
The Major Hazard Assessment Unit of the Health and Safety Executive (HSE) provides advice to local planning authorities on land use planning in the vicinity of major hazard sites. For sites with the potential for large scale releases of toxic heavy gases such as chlorine this advice is based on risk levels and is informed by use of the computerised risk assessment tool RISKAT [C. Nussey, M. Pantony, R. Smallwood, HSE's risk assessment tool RISKAT, Major Hazards: Onshore and Offshore, October, 1992]. At present RISKAT uses consequence models for heavy gas dispersion that assume flat terrain. This paper is the first part of a three part paper. Part 1 describes the mathematical basis of TWODEE, the Health and Safety Laboratory's shallow layer model for heavy gas dispersion. The shallow layer approach used by TWODEE is a compromise between the complexity of CFD models and the simpler integral models. Motivated by the low aspect ratio of typical heavy gas clouds, shallow layer models use depth-averaged variables to describe the flow behaviour. This approach is particularly well suited to assess the effect of complex terrain because the downslope buoyancy force is easily included. Entrainment may be incorporated into a shallow layer model by the use of empirical formulae. Part 2 of this paper presents the numerical scheme used to solve the TWODEE mathematical model, and validated against theoretical results. Part 3 compares the results of the TWODEE model with the experimental results taken at Thorney Island [J. McQuaid, B. Roebuck, The dispersion of heavier-than-air gas from a fenced enclosure. Final report to the US Coast Guard on contract with the Health and Safety Executive, Technical Report RPG 1185, Safety Engineering Laboratory, Research and Laboratory Services Division, Broad Lane, Sheffield S3 7HQ, UK, 1985]. Crown Copyright Copyright 1999 Published by Elsevier Science B.V.
Mathematical Modeling Using MATLAB
National Research Council Canada - National Science Library
Phillips, Donovan
1998-01-01
.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...
International Nuclear Information System (INIS)
Dimkovski, Sasho
2014-01-01
The greater energy demand by today society sets a number of new challenges in the energy sector. The climate extremes impose new modes of operation of the power plants, with high flexibility in production. Combined cycle co generative power plants are the latest trend in the energy sector. Their high prevalence is due to the great efficiency and the good environmental characteristics. The main work horse in these cogeneration plants is the gas turbine, which power production and efficiency strongly depends on the external climate conditions. In warmer periods when there is increased demand for electricity, the power production from the gas turbines significantly declines. Because of the high electricity demand from the grid and reduced power production from the gas turbines at the same time, the need for application of appropriate technology for preserving the performances and power of the gas turbines arises. This master thesis explores different methods to improve the power in gas turbines by cooling the air on the compressor inlet, analyzing their applicability and effectiveness in order to choose the optimal method for power augmentation for the climatic conditions in the city Skopje. The master thesis gives detailed analysis of the weather in Skopje and the time frame in which the chosen method is applicable. At the end in the master thesis, the economic feasibility of the given method for power augmentation is clearly calculated, using a model of a power plant and calculating the resulting amount of gained energy, the amount of the initial investment, the cost for maintenance and operation of the equipment. By these calculations the period for initial return of investment is obtained. As an added benefit the positive environmental impacts of the applied technology for inlet air cooling is analyzed. (author)
International Nuclear Information System (INIS)
Bracco, Stefano; Delfino, Federico
2017-01-01
Microturbines represent a suitable technology to be adopted in smart microgrids since they are characterized by affordable capital and maintenance costs, high reliability and flexibility, and low environmental impact; moreover, they can be fed by fossil fuels or biofuels. They can operate in cogeneration and trigeneration mode, thus permitting to attain high global efficiency values of the energy conversion system from primary energy to electrical and thermal energy; from the electrical point of view, microturbines can operate connected to the distribution grid but also in islanded mode, thus enabling their use in remote areas without electrification. The paper describes the mathematical model that has been developed to simulate in off-design and transient conditions the operation of a 65 kW el cogeneration microturbine installed within a smart microgrid. The dynamic simulation model is characterized by a flexible architecture that permits to simulate other different size single-shaft microturbines. The paper reports the main equations of the model, focusing on the architecture of the simulator and the microturbine control system; furthermore the most significant results derived from the validation phase are reported too, referring to the microturbine installed in the Smart Polygeneration Microgrid of the Savona Campus at the University of Genoa in Italy. - Highlights: • Dynamic simulation model of a cogeneration microturbine. • Off-design and transient performances of the microturbine. • Simulator validated on the Smart Polygeneration Microgrid at the Savona Campus.
Mathematical modeling of heat transfer in production premises heated by gas infrared emitters
Directory of Open Access Journals (Sweden)
Maksimov Vyacheslav I.
2017-01-01
Full Text Available The results of numerical modeling of the process of free convective heat transfer in the regime of turbulent convection in a closed rectangular region heated by an infrared radiator are presented. The system of Navier-Stokes equations in the Boussinesq approximation is solved, the energy equation for the gas and the heat conduction equations for the enclosing vertical and horizontal walls. A comparative analysis of the heat transfer regimes in the considered region for different Grashof numbers is carried out. The features of the formation of heated air flows relative to the infrared emitter located at some distance from the upper horizontal boundary of the region are singled out.
Bauer, Stefan; Janßen, Marco; Schmitz, Martin; Ott, Günter
2017-11-01
Arc welding is accompanied by intense optical radiation emission that can be detrimental not only for the welder himself but also for people working nearby or for passersby. Technological progress advances continuously in the field of joining, so an up-to-date radiation database is necessary. Additionally, many literature irradiance data have been measured for a few welding currents or for parts of the optical spectral region only. Within this paper, a comprehensive study of contemporary metal active gas, metal inert gas, and cold metal transfer welding is presented covering optical radiation emission from 200 up to 2,700 nm by means of (spectro-) radiometric measurements. The investigated welding currents range from 70 to 350 A, reflecting values usually applied in industry. Based upon these new irradiance data, three mathematical models were derived in order to describe optical radiation emission as a function of welding power. The linear, exponential, and sigmoidal emission models depend on the process variant (standard or pulsed) as well as on the welding material (mild and stainless steel, aluminum). In conjunction with the corresponding exposure limit values for incoherent optical radiation maximum permissible exposure durations were calculated as a function of welding power. Typical times are shorter than 1 s for the ultraviolet spectral region and range from 1 to 10 s for visible radiation. For the infrared regime, exposure durations are of the order of minutes to hours. Finally, a validation of the metal active gas emission models was carried out with manual arc welding.
Directory of Open Access Journals (Sweden)
Li Li
2010-01-01
Full Text Available A mathematical model to predict oxygen, carbon dioxide, and water vapour exchanges in non-perforated and micro-perforated modified atmosphere packaging films has successfully been proposed. The transmission rate of gases was measured for films with thickness of 0.03 and 0.05 mm, perforation diameters of 0.5 and 2.0 mm, and temperatures of 0, 10 and 20 °C. Under most conditions, the increase in temperature and perforation diameter increased the transmission rate of oxygen, carbon dioxide, and water vapour, whereas the increase in film thickness decreased the transmission rate of the various gases. Validation of the proposed modified atmosphere packaging model was found to yield good prediction for gas concentrations and percentage losses in the mass of the produce after comparison with the experimental results of modified atmosphere packaging for tomato (Lycopersicon esculentum.
Mathematical modeling using Maple
Beauchamp, Robert Edward.
1996-01-01
The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab...
Mathematical modeling of blood-gas kinetics for the volatile organic compounds isoprene and acetone
International Nuclear Information System (INIS)
King, J.
2010-01-01
Breath gas analysis is based on the compelling concept that the exhaled breath levels of endogenously produced volatile organic compounds (VOCs) can provide a direct, non-invasive window to the blood and hence, by inference, to the body. In this sense, breath VOCs are regarded as a comprehensive repository of valuable physiological and clinical information, that might be exploited in such diverse areas as diagnostics, therapeutic monitoring or general dynamic assessments of metabolic function, pharmacodynamics (e.g., in drug testing) and environmental exposure (e.g., in occupational health). Despite this enormous potential, the lack of standardized breath sampling regimes as well as the poor mechanistic understanding of VOC exhalation kinetics could cast a cloud over the widespread use of breath gas analysis in the biomedical sciences. In this context, a primary goal of the present thesis is to provide a better quantitative insight into the breath behavior of two prototypic VOCs, isoprene and acetone. A compartmental modeling framework is developed and validated by virtue of real-time breath measurements of these trace gases during distinct physiological states. In particular, the influence of various hemodynamic and ventilatory parameters on VOC concentrations in exhaled breath is investigated. This approach also complements previous steady state investigations in toxicology. From a phenomenological point of view, both acetone and isoprene concentrations in end-tidal breath are demonstrated to exhibit a reproducible non-steady state behavior during moderate workload challenges on a stationary bicycle. However, these dynamics depart drastically from what is expected on the basis of classical pulmonary inert gas elimination theory. More specifically, the start of exercise is accompanied by an abrupt increase in breath isoprene levels, usually by a factor of 3 to 4 compared with the steady state value during rest. This phase is followed by a gradual decline and the
Mathematical Modelling Approach in Mathematics Education
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Mathematical model of a multi-loop network of gas pipelines at various modes of current
Directory of Open Access Journals (Sweden)
Orifjon Sh. Bozorov
2012-05-01
Full Text Available A method of hydraulic calculation of a multi-loop network of gas pipelines based on Kirchhoff’s laws is offered. As completing relations, the formula for the change of pressure on elementary sites of the horizontal gas pipe, received on the basis of Leybenzon’s generalized formula of resistance is used.
Mathematical modelling in science and mathematics education
Teodoro, Vítor Duarte; Neves, Rui Gomes
2011-01-01
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Mathematical modeling of aeroelastic systems
Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.
2017-12-01
In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Mathematical modeling in realistic mathematics education
Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo
2017-12-01
The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.
Mathematical modeling of the complete thermodynamic cycle of a new Atkinson cycle gas engine
International Nuclear Information System (INIS)
Shojaeefard, Mohammad Hassan; Keshavarz, Mojtaba
2015-01-01
The Atkinson cycle provides the potential to increase the efficiency of SI engines using overexpansion concept. This also will suggest decrease in CO 2 generation by internal combustion engine. In this study a mathematical modeling of complete thermodynamic cycle of a new two-stroke Atkinson cycle SI engine will be presented. The mathematical modeling is carried out using two-zone combustion analysis in order to make the model predict exhaust emission so that its values could be compared with the values of conventional SI engine. The model also is validated against experimental tests in that increase in efficiency is achieved compared to conventional SI engines. - Highlights: • The complete cycle model for the rotary Atkinson engine was developed. • Comparing the results with experimental data shows good model validity. • The model needs further improvement for the scavenging phase. • There is 5% increment in thermal efficiency with new engine compared to conventional SI engines.
International Nuclear Information System (INIS)
Starchenko, A.V.; Bubenchikov, A.M.; Burlutskij, E.S.
2002-01-01
The mathematical model of the gas suspension nonisothermal turbulent flow in a pipe is formulated within the frames of the mixed Eulerian-Lagrangian representation. The model testing showed good agreement of the calculational results with the experiments as well as with the continuous model data. Application of two essentially differing approaches (the continuous and mixed ones) to modeling the density flow practically to similar results by the fields of averaged velocities and temperatures as well as by the coefficient of accommodation of the tangential velocity component and essentially of the particles collision with the wall surface [ru
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Mathematical Modeling: A Structured Process
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Szwast Maciej; Szwast Zbigniew
2015-01-01
The paper presents the mathematical modelling of selected isothermal separation processes of gaseous mixtures, taking place in plants using membranes, in particular nonporous polymer membranes. The modelling concerns membrane modules consisting of two channels - the feeding and the permeate channels. Different shapes of the channels cross-section were taken into account. Consideration was given to co-current and counter-current flows, for feeding and permeate streams, respectively, flowing to...
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Richardson, mathematical modeller
Vreugdenhil, C. B.
1994-03-01
On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
A Primer for Mathematical Modeling
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
International Nuclear Information System (INIS)
Castillo M, J.A.; Pimentel P, A.E.
2000-01-01
This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)
Mathematical models of human retina.
Tălu, Stefan
2011-01-01
To describe the human retina, due the absence of complete topographical data, mathematical models are required. The mathematical formula permits a relatively simple representation to explore the physical and optical characteristics of the retina, with particular parameters. Advanced mathematical models are applied for human vision studies, solid modelling and biomechanical behavior of the retina. The accurate modelling of the retina is important in the development of visual prostheses. The objective of this paper is to present an overview of researches for human retina modelling using mathematical models.
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
Nachaisin, Mali; Teeta, Suminya; Deejing, Konlayut; Pharanat, Wanida
2017-09-01
Instant food is a product produced for convenience for consumer. Qualities are an important attribute of food materials reflecting consumer acceptance. The most problem of instant rice is casehardening during drying process resulted in the longer rehydration time. The objective of this research was to study the qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying. Additionally, the mathematical models for gas-fired infrared assisted thin-layer drying of shredded Thai-style rice for traditional was investigated. The thin-layer drying of shredded Thai-style rice was carried out under gas-fired infrared intensities of 1000W/m2, air temperatures of 70°C and air velocities of 1 m/s. The drying occurred in the falling rate of drying period. The Page model was found to satisfactorily describe the drying behavior of shredded Thai-style rice, providing the highest R2 (0.997) and the lowest MBE and RMSE (0.01 and 0.18) respectively. A 9 point hedonic test showed in softness and color, but odor and overall acceptance were very similar.
Duxbury, N. S.; Romanovsky, V. E.; Romanovskii, N. N.; Garagulya, L. S.; Brouchkov, A. V.; Komarov, I. A.; Roman, L. T.; Tipenko, G. S.; Buldovich, S. N.; Maximova, L. N.
2012-12-01
We have developed coupled permafrost - carbon physical and numerical models, where carbon is in the form of methane clathrate hydrate ( CH4*6H2O ) in a porous subsurface environment. The driving force for the subsurface temperature field dynamics is climate variations on the Earth's surface. This is an upper boundary condition for the nonlinear evolutionary system of partial differential equations (PDEs) describing subsurface heat transfer (parabolic PDEs) in a generalized Stefan formulation. The developed numerical model is a valuable computational tool to quantitatively study nonlinear dynamical thermal processes with phase transitions in terrestrial and Martian subsurfaces. Our model is multifrontal and therefore allows one to perform computations for a problem with any number of emerging/vanishing phase transition interfaces (both in methane gas hydrate deposits and in permafrost), since the model treats these fronts implicitly in an enthalpy formulation and in corresponding finite-difference scheme. This model takes into account the pressure (and therefore the depth) dependence of the phase transition temperature for methane clathrate hydrate. We have performed model computations using the thermophysical characteristics (heat capacity, density/porosity, thermal conductivity) for the Siberian subsurface. It can be used as a terrestrial analog for the Martian subsurface (e.g., Duxbury et al., 2001). Also, thermophysical coefficients from laboratory experiments for methane clathrate hydrate were used in our model. In addition, our model takes into account the dependence of subsurface thermophysical characteristics on temperature and spatial coordinates. The results of our computations and their interpretation will be presented. References. N. S. Duxbury, I. A. Zotikov, K. H. Nealson, V. E. Romanovsky, F. D. Carsey (2001). A numerical model for an alternative origin of Lake Vostok and its exobiological implications for Mars, Journal of Geophysical Research
Physical and mathematical modelling of gas-fired glass melting furnaces with regard to NO-formation
International Nuclear Information System (INIS)
May, F.; Stuchlik, O.; Kremer, H.
1999-01-01
The increasing demand in quality, efficiency, energy conservation and the environmental issues drive the operators of high temperature processes to optimize their furnaces. Especially the glass manufacturing industry with their high working temperatures from about 1850 K to more than 1950 K and high air preheating temperatures of above 1480 K will produce high NOx-concentrations in the flue gas if no primary measures are taken. Considering the three different paths for NO-formation it is obvious that increased thermal NO is responsible for higher emissions. The German environmental regulations on air ''TA Luft'' requires a maximum value of 500 mg/mN3 in the flue gas for most of the combustion processes but for glass melting furnaces a temporary regulation of 1200 mg/mN3 and further on to 800 mg/mN3 is valid. Due to economical reasons the level of secondary measures is to be minimized thus the main objective of research is to reduce the NOx-emissions via primary measures. The design of the furnace is very important due to its strong influence on the distribution of velocity and species. That consequently affects the temperature field and the heat transfer to the load and further on the emissions. For the understanding of the processes within these furnaces numerical simulations, which are successfully validated with experiments, can give valuable indications to optimize furnace design for the reduction of NOx-emissions. The glass melting furnace modelled here is a regenerative horseshoe furnace fired with natural gas. Combustion air is preheated within the regenerator onto a level of temperature of 1650 K. (author)
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Mathematical models of viscous friction
Buttà, Paolo; Marchioro, Carlo
2015-01-01
In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
Mathematical modelling of the calcination process | Olayiwola ...
African Journals Online (AJOL)
High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces, steelmaking, alumina production etc. Decrease in fuel consumption in metallurgical furnaces is a tremendous opportunity for reduction of greenhouse gas emissions into the atmosphere. In this paper, a mathematical model ...
MATHEMATICAL MODELLING FOR MAGNETITE (CRUDE ...
African Journals Online (AJOL)
The present research focuses to develop mathematical model for the removal of iron (magnetite) by ion-exchange resin from primary heat transfer loop of process industries. This mathematical model is based on operating capacities (that's provide more effective design as compared to loading capacity) from static laboratory ...
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Explorations in Elementary Mathematical Modeling
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Musakaev, N. G.; Khasanov, M. K.; Rafikova, G. R.
2018-03-01
The problem of the replacement of methane in its hydrate by carbon dioxide in a porous medium is considered. The gas-exchange kinetics scheme is proposed in which the intensity of the process is limited by the diffusion of CO2 through the hydrate layer formed between the gas mixture flow and the CH4 hydrate. Dynamics of the main parameters of the process is numerically investigated. The main characteristic stages of the process are determined.
An introduction to mathematical modeling
Bender, Edward A
2000-01-01
Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The
Mathematical Modeling of Diverse Phenomena
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.
Tawfik, Hazem H.
1996-01-01
Thermally sprayed coatings have been extensively used to enhance materials properties and provide surface protection against their working environments in a number of industrial applications. Thermal barrier coatings (TBC) are used to reduce the thermal conductivity of aerospace turbine blades and improve the turbine overall thermal efficiency. TBC allows higher gas operating temperatures and lower blade material temperatures due to the thermal insulation provided by these ceramic coatings. In the automotive industry, coatings are currently applied to a number of moving parts that are subjected to friction and wear inside the engine such as pistons, cylinder liners, valves and crankshafts to enhance their wear resistance and prolong their useful operation and lifetime.
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
The Spectrum of Mathematical Models.
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…
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Mathematical aspects of subsonic and transonic gas dynamics
Bers, Lipman
2016-01-01
Concise treatment by prominent mathematician covers differential equations of potential gas flow, mathematical background of subsonic flow theory, behavior of flow at infinity, flows in channels and with free boundary, more. 1958 edition.
Mathematical Models of Gene Regulation
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Using Covariation Reasoning to Support Mathematical Modeling
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...... and the rejection coefficient. The second model is a stationary model for the flux of solvent and solute in a hollow fibre membrane. In the model we solve the time independent equations for transport of solvent and solute within the hollow fibre. Furthermore, the flux of solute and solvent through the membrane...
The 24-Hour Mathematical Modeling Challenge
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical Modeling: A Bridge to STEM Education
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Mathematical modeling of inhalation exposure
Fiserova-Bergerova, V.
1976-01-01
The paper presents a mathematical model of inhalation exposure in which uptake, distribution and excretion are described by exponential functions, while rate constants are determined by tissue volumes, blood perfusion and by the solubility of vapors (partition coefficients). In the model, tissues are grouped into four pharmokinetic compartments. The model is used to study continuous and interrupted chronic exposures and is applied to the inhalation of Forane and methylene chloride.
Teachers' Conceptions of Mathematical Modeling
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical Modeling in the Undergraduate Curriculum
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Mathematical model for bone mineralization
Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica
2015-01-01
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized usin...
Mathematical modelling in economic processes.
Directory of Open Access Journals (Sweden)
L.V. Kravtsova
2008-06-01
Full Text Available In article are considered a number of methods of mathematical modelling of economic processes and opportunities of use of spreadsheets Excel for reception of the optimum decision of tasks or calculation of financial operations with the help of the built-in functions.
Film dosimetry: a mathematical model
International Nuclear Information System (INIS)
Mafra Neto, F.
1993-01-01
A mathematical model for electromagnetic radiation dosimetry using photosensitive emulsions is presented. A Kodak odontological radiographic film was used for that purpose. Some properties such as energy dependence, reproductiveness and the characteristic curve were studied. A linear and energy-independent dosimeter for beams above 50 KeV was obtained by adding 1 mm lead filters. 4 refs, 8 figs, 2 tabs
Directory of Open Access Journals (Sweden)
Leonardo Neves
2015-03-01
Full Text Available Continuous casting is a solidification process, in which the knowledge about its variables is very important in order to produce steel with good quality. The tundish distributes the steel coming from the ladle to the metallurgical mold as the traditional function, besides, it also has some other important functions. Because of its importance in the process, this work aim to carry out studies on the steel flow in the tundish with two different configurations, with and without inert gas injection. A Computational Fluid Dynamic (CFD software were used to make the mathematical simulations making possible to note the difference in terms of the Residence Time Distribution curves (RTD curves, levels of turbulence and velocity profiles with or without inert gas injection
Mathematical modeling of biological processes
Friedman, Avner
2014-01-01
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Directory of Open Access Journals (Sweden)
CHORNOMORETS H. Y.
2016-02-01
Full Text Available Raising of problem. For the design and construction of tube gas heaters in building structures to need solve the problems of analysis and synthesis of such heating system. The mathematical model of this system is consists of: mathematical model of the tube gas heater, mathematical model of heat distribution in the building structure and corresponding boundary conditions. To solve the tasks of analysis and synthesis must be appropriate mathematical and information support. Purpose. The purpose of this paper is to describe the developed mathematical and information support that solve the problems of analysis and synthesis of heating systems with gas tube heaters, located in building constructions.Conclusion. Mathematical support includes the development of algorithms and software for the numerical solution of problems analysis and synthesis heating system. Information support includes all the necessary parameters characterizing the thermal properties of materials which used in the heating system, and the parameters characterizing the heat exchange between the coolant and components of the heating system. It was developed algorithms for solving problems of analysis and synthesis heating system with tube gas heater located in structures to use evolutionary search algorithm and software. It was made experimental study and was obtained results allow to calculate the heat transfer from the gas-air mixture to the boundary surface of the building structure. This results and computation will provide full information support for solving problems of analysis and synthesis of the heating system. Was developed mathematical and software support, which allows to solve the problems of analysis and synthesis heating systems with gas tube heaters, located in building structures. Tube gas heaters located in the building structures allows with small capital expenditures to provide space heating. Is necessary to solve the problems of analysis (calculation and
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Mathematical models in genetics.
Traykov, M; Trenchev, Iv
2016-09-01
In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.
Exploring Yellowstone National Park with Mathematical Modeling
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…
Strategies to Support Students' Mathematical Modeling
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
Mathematical Modeling in the High School Curriculum
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
Mathematical modeling of drug delivery.
Siepmann, J; Siepmann, F
2008-12-08
Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design
Mathematical Model of Age Aggression
Golovinski, P. A.
2013-01-01
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...
Energy Technology Data Exchange (ETDEWEB)
Ramirez-Argaez, M. A.; Conteras, F.; Gonzalez, C.
2006-07-01
In this work a fundamental Eulerian mathematical model was developed to study fluid flow and mixing phenomena in aluminium ladles equipped with impeller for deshidrogenization treatment. The effect of critical process parameters such as rotor speed, depth of immersion, gas flow rate, and type of rotor on the mixing behavior and vortex formation was analyzed with this model. The model simulates operation with and without gas injection and it was developed on the commercial CFD code PHOENICS 3.4 in order to solve all conservation equations governing the process, i. e. continuity, 3D turbulent Navier-Stockers and the k{epsilon} turbulence model for a two-phase fluid flow problem using the Inter Phase Slip Algorithm (IPSA). (Author). 20 refs.
Summer Camp of Mathematical Modeling in China
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Mathematical modeling of laser lipolysis
Directory of Open Access Journals (Sweden)
Reynaud Jean
2008-02-01
Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
Mathematical models of bipolar disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Explorations in Elementary Mathematical Modeling
Directory of Open Access Journals (Sweden)
Mazen Shahin
2010-06-01
Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Mathematical model for gyroscope effects
Usubamatov, Ryspek
2015-05-01
Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).
Zagatto, A; Miranda, M F; Gobatto, C A
2011-07-01
The purposes of this study were to determine and to compare the critical power concept adapted for the specific table tennis test (critical frequency - C F ) estimated from 5 mathematical models and using 2 different exhaustion criteria (voluntary and technical exhaustions). Also, it was an aim to assess the relationship between C F estimated from mathematical models and respiratory compensation point (RCP), peak oxygen uptake ( V˙O (2PEAK)) and minimal intensity at which V˙O (2PEAK) ( F V˙O (2PEAK)) appears. 9 male table tennis players [18(1) years; 62.3(4.4) kg] performed the maximal incremental test and 3-4 exhaustive exercise bouts to estimate C F s (balls · min (-1)). The exhaustion time and C F obtained were independent of the exhaustion criteria. The C F from 3-parameter model [45.2(7.0)-voluntary, 43.2(5.6)-technical] was lower than C F estimated by linear 2-parameter models, frequency-time (-1) [53.5(3.6)-voluntary, 53.5(3.5)-technical] and total ball thrown-time [52.2(3.5)-voluntary, 52.2(3.5)-technical] but significantly correlated. C F values from 2 linear models were significantly correlated with RCP [47.4(3.4) balls · min (-1)], and C F values of the linear and nonlinear models were correlated with F V˙O (2PEAK) [56.7(3.4) balls · min (-1)]. However, there were no significant correlations between C F values and V˙O (2PEAK) [49.8(1.1)ml · kg (-1) · min (-1)]. The results were not modified by exhaustion criteria. The 2 linear and non-linear 2-parameter models can be used to estimate aerobic endurance in specific table tennis tests. © Georg Thieme Verlag KG Stuttgart · New York.
Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling
Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Precipitation of metal sulphides using gaseous hydrogen sulphide: mathematical modelling
Al Tarazi, M.Y.M.; Heesink, Albertus B.M.; Versteeg, Geert
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulffides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Reflexion and control mathematical models
Novikov, Dmitry A
2014-01-01
This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, re...
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
On Fences, Forms and Mathematical Modeling
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
Mathematical model for classification of EEG signals
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
Mathematical modeling of drug dissolution.
Siepmann, J; Siepmann, F
2013-08-30
The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.
Mathematical model for bone mineralization
Directory of Open Access Journals (Sweden)
Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...
Surface EXAFS - A mathematical model
International Nuclear Information System (INIS)
Bateman, J.E.
2002-01-01
Extended X-ray absorption fine structure (EXAFS) studies are a powerful technique for studying the chemical environment of specific atoms in a molecular or solid matrix. The study of the surface layers of 'thick' materials introduces special problems due to the different escape depths of the various primary and secondary emission products which follow X-ray absorption. The processes are governed by the properties of the emitted fluorescent photons or electrons and of the material. Their interactions can easily destroy the linear relation between the detected signal and the absorption cross-section. Also affected are the probe depth within the surface and the background superimposed on the detected emission signal. A general mathematical model of the escape processes is developed which permits the optimisation of the detection modality (X-rays or electrons) and the experimental variables to suit the composition of any given surface under study
The Activity System of School-Teaching Mathematics and Mathematical Modelling.
Julie, Cyril
2002-01-01
Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...... Modeling on 6th semester being the latest addition. Some of the reasoning behind curriculum development, lessons learned and remaining issues are presented and discussed. ...
Mathematical model on Alzheimer's disease.
Hao, Wenrui; Friedman, Avner
2016-11-18
Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.
Natural gas supply in Denmark - A model of natural gas transmission and the liberalized gas market
International Nuclear Information System (INIS)
Bregnbaek, L.
2005-01-01
In the wake of the liberalization of European energy markets a large area of research has spawned. This area includes the development of mathematical models to analyze the impact of liberalization with respect to efficiency, supply security and environment, to name but a few subjects. This project describes the development of such a model. In Denmark the parallel liberalization of the markets of natural gas and electricity and the existence of an abundance of de-centralized combined heat and power generators of which most are natural gas fired, leads to the natural assumption that the future holds a greater deal of interdependency for these markets. A model is developed describing network flows in the natural gas transmission system, the main arteries of natural gas supply, from a technical viewpoint. This yields a technical bounding on the supply available in different parts of the country. Additionally the economic structure of the Danish natural gas market is formulated mathematically giving a description of the transmission, distribution and storage options available to the market. The supply and demand of natural gas is put into a partial equilibrium context by integrating the developed model with the Balmorel model, which describes the markets for electricity and district heat. Specifically on the demand side the consumption of natural gas for heat and power generation is emphasized. General results and three demonstration cases are presented to illustrate how the developed model can be used to analyze various energy policy issues, and to disclose the strengths and weaknesses in the formulation. (au)
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers...
Leading Undergraduate Research Projects in Mathematical Modeling
Seshaiyer, Padmanabhan
2017-01-01
In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…
Modeling pressure rise in gas targets
Jahangiri, P.; Lapi, S. E.; Publicover, J.; Buckley, K.; Martinez, D. M.; Ruth, T. J.; Hoehr, C.
2017-05-01
The purpose of this work is to introduce a universal mathematical model to explain a gas target behaviour at steady-state time scale. To obtain our final goal, an analytical model is proposed to study the pressure rise in the targets used to produce medical isotopes on low-energy cyclotrons. The model is developed based on the assumption that during irradiation the system reaches steady-state. The model is verified by various experiments performed at different beam currents, gas type, and initial pressures at 13 MeV cyclotron at TRIUMF. Excellent agreement is achieved.
Mathematical model of radon activity measurements
Energy Technology Data Exchange (ETDEWEB)
Paschuk, Sergei A.; Correa, Janine N.; Kappke, Jaqueline; Zambianchi, Pedro, E-mail: sergei@utfpr.edu.br, E-mail: janine_nicolosi@hotmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Denyak, Valeriy, E-mail: denyak@gmail.com [Instituto de Pesquisa Pele Pequeno Principe, Curitiba, PR (Brazil)
2015-07-01
Present work describes a mathematical model that quantifies the time dependent amount of {sup 222}Rn and {sup 220}Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of {sup 222}Rn and {sup 220}Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since {sup 220}Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to {sup 222}Rn, only. Furthermore, the model also addresses the activity of {sup 220}Rn and {sup 222}Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure. (author)
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
A mathematical model for iodine kinetics
International Nuclear Information System (INIS)
Silva, E.A.T. da.
1976-01-01
A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Lowe, James; Carter, Merilyn; Cooper, Tom
2018-01-01
Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…
Modelling gas generation in radioactive waste repositories
International Nuclear Information System (INIS)
Agg, P.J.
1992-07-01
In a repository containing low- and intermediate-level waste, gas generation will occur principally by the coupled processes of metal corrosion and microbial degradation of cellulosic waste. This paper describes a mathematical model designed to address gas generation by these mechanisms. The metal corrosion model incorporates a three-stage process encompassing both aerobic and anaerobic corrosion regimes; the microbial degradation model simulates the activities of eight different microbial populations, which are maintained as functions both of pH and of the concentrations of particular chemical species. Gas concentrations have been measured over a period of three years in large-scale drum experiments designed to simulate repository conditions. Model predictions are confirmed against the experimental measurements, and a prediction is then made of gas concentrations and generation rates over an assessment period of one million years in a radioactive waste repository. (Author)
Modelling gas generation in radioactive waste repositories
International Nuclear Information System (INIS)
Agg, P.J.
1993-02-01
In a repository containing low- and intermediate-level waste, gas generation will occur principally by the coupled processes of metal corrosion and microbial degradation of cellulosic waste. This Paper describes a mathematical model design to address gas generation by these mechanisms. The metal corrosion model incorporates a three-stage process encompassing both aerobic and anaerobic corrosion regimes; the microbial degradation model simulates the activities of eight different microbial populations, which are maintained as functions both of pH and of the concentrations of particular chemical species. Gas concentrations have been measured over a period of three years in large-scale drum experiments designed to simulate repository conditions. Model predictions are confirmed against the experimental measurements, and a prediction is then made of gas concentrations and generation rates over an assessment period of one million years in a radioactive waste repository. (author)
International Nuclear Information System (INIS)
Charles, F.
2009-11-01
The thesis deals with kinetic models describing a rarefied spray. These models rely on coupling two Partial Differential Equations which describe the spatio-temporal evolution of the distribution of molecules and dust particles. The model presented in the first part is described by two Boltzmann-type equations where collisions between molecules and particles are modeled by two collision operators. We suggest two models of this collision operators. In the first one, collisions between dust particles and molecules are supposed to be elastic. In the second one, we assume those collisions are inelastic and given by a diffuse reflexion mechanism on the surface of dust specks. This leads to establish non classical collision operators. We prove that in the case of elastic collisions, the spatially homogeneous system has weak solutions which preserve mass and energy, and which satisfy an entropy inequality. We then describe the numerical simulation of the inelastic model, which is based on a Direct Simulation Method. This brings to light that the numerical simulation of the system becomes too expensive because the typical size of a dust particle is too large. We therefore introduce in the second part of this work a model constituted of a coupling (by a drag force term) between a Boltzmann equation and a Vlasov equation. To this end, we perform a scaling of the Boltzmann/Boltzmann system and an asymptotic expansion of one of the dimensionless collision operators with respect to the ratio of mass between a molecule of gas and a particle. A rigorous proof of the passage to the limit is given in the spatially homogeneous setting, for the elastic model of collision operators. It includes a new variant of Povzner's inequality in which the vanishing mass ratio is taken into account. Moreover, we numerically compare the Boltzmann/Boltzmann and Vlasov/Boltzmann systems with the inelastic collision operators. The simulation of the Vlasov equation is performed with a Particle
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
Alexeeva, I. V.; Budnik, A. P.; Sipachev, A. V.; Slyunyaev, M. N.
2017-02-01
The theoretical model and program complex for mathematical simulation of processes of transformation the nuclear energy into optical radiation energy was developed. The model includes the equations of gas dynamics, as well as the equations describing the kinetic processes in the non-equilibrium plasma excited by uranium fission fragments. The kinetic processes in the moving irradiated by neutrons argon-xenon gas medium containing uranium nanoparticles was investigated. The space-time evolution of this medium in nonuniform changing over time neutron field was studied. The space-time evolution of the gas parameters (temperature, density, velocity, pressure), as well as the distribution of the concentration of uranium nanoparticles under different initial velocities of the gas and the size of the nanoparticles was calculated. The amplifying properties of a laser-active space-nonuniform nuclear-excited moving argon-xenon medium, containing uranium nanoparticles and irradiated by neutrons, was studied.
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Mathematical modelling of cucumber (cucumis sativus) drying
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Mathematical models of behavior of individual animals.
Tsibulsky, Vladimir L; Norman, Andrew B
2007-01-01
This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.
Mathematical models for quantum point contact spectroscopy
International Nuclear Information System (INIS)
Exner, P.; Seba, P.
1986-01-01
Two mathematical models intended to describe the point contact spectroscopical experiments are constructed. It adds a new item to the list of recently discovered applications of the self-adjoint extension theory
Mathematical Modeling of Circadian/Performance Countermeasures
National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
SECURE MATHEMATICALLY- ASSURED COMPOSITION OF CONTROL MODELS
2017-09-27
SECURE MATHEMATICALLY-ASSURED COMPOSITION OF CONTROL MODELS ROCKWELL COLLINS SEPTEMBER 2017 FINAL TECHNICAL REPORT APPROVED FOR PUBLIC RELEASE...collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE...MATHEMATICALLY-ASSURED COMPOSITION OF CONTROL MODELS 5a. CONTRACT NUMBER FA8750-12-9-0179 5b. GRANT NUMBER N/A 5c. PROGRAM ELEMENT NUMBER 62303E
Decision support models for natural gas dispatch
Energy Technology Data Exchange (ETDEWEB)
Chin, L. (Bentley College, Waltham, MA (United States)); Vollmann, T.E. (International Inst. for Management Development, Lausanne (Switzerland))
A decision support model is presented which will give utilities the support tools to manage the purchasing of natural gas supplies in the most cost effective manner without reducing winter safety stocks to below minimum levels. In Business As Usual (BAU) purchasing quantities vary with the daily forecasts. With Material Requirements Planning (MRP) and Linear Programming (LP), two types of factors are used: seasonal weather and decision rule. Under current practices, BAU simulation uses the least expensive gas source first, then adding successively more expensive sources. Material Requirements Planning is a production planning technique which uses a parent item master production schedule to determine time phased requirements for component points. Where the MPS is the aggregate gas demand forecasts for the contract year. This satisfies daily demand with least expensive gas and uses more expensive when necessary with automatic computation of available-to-promise (ATP) gas a dispacher knows daily when extra gas supplies may be ATP. Linear Programming is a mathematical algorithm used to determine optimal allocations of scarce resources to achieve a desired result. The LP model determines optimal daily gas purchase decisions with respect to supply cost minimization. Using these models, it appears possible to raise gross income margins 6 to 10% with minimal additions of customers and no new gas supply.
Decision support models for natural gas dispatch
International Nuclear Information System (INIS)
Chin, L.; Vollmann, T.E.
1992-01-01
A decision support model is presented which will give utilities the support tools to manage the purchasing of natural gas supplies in the most cost effective manner without reducing winter safety stocks to below minimum levels. In Business As Usual (BAU) purchasing quantities vary with the daily forecasts. With Material Requirements Planning (MRP) and Linear Programming (LP), two types of factors are used: seasonal weather and decision rule. Under current practices, BAU simulation uses the least expensive gas source first, then adding successively more expensive sources. Material Requirements Planning is a production planning technique which uses a parent item master production schedule to determine time phased requirements for component points. Where the MPS is the aggregate gas demand forecasts for the contract year. This satisfies daily demand with least expensive gas and uses more expensive when necessary with automatic computation of available-to-promise (ATP) gas a dispacher knows daily when extra gas supplies may be ATP. Linear Programming is a mathematical algorithm used to determine optimal allocations of scarce resources to achieve a desired result. The LP model determines optimal daily gas purchase decisions with respect to supply cost minimization. Using these models, it appears possible to raise gross income margins 6 to 10% with minimal additions of customers and no new gas supply
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Introduction to mathematical modeling and chaotic dynamics
Upadhyay, Ranjit Kumar
2013-01-01
""The presentation is so clear that anyone with even a basic mathematical background can study it and get a clear picture. … Unlike many other similar textbooks, a rich reference section is given at the end of each chapter. The cautious selection of worked out examples and exercises throughout the book is superb. For anyone with previous experience of having run into books in mathematical modeling and chaotic dynamics that rapidly move into advanced mathematical content, the book offers a pleasant recourse at an introductory level and therefore can be very inspirational.""-MAA Reviews, Decembe
An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers
Thrasher, Emily Plunkett
2016-01-01
The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Zbiek, Rose Mary; Conner, Annamarie
2006-01-01
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
Mathematical Modelling of Intraretinal Oxygen Partial Pressure ...
African Journals Online (AJOL)
Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model ...
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...
Mathematical Model of Hot Metal Desulfurization by Powder Injection
Directory of Open Access Journals (Sweden)
Yolanda Cepeda Rodríguez
2012-01-01
Full Text Available Although there have been a numerous number of studies on mathematical model of hot metal desulfurization by deep injection of calcium carbide, the research field as a whole is not well integrated. This paper presents a model that takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal throughout a blow. The model could be utilized to assess the influence of the treatment temperature, rate of injection, gas flow rate, and initial concentration of sulfur on the desulfurization kinetics. In the second part of this paper an analysis of the industrial data for injection of calcium carbide using this model is described. From a mathematical model that describes the characteristics of a system, it is possible to predict the behavior of the variables involved in the process, resulting in savings of time and money. Discretization is realized through the finite difference method combined with interpolation in the border domain by Taylor series.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Mathematical Models of Tuberculosis Reactivation and Relapse
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Mathematical models and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
Mathematical model in economic environmental problems
Energy Technology Data Exchange (ETDEWEB)
Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)
1996-12-31
The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.
International Nuclear Information System (INIS)
Mariner-Volpe, B.; Trapmann, W.
1989-01-01
The Gas Analysis Modeling System is a large computer-based model for analyzing the complex US natural gas industry, including production, transportation, and consumption activities. The model was developed and first used in 1982 after the passage of the NGPA, which initiated a phased decontrol of most natural gas prices at the wellhead. The categorization of gas under the NGPA and the contractual nature of the natural gas market, which existed at the time, were primary factors in the development of the basic structure of the model. As laws and regulations concerning the natural gas market have changed, the model has evolved accordingly. Recent increases in competition in the wellhead market have also led to changes in the model. GAMS produces forecasts of natural gas production, consumption, and prices annually through 2010. It is an engineering-economic model that incorporates several different mathematical structures in order to represent the interaction of the key groups involved in the natural gas market. GAMS has separate supply and demand components that are equilibrated for each year of the forecast by means of a detailed transaction network
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
Building Mathematical Models Of Solid Objects
Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.
1989-01-01
Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.
A mathematical model of embodied consciousness
Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.
2017-01-01
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM
Mathematical model of the reactor coolant pump
International Nuclear Information System (INIS)
Kozuh, M.
1989-01-01
The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Uncertainty and Complexity in Mathematical Modeling
Cannon, Susan O.; Sanders, Mark
2017-01-01
Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…
Mathematical Modeling: Are Prior Experiences Important?
Czocher, Jennifer A.; Moss, Diana L.
2017-01-01
Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in
Mathematical modeling and analysis of WEDM machining ...
Indian Academy of Sciences (India)
Home; Journals; Sadhana; Volume 42; Issue 6. Mathematical modeling and analysis ... The present work is mainly focused on the analysis and optimization of the WEDM process parameters of Inconel 625. The four machining ... Response surface methodology was used to develop the experimental models. The parametric ...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Zero-dimensional mathematical model of the torch ignited engine
International Nuclear Information System (INIS)
Cruz, Igor William Santos Leal; Alvarez, Carlos Eduardo Castilla; Teixeira, Alysson Fernandes; Valle, Ramon Molina
2016-01-01
Highlights: • Publications about the torch ignition system are mostly CFD or experimental research. • A zero-dimensional mathematical model is presented. • The model is based on classical thermodynamic equations. • Approximations are based on empirical functions. • The model is applied to a prototype by means of a computer code. - Abstract: Often employed in the analysis of conventional SI and CI engines, mathematical models can also be applied to engines with torch ignition, which have been researched almost exclusively by CFD or experimentally. The objective of this work is to describe the development and application of a zero-dimensional model of the compression and power strokes of a torch ignited engine. It is an initial analysis that can be used as a basis for future models. The processes of compression, combustion and expansion were described mathematically and applied to an existing prototype by means of a computer code written in MATLAB language. Conservation of energy and mass and the ideal gas law were used in determining gas temperature, pressure, and mass flow rate within the cylinder. Gas motion through the orifice was modelled as an isentropic compressible flow. The thermodynamic properties of the mixture were found by a weighted arithmetic mean of the data for each component, computed by polynomial functions of temperature. Combustion was modelled by the Wiebe function. Heat transfer to the cylinder walls was estimated by Annand’s correlations. Results revealed the behaviour of pressure, temperature, jet velocity, energy transfer, thermodynamic properties, among other variables, and how some of these are influenced by others.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Mathematical Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Mathematical modelling of unmanned aerial vehicles
International Nuclear Information System (INIS)
Sarwar, S.; Rehman, S.U.
2013-01-01
UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)
Applied Mathematics, Modelling and Computational Science
Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan
2015-01-01
The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
The (Mathematical) Modeling Process in Biosciences.
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.
Mathematical model of concentrating solar cooker
Avilés, Mauricio González; Avilés, José Juan González
2013-01-01
The main purpose of this work is to obtain a mathematical model consistent with the thermal behavior of concentrating solar cookers, such as Jorhejpataranskua. We also want to simulate different conditions respect to the parameters involved of several materials for its construction and efficiency. The model is expressed in terms of a coupled nonlinear system of differential equations which are solved using Mathematica 8. The results obtained by our model are compared with measurements of sola...
Mathematical model of subscriber extension line
Petříková, Iva; Diviš, Zdeněk; Tesař, Zdeněk
2012-01-01
The paper focuses on measurement properties of metallic subscriber extension lines to build regression mathematical model for a symmetric pair cable. The regression model is compared with an analytical model based on a theoretical description of transfer parameters for this type of line. The output of the paper should demonstrate the impact of electromagnetic interference on the symmetric pair. The paper also describes the method to identify the interference sources and ...
Mathematical model of self-cycling fermentation
Energy Technology Data Exchange (ETDEWEB)
Wincure, B.M.; Cooper, D.G.; Rey, A. [McGill Univ., Montreal, Quebec (Canada). Dept. of Chemical Engineering
1995-04-20
This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation.
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model for intraretinal oxygen partial pressure distribution was developed using Fick's law of diffusion, Michaelis-Menten kinetics, and oxygen delivery in the inner retina. The system of non-linear differential ...
Identification of the noise using mathematical modelling
Directory of Open Access Journals (Sweden)
Dobeš Josef
2016-01-01
Full Text Available In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today’s computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
Description of a comprehensive mathematical model
DEFF Research Database (Denmark)
Li, Xiyan; Yin, Chungen
2017-01-01
Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed i...
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
This minimum pressure may fall below the critical level of oxygen partial pressure and affect the retinal function. In order to restore normal retinal function, extreme hyperoxia may assist to make the choroid capable of supplying oxygen to the whole retina during total retinal artery occlusion. Keywords: Mathematical modeling ...
Mathematical Modeling Projects: Success for All Students
Shelton, Therese
2018-01-01
Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…
Mathematical modeling of fructose production by immobilised ...
African Journals Online (AJOL)
Production of fructose from glucose isomerisation process using commercial immobilized glucose isomerase (IGI) was conducted in a batch type of stirred tank bioreactor. A mathematical model was developed to describe the effect of temperature and pH on the kinetic parameters of fructose production. Modified Santos ...
ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS
Directory of Open Access Journals (Sweden)
D.V. Makarov
2014-06-01
Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.
A Model for Community Partnerships in Mathematics
Forrest, Bradley; Kosick, Pamela; Vogel, Judith; Wu, Chia-Lin
2012-01-01
This article describes a partnership involving a college and its surrounding public high schools in order to offer a model for transforming professional development initiatives into collaborative, reciprocal community engagement opportunities. This ongoing partnership addresses the shared goal of improving the mathematical college readiness of…
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers to as a geomag...
Mathematical Modeling of Loop Heat Pipes
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
Mathematical models of skin permeability: an overview.
Mitragotri, Samir; Anissimov, Yuri G; Bunge, Annette L; Frasch, H Frederick; Guy, Richard H; Hadgraft, Jonathan; Kasting, Gerald B; Lane, Majella E; Roberts, Michael S
2011-10-10
Mathematical models of skin permeability play an important role in various fields including prediction of transdermal drug delivery and assessment of dermal exposure to industrial chemicals. Extensive research has been performed over the last several decades to yield predictions of skin permeability to various molecules. These efforts include the development of empirical approaches such as quantitative structure-permeability relationships and porous pathway theories as well as the establishment of rigorous structure-based models. In addition to establishing the necessary mathematical framework to describe these models, efforts have also been dedicated to determining the key parameters that are required to use these models. This article provides an overview of various modeling approaches with respect to their advantages, limitations and future prospects. Copyright © 2011 Elsevier B.V. All rights reserved.
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Mathematical modeling models, analysis and applications
Banerjee, Sandip
2014-01-01
""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298
Modeling life the mathematics of biological systems
Garfinkel, Alan; Guo, Yina
2017-01-01
From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...
Mathematical modeling of compression processes in air-driven boosters
International Nuclear Information System (INIS)
Li Zeyu; Zhao Yuanyang; Li Liansheng; Shu Pengcheng
2007-01-01
The compressed air in normal pressure is used as the source of power of the air-driven booster. The continuous working of air-driven boosters relies on the difference of surface area between driven piston and driving piston, i.e., the different forces acting on the pistons. When the working surface area of the driving piston for providing power is greater than that of the driven piston for compressing gas, the gas in compression chamber will be compressed. On the basis of the first law of thermodynamics, the motion regulation of piston is analyzed and the mathematical model of compression processes is set up. Giving a calculating example, the vary trends of gas pressure and pistons' move in working process of booster have been gotten. The change of parameters at different working conditions is also calculated and compared. And the corresponding results can be referred in the design of air-driven boosters
Mathematical Models of Breast and Ovarian Cancers
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-01-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061
Causal Bayes Model of Mathematical Competence in Kindergarten
Directory of Open Access Journals (Sweden)
Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
MATHEMATICAL MODEL FOR RIVERBOAT DYNAMICS
Directory of Open Access Journals (Sweden)
Aleksander Grm
2017-01-01
Full Text Available Present work describes a simple dynamical model for riverboat motion based on the square drag law. Air and water interactions with the boat are determined from aerodynamic coefficients. CFX simulations were performed with fully developed turbulent flow to determine boat aerodynamic coefficients for an arbitrary angle of attack for the air and water portions separately. The effect of wave resistance is negligible compared to other forces. Boat movement analysis considers only two-dimensional motion, therefore only six aerodynamics coefficients are required. The proposed model is solved and used to determine the critical environmental parameters (wind and current under which river navigation can be conducted safely. Boat simulator was tested in a single area on the Ljubljanica river and estimated critical wind velocity.
Constraint theory multidimensional mathematical model management
Friedman, George J
2017-01-01
Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...
Mathematical modelling of flooding at Magela Creek
International Nuclear Information System (INIS)
Vardavas, I.
1989-01-01
The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills
Mathematical modelling of the decomposition of explosives
International Nuclear Information System (INIS)
Smirnov, Lev P
2010-01-01
Studies on mathematical modelling of the molecular and supramolecular structures of explosives and the elementary steps and overall processes of their decomposition are analyzed. Investigations on the modelling of combustion and detonation taking into account the decomposition of explosives are also considered. It is shown that solution of problems related to the decomposition kinetics of explosives requires the use of a complex strategy based on the methods and concepts of chemical physics, solid state physics and theoretical chemistry instead of empirical approach.
Wind tunnel modeling of roadways: Comparison with mathematical models
International Nuclear Information System (INIS)
Heidorn, K.; Davies, A.E.; Murphy, M.C.
1991-01-01
The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
Models and structures: mathematical physics
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems.
mathematical modelling of atmospheric dispersion of pollutants
International Nuclear Information System (INIS)
Mohamed, M.E.
2002-01-01
the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established
Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification
Directory of Open Access Journals (Sweden)
Grzegorz Mikułowski
2016-01-01
Full Text Available Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA, which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.
The stability of colorectal cancer mathematical models
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.
Mathematical Models of College Myopia.
Greene, Peter R; Grill, Zachary W; Medina, Antonio
2016-01-01
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/-0.31 D. over a 14 year interval. Typical college myopia rate is -0.3 to -0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Mathematical Modelling of Turbidity Currents
Fay, G. L.; Fowler, A.; Howell, P.
2011-12-01
A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.
Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.
Swetz, Frank
1991-01-01
Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)
Mathematical modeling of microbial growth in milk
Directory of Open Access Journals (Sweden)
Jhony Tiago Teleken
2011-12-01
Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.
Mathematical Model of Serodiagnostic Immunochromatographic Assay.
Sotnikov, Dmitriy V; Zherdev, Anatoly V; Dzantiev, Boris B
2017-04-18
This article describes the mathematical model for an immunochromatographic assay for the detection of specific immunoglobulins against a target antigen (antibodies) in blood/serum (serodiagnosis). The model utilizes an analytical (non-numerical) approach and allows the calculation of the kinetics of immune complexes' formation in a continuous-flow system using commonly available software, such as Microsoft Excel. The developed model could identify the nature of the influence of immunochemical interaction constants and reagent concentrations on the kinetics of the formation of the detected target complex. On the basis of the model, recommendations are developed to decrease the detection limit for an immunochromatographic assay of specific immunoglobulins.
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...
Building Mathematical Models of Simple Harmonic and Damped Motion.
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Energy Technology Data Exchange (ETDEWEB)
Stoehr, Michael [Bundesdeutscher Arbeitskreis fuer Umweltbewusstes Management e.V., B.A.U.M., Muenchen (Germany); Pickel, Peter [John Deere European Technology Innovation Center, Kaiserslautern (Germany)
2012-07-01
The use of biofuels in agricultural machinery is an option to respond to climate requirements. This option is being imposed from the European Commission to manufacturers of mobile machines. The contribution under consideration formulates a mathematical model that implements the regulations of the EU Fuel Quality Directive for complex manufacturing processes in the calculation rules. Initially, this model was tested and verified by the example of the standard manufacturing process of pure rapeseed oil. Then, possibilities of optimization for the production of rapeseed oil are explored. Finally, the mathematical model was applied to the calculation of greenhouse gas emissions from camelina oil from mixed cultivation with wheat.
Mathematical modeling of vertebrate limb development.
Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A
2013-05-01
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton. Copyright © 2012 Elsevier Inc. All rights reserved.
Mathematical models for centrifugal pumps. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primary concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc- friction and leakage losses, thereby giving the all-over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical models for centrifugal pumps. Pt. 2
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primarily concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc-friction and leakage losses, thereby giving the all- over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical models for centrifugal pumps. Pt. 3
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primary concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc-friction and leakage losses, thereby giving the all-over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical model of integrated thermal apparatus
Directory of Open Access Journals (Sweden)
Katarína Mikulová Polčová
2010-03-01
Full Text Available Mathematical model for the integrated thermal apparatus was developed. It consists of program modules from which individualfurnace model can be generated. For the model generation elementary balance method was used. Generation of the individual modelincludes model formulation and parameters determination. Model formulation is based on first principles, heuristics and empirical results.Parameters determination is generally based on priory information, but it has to take into account specific conditions. The developed modelwas adapted for real time applications. For quantitative application developed model has to be calibrated. For the calibration theoperational furnace can be used. For model calibration of not existing furnace the priory knowledge and physical model can be used.Presented model was calibrated on experimental furnace. The results were gained by simulations.
Energy Technology Data Exchange (ETDEWEB)
Vianna, Savio S.V. [Det Norske Veritas PRINCIPIA, Rio de Janeiro, RJ (Brazil); Ferreira Filho, Virgilio Jose [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia de Producao
2004-07-01
Nowadays, worry about produce under safe conditions increased. This compromising with environment and safety systems is somehow careless regarding mathematics models in order to foreseen day by day production scenarios. The present paper suggests a methodology based on computational fluid dynamics and mathematics programming using graph theory to optimize gas detectors location on offshore facility plant. (author)
MATHEMATICAL MODEL FOR DETERMINING THE INDICATORS OF TRACTIVE VEHICLES
Directory of Open Access Journals (Sweden)
A. F. Golovchuk
2017-06-01
Full Text Available Purpose. The research paper involves solving of the following tasks: 1 refinement of the mathematical model for determining the traction and dynamic, fuel and economic, environmental indicators of mobile energy facilities; 2 methodology development of theoretical studies of automatic control systems, static and dynamic characteristics automotive-tractor diesel with a gas turbine supercharger and a mobile power facility. Methodology. The work studies the working processes of vehicles and machine-tractor aggregates by mathematical simulation and the development of algorithms and programs for the calculation of these processes in actual operational conditions. The system of equations has been developed for theoretical research. It describes a nonlinear mathematical model of the automatic control system of an automotive-tractor diesel rotating frequency. In addition to the differential equations of the first and second order, equations are used in mathematical simulation of working processes of traction vehicles. These equations describe experimental characteristics of an automatic regulator, a high-pressure fuel pump, a turbocharger and an engine, as well as moments of engine mechanical losses and an external load. Findings. The developed mathematical model allows determining the effectiveness of new design, operational and technological developments, as well as various measures in order to improve the fuel-economic and environmental performances of vehicles and machine-tractor aggregates in operating conditions. Originality. For the first time, the mathematical model "Tractor driver – machine-tractor aggregate – road (field" was developed. It allows conducting research of transport tractor aggregates by driving cycles, taking into account the processes of starting and speeding up the mobile-power sources with gear shift. Practical value. In conditions of a protracted economic crisis, in the absence of the necessary equipment, instruments
Mathematical models of HIV replication and pathogenesis.
Wodarz, Dominik
2014-01-01
This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.
Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard
2008-01-01
This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…
Mathematical modelling of wood and briquettes torrefaction
Energy Technology Data Exchange (ETDEWEB)
Felfli, Felix Fonseca; Luengo, Carlos Alberto [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Fisica Gleb Wataghin. Grupo Combustiveis Alternativos; Soler, Pedro Beaton [Universidad de Oriente, Santiago de Cuba (Cuba). Fac. de Ingenieria Mecanica. Centro de Estudios de Eficiencia Energetica; Rocha, Jose Dilcio [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Nucleo Interdisciplinar de Planejamento Energetico (NIPE)
2004-07-01
A mathematical model valid for the torrefaction of wood logs and biomass briquettes is presented. The model described both chemical and physical processes, which take place in a moist piece of wood heated at temperatures between 503 and 573 K. Calibration measurements of the temperature profile and mass loss, were performed on dry cylinders of wood samples during torrefaction in an inert atmosphere at 503, 533, and 553 K. The calculated data shows a good agreement with experiments. The model can be a useful tool to estimate projecting and operating parameters for torrefaction furnaces such as minimum time of torrefaction, energy consumption and the mass yield. (author)
Khusna, H.; Heryaningsih, N. Y.
2018-01-01
The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.
Learning to teach mathematical modelling in secondary and tertiary education
Ferri, Rita Borromeo
2017-07-01
Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Mathematical Models and the Experimental Analysis of Behavior
Mazur, James E.
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…
Laser filamentation mathematical methods and models
Lorin, Emmanuel; Moloney, Jerome
2016-01-01
This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...
Thermoregulation in premature infants: A mathematical model.
Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen
2016-12-01
In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright Â© 2016 Elsevier Ltd. All rights reserved.
Mathematical models for atmospheric pollutants. Final report
International Nuclear Information System (INIS)
Drake, R.L.; Barrager, S.M.
1979-08-01
The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT. Copyright © 2015 Elsevier Ltd. All rights reserved.
Mathematical modeling of deformation during hot rolling
Energy Technology Data Exchange (ETDEWEB)
Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K. [Univ. of British Columbia, Vancouver, British Columbia (Canada). Centre for Metallurgical Processing Engineering
1994-12-31
The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Mathematical methods and models in composites
Mantic, Vladislav
2014-01-01
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover
An introduction to mathematical modeling of infectious diseases
Li, Michael Y
2018-01-01
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.
Modelling gas generation for landfill.
Chakma, Sumedha; Mathur, Shashi
2017-06-01
A methodology was developed to predict the optimum long-term spatial and temporal generation of landfill gases such as methane, carbon dioxide, ammonia, and hydrogen sulphide on post-closure landfill. The model incorporated the chemical and the biochemical processes responsible for the degradation of the municipal solid waste. The developed model also takes into account the effects of heterogeneity with different layers as observed at the site of landfills' morphology. The important parameters for gas generation due to biodegradation such as temperature, pH, and moisture content were incorporated. The maximum and the minimum generations of methane and hydrogen sulphide were observed. The rate of gas generation was found almost same throughout the depth after 30 years of landfill closure. The proposed model would be very useful for landfill engineering in the mining landfill gas and proper design for landfill gas management systems.
Declarative representation of uncertainty in mathematical models.
Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Declarative representation of uncertainty in mathematical models.
Directory of Open Access Journals (Sweden)
Andrew K Miller
Full Text Available An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Mathematical Modeling of an Oscillating Droplet
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
Development of a Multidisciplinary Middle School Mathematics Infusion Model
Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura
2011-01-01
The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…
Assessment of Primary 5 Students' Mathematical Modelling Competencies
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Assessing Children's Mathematical Thinking in Practical Modelling Situations.
Tanner, Howard; Jones, Sonia
2002-01-01
Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary investigation...
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical...... for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary investigation...
Mathematical model and software for control of commissioning blast furnace
Spirin, N. A.; Onorin, O. P.; Shchipanov, K. A.; Lavrov, V. V.
2016-09-01
Blowing-in is a starting period of blast furnace operation after construction or major repair. The current approximation methods of blowing-in burden analysis are based on blowing-in practice of previously commissioned blast furnaces. This area is theoretically underexplored; there are no common scientifically based methods for selection of the burden composition and blast parameters. The purpose of this paper is development and scientific substantiation of the methods for selection of the burden composition and blast parameters in the blast furnace during the blowing-in period. Research methods are based on physical regularities of main processes running in the blast furnace, system analysis, and application of modern principles for development and construction of mathematical models, algorithms and software designed for automated control of complex production processes in metallurgy. As consequence of the research made by the authors the following results have been achieved: 1. A set of mathematical models for analysis of burden arrangement throughout the height of the blast furnace and for selection of optimal blast and gas dynamic parameters has been developed. 2. General principles for selection of the blowing-in burden composition and blast and gas dynamic parameters have been set up. 3. The software for the engineering and process staff of the blast furnace has been developed and introduced in the industry.
Directory of Open Access Journals (Sweden)
Shestakov Igor A.
2015-01-01
Full Text Available The article shows the results of mathematical modeling of convective heat transfer in the low-temperature storage of liquefied natural gas. Regime of natural convection in an enclosure with different intensity of the heat flux at the external borders are investigated. Was examined two-dimensional nonstationary problem within the model of Navier-Stokes in dimensionless variables “vorticity - stream function - temperature”. Distributions of hydrodynamic parameters and temperatures that characterize the basic regularities of the processes are obtained. Circulating flows are determined and carried out the analysis of vortices formation mechanism and the temperature distribution in solution at conditions of natural convection when the Grashof number (Gr = 106. A significant influence of heat transfer rate on solutions boundary on flow structure and temperature field in LNG storage tanks.
A Mathematical Model of Network Communication
2010-05-03
who achieved a 3.5 GPA to 4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education ...1973 [25] Daniel H. Rothman and Stéphane Zaleski Lattice Gas Cellular Automata; Simple Models of Complex hydrodynamics. Cambridge Univesity text, 1997
Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter
Directory of Open Access Journals (Sweden)
Tufan Gürkan YILMAZ
2016-05-01
Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.
Modelling gas markets - a survey
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-12-31
This report reviews research of relevance to the analysis of present and future developments of the European natural gas market. The research activities considered are confined to (1) numerical models for gas markets, (2) analyses of energy demand, and (3) analyses of behaviour and cost structures in the transmission and distribution sector. Most of the market models are strictly micro economic and assume perfect competition or a game-theoretical equilibrium. They use sophisticated solution concepts, but very simplified specifications of supply and demand functions. Most of the research on demand is econometric analyses. These have more detailed model specification than have the aggregated market models. It is found, however, that the econometric literature based on neo-classical economics has not yielded unambiguous results and the specifications disregard important real world aspects of gas demand. The section on demand concludes that the extent of the gas grid is an important determinant for gas demand, but there has been virtually no research on what determines this variable. Data about transmission and distribution of gas in Europe is scarce and only a few non-econometric and virtually no econometric analyses are available. However, some conclusions can be made from relevant North American literature: (1) there has been significant autonomous technical progress in the transmission industry, (2) distribution costs strongly depend on geographical and other conditions, and (3) ownership, whether private or public, may be important for distribution costs and pricing policies. 56 refs., 3 figs., 1 tab.
Modelling gas markets - a survey
International Nuclear Information System (INIS)
1997-01-01
This report reviews research of relevance to the analysis of present and future developments of the European natural gas market. The research activities considered are confined to (1) numerical models for gas markets, (2) analyses of energy demand, and (3) analyses of behaviour and cost structures in the transmission and distribution sector. Most of the market models are strictly micro economic and assume perfect competition or a game-theoretical equilibrium. They use sophisticated solution concepts, but very simplified specifications of supply and demand functions. Most of the research on demand is econometric analyses. These have more detailed model specification than have the aggregated market models. It is found, however, that the econometric literature based on neo-classical economics has not yielded unambiguous results and the specifications disregard important real world aspects of gas demand. The section on demand concludes that the extent of the gas grid is an important determinant for gas demand, but there has been virtually no research on what determines this variable. Data about transmission and distribution of gas in Europe is scarce and only a few non-econometric and virtually no econometric analyses are available. However, some conclusions can be made from relevant North American literature: (1) there has been significant autonomous technical progress in the transmission industry, (2) distribution costs strongly depend on geographical and other conditions, and (3) ownership, whether private or public, may be important for distribution costs and pricing policies. 56 refs., 3 figs., 1 tab
Simulation modelling for new gas turbine fuel controller creation.
Vendland, L. E.; Pribylov, V. G.; Borisov, Yu A.; Arzamastsev, M. A.; Kosoy, A. A.
2017-11-01
State of the art gas turbine fuel flow control systems are based on throttle principle. Major disadvantage of such systems is that they require high pressure fuel intake. Different approach to fuel flow control is to use regulating compressor. And for this approach because of controller and gas turbine interaction a specific regulating compressor is required. Difficulties emerge as early as the requirement definition stage. To define requirements for new object, his properties must be known. Simulation modelling helps to overcome these difficulties. At the requirement definition stage the most simplified mathematical model is used. Mathematical models will get more complex and detailed as we advance in planned work. If future adjusting of regulating compressor physical model to work with virtual gas turbine and physical control system is planned.
A Mathematical Model of Cardiovascular Response to Dynamic Exercise
National Research Council Canada - National Science Library
Magosso, E
2001-01-01
A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...
Mathematical model of the Amazon Stirling engine
Energy Technology Data Exchange (ETDEWEB)
Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br
2010-07-01
The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
A mathematical model of Chagas disease transmission
Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning
2018-03-01
Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.
Modellus: Learning Physics with Mathematical Modelling
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
International Nuclear Information System (INIS)
Steinhauer, L. C.; Kimura, W. D.
2006-01-01
We have developed a 1-D, quasi-steady-state numerical model for a gas-filled capillary discharge that is designed to aid in selecting the optimum capillary radius in order to guide a laser beam with the required intensity through the capillary. The model also includes the option for an external solenoid B-field around the capillary, which increases the depth of the parabolic density channel in the capillary, thereby allowing for propagation of smaller laser beam waists. The model has been used to select the parameters for gas-filled capillaries to be utilized during the Staged Electron Laser Acceleration -- Laser Wakefield (STELLA-LW) experiment
Mathematical modeling of infectious disease dynamics.
Siettos, Constantinos I; Russo, Lucia
2013-05-15
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host-pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
Mathematical modeling of the voloxidation process. Final report
International Nuclear Information System (INIS)
Stanford, T.G.
1979-06-01
A mathematical model of the voloxidation process, a head-end reprocessing step for the removal of volatile fission products from spent nuclear fuel, has been developed. Three types of voloxidizer operation have been considered; co-current operation in which the gas and solid streams flow in the same direction, countercurrent operation in which the gas and solid streams flow in opposite directions, and semi-batch operation in which the gas stream passes through the reactor while the solids remain in it and are processed batch wise. Because of the complexity of the physical ahd chemical processes which occur during the voloxidation process and the lack of currently available kinetic data, a global kinetic model has been adapted for this study. Test cases for each mode of operation have been simulated using representative values of the model parameters. To process 714 kgm/day of spent nuclear fuel, using an oxidizing atmosphere containing 20 mole percent oxygen, it was found that a reactor 0.7 m in diameter and 2.49 m in length would be required for both cocurrent and countercurrent modes of operation while for semibatch operation a 0.3 m 3 reactor and an 88200 sec batch processing time would be required
Mathematical modelling of a continuous biomass torrefaction reactor: TORSPYDTM column
International Nuclear Information System (INIS)
Ratte, J.; Fardet, E.; Mateos, D.; Hery, J.-S.
2011-01-01
Torrefaction is a soft thermal process usually applied to cocoa or coffee beans to obtain the Maillard reaction to produce aromatics and enhance the flavour. In the case of biomass the main interest of torrefaction it is to break the fibers. To do so, Thermya company has developed and patented a biomass torrefaction/depolymerisation process called TORSPYD TM . It is a homogeneous 'soft' thermal process that takes place in an inert atmosphere. The process progressively eliminates the biomass water content transforms a portion of the biomass organic matter and breaks the biomass structure by depolymerisation of the fibers. This produces a high performance solid fuel, called Biocoal, which offers a range of benefits over and above that of normal biomass fuel. To develop such a process, this company has developed two main tools: - a continuous torrefaction laboratory pilot with a capacity to produce 3 - 8 kg/h of torrefied biomass; - a mathematical model dedicated to the design and optimisation of the TORSPYD reactor. The mathematical model is able to describe the chemical and physical processes that take place in the torrefaction column at two different scales, namely: the particle, and the surrounding gas. The model enables the gas temperature profiles inside the column to be predicted, and the results of the model are then validated through experiment in the laboratory pilot. The model also allows us to estimate the thermal power necessary to torrefy any type of biomass for a given moisture content. -- Highlights: → We model a patented torrefaction/depolymerisation biomass process: TORPSPYD. → We compare simulated results to experimental data obtained from our torrefaction pilot plant. → We describe phenomenon that occurs in our torrefaction reactor and discuss about the influence of moisture of the input biomass.
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
Mathematical modeling of the Phoenix Rising pathway.
Directory of Open Access Journals (Sweden)
Chad Liu
2014-02-01
Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.
Dalla Vecchia, Rodrigo
2015-01-01
This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…
Mathematical Modeling of Hybrid Electrical Engineering Systems
Directory of Open Access Journals (Sweden)
A. A. Lobaty
2016-01-01
Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the
Mathematical model of highways network optimization
Sakhapov, R. L.; Nikolaeva, R. V.; Gatiyatullin, M. H.; Makhmutov, M. M.
2017-12-01
The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Mathematical models for therapeutic approaches to control HIV disease transmission
Roy, Priti Kumar
2015-01-01
The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...
Description of mathematical models and computer programs
International Nuclear Information System (INIS)
1977-01-01
The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......-mentioned factors, initial loss of aerosol by impact on the chamber wall is most important for the efficiency of a spacer. With a VT of 195 mL, the AeroChamber and Babyhaler were emptied in two breaths, the NebuChamber in four breaths, and the Nebuhaler in six breaths. Insufficiencies of the expiratory valves were...
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Mathematical modeling of a thermovoltaic cell
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
Missing the Promise of Mathematical Modeling
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Villa-Ochoa, Jhony; Córdoba, Francisco
2013-01-01
In Colombia, the mathematical training of students in primary and secondary school has, among other purposes, to recognize the cultural diversity, the need for greater equity levels and individuals able to be have a critic position facing the different social and democratic requirements; hence the mathematical modeling has gained ground as a way to meet these education purposes and, therefore, it is suggested as one of the processes the mathematics curriculum must articulate. Such realities r...
Rudolph, Lee
2012-01-01
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in
Mathematical Model of the Laser Gyro Errors
Directory of Open Access Journals (Sweden)
V. N. Enin
2017-01-01
Full Text Available The paper presents the analysed and systemised results of the experimental study of laser gyro (LG errors. Determines a structure of the resulting LG error, as a linear combination of the random processes, characterizing natural and technical fluctuations of difference frequency of the counter-propagating waves, with a random constant zero shift available in the sensor readings. Formulates the requirements for the structure and form of the analytic description of the error model. Shows a generalized model of the LG fluctuation processes, on the basis of which a mathematical model of LG errors was developed as an inertial sensor.The model is represented by a system of the stochastic differential equations and functional relationships to characterize a resulting error of the sensor. The paper provides a correlation analysis of the model equations and final equations obtained for the mean-square values of the particular components, which allow us to identify the resulting error parameters. The model parameters are presented through the values of the power spectral density of the particular components. The discrete form of the model is considered, the convergence of continuous and difference equations is shown in fulfilling conditions of the limiting transition. Further research activities are defined.
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Jennifer M. Suh
2017-06-01
Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
Mathematical Model of Evolution of Brain Parcellation.
Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals.
Perumusan Model Moneter Berdasarkan Perilaku Gas Ideal
Directory of Open Access Journals (Sweden)
Rachmad Resmiyanto
2014-04-01
Full Text Available Telah disusun sebuah model moneter yang berdasarkan perilaku gas ideal. Model disusun dengan menggunakan metode kias/analogi. Model moneter gas ideal mengiaskan jumlah uang beredar dengan volume gas, daya beli dengan tekanan gas dan produksi barang dengan suhu gas. Model ini memiliki formulasi yang berbeda dengan Teori Kuantitas Uang (Quantity Theory of Money yang dicetuskan oleh Irving Fisher, model moneter Marshal-Pigou dari Cambridge serta model moneter ala Keynes. Selama ini 3 model tersebut dianggap sebagai model yang mapan dalam teori moneter pada buku-buku teks ekonomi. Model moneter gas ideal dapat menjadi cara pandang baru terhadap sistem moneter.
Mathematical problems in modeling artificial heart
Directory of Open Access Journals (Sweden)
Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....
Mathematical modeling of wiped-film evaporators
International Nuclear Information System (INIS)
Sommerfeld, J.T.
1976-05-01
A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes
Mathematical models for indoor radon prediction
International Nuclear Information System (INIS)
Malanca, A.; Pessina, V.; Dallara, G.
1995-01-01
It is known that the indoor radon (Rn) concentration can be predicted by means of mathematical models. The simplest model relies on two variables only: the Rn source strength and the air exchange rate. In the Lawrence Berkeley Laboratory (LBL) model several environmental parameters are combined into a complex equation; besides, a correlation between the ventilation rate and the Rn entry rate from the soil is admitted. The measurements were carried out using activated carbon canisters. Seventy-five measurements of Rn concentrations were made inside two rooms placed on the second floor of a building block. One of the rooms had a single-glazed window whereas the other room had a double pane window. During three different experimental protocols, the mean Rn concentration was always higher into the room with a double-glazed window. That behavior can be accounted for by the simplest model. A further set of 450 Rn measurements was collected inside a ground-floor room with a grounding well in it. This trend maybe accounted for by the LBL model
A Mathematical Model of Cigarette Smoldering Process
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Chen P
2014-12-01
Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.
Mathematical modeling of diphtheria transmission in Thailand.
Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin
2017-08-01
In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical foundations of the dendritic growth models.
Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos
2007-11-01
At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Lamb, Janeen; Kawakami, Takashi; Saeki, Akihiko; Matsuzaki, Akio
2014-01-01
The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…
Mathematical analysis of epidemiological models with heterogeneity
Energy Technology Data Exchange (ETDEWEB)
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
Mathematical modeling of alcohol distillation columns
Directory of Open Access Journals (Sweden)
Ones Osney Pérez
2011-04-01
Full Text Available New evaluation modules are proposed to extend the scope of a modular simulator oriented to the sugar cane industry, called STA 4.0, in a way that it can be used to carry out x calculation and analysis in ethanol distilleries. Calculation modules were developed for the simulation of the columns that are combined in the distillation area. Mathematical models were supported on materials and energy balances, equilibrium relations and thermodynamic properties of the ethanol-water system. Ponchon-Savarit method was used for the evaluation of the theoretical stages in the columns. A comparison between the results using Ponchon- Savarit method and those obtained applying McCabe-Thiele method was done for a distillation column. These calculation modules for ethanol distilleries were applied to a real case for validation.
Mathematical Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: Levels and mathematical model
Directory of Open Access Journals (Sweden)
Wai Ming To
2014-01-01
Full Text Available Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (Leq,1-h was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2016-01-01
This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…
Mathematical modeling plasma transport in tokamaks
International Nuclear Information System (INIS)
Quiang, Ji
1995-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10 20 /m 3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%
Mathematics in Nature Modeling Patterns in the Natural World
Adam, John A
2011-01-01
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
Practical Techniques for Modeling Gas Turbine Engine Performance
Chapman, Jeffryes W.; Lavelle, Thomas M.; Litt, Jonathan S.
2016-01-01
The cost and risk associated with the design and operation of gas turbine engine systems has led to an increasing dependence on mathematical models. In this paper, the fundamentals of engine simulation will be reviewed, an example performance analysis will be performed, and relationships useful for engine control system development will be highlighted. The focus will be on thermodynamic modeling utilizing techniques common in industry, such as: the Brayton cycle, component performance maps, map scaling, and design point criteria generation. In general, these topics will be viewed from the standpoint of an example turbojet engine model; however, demonstrated concepts may be adapted to other gas turbine systems, such as gas generators, marine engines, or high bypass aircraft engines. The purpose of this paper is to provide an example of gas turbine model generation and system performance analysis for educational uses, such as curriculum creation or student reference.
An introduction to mathematical modeling a course in mechanics
Oden, Tinsley J
2011-01-01
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...
A mathematical model of glutathione metabolism
Directory of Open Access Journals (Sweden)
James S Jill
2008-04-01
Full Text Available Abstract Background Glutathione (GSH plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism. Approach We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data. Conclusion We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.
A mathematical model of aerobic methane oxidation coupled to denitrification.
Modin, Oskar
2018-05-01
Aerobic methanotrophic bacteria use methane as their only source of energy and carbon. They release organic compounds that can serve as electron donors for co-existing denitrifiers. This interaction between methanotrophs and denitrifiers is known to contribute to nitrogen losses in natural environments and has also been exploited by researchers for denitrification of nitrate-contaminated wastewater. The purpose of this study was to develop a mathematical model describing aerobic methane oxidation coupled to denitrification in suspended-growth reactors. The model considered the activities of three microbial groups: aerobic methanotrophs, facultative methylotrophs, and facultative heterotrophs. The model was tested against data from the scientific literature and used to explore the effects of the oxygen mass transfer coefficient, the solids retention time, and the fraction methane in the feed gas on nitrate removal. The fraction of methane in the feed gas was found to be critical for the nitrate removal rate. A value of about 15% in air was optimal. A lower methane fraction led to excess oxygen, which was detrimental for denitrification. A higher fraction led to oxygen-limitation, which restricted the growth rate of methanotrophs in the reactor.
Atmosphere Behavior in Gas-Closed Mouse-Algal Systems: An Experimental and Modelling Study
Averner, M. M.; Moore, B., III; Bartholomew, I.; Wharton, R.
1985-01-01
A dual approach of mathematical modelling and laboratory experimentation aimed at examining the gas exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere was initiated. The development of control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels is examined. A mathematical model simulating the atmospheric behavior in these systems was developed and an experimental gas closed system was constructed. These systems are described and preliminary results are presented.
Ocular hemodynamics and glaucoma: the role of mathematical modeling.
Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A
2013-01-01
To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.
Mathematical modeling of solid oxide fuel cells
Lu, Cheng-Yi; Maloney, Thomas M.
1988-01-01
Development of predictive techniques, with regard to cell behavior, under various operating conditions is needed to improve cell performance, increase energy density, reduce manufacturing cost, and to broaden utilization of various fuels. Such technology would be especially beneficial for the solid oxide fuel cells (SOFC) at it early demonstration stage. The development of computer models to calculate the temperature, CD, reactant distributions in the tubular and monolithic SOFCs. Results indicate that problems of nonuniform heat generation and fuel gas depletion in the tubular cell module, and of size limitions in the monolithic (MOD 0) design may be encountered during FC operation.
Manual on mathematical models in isotope hydrogeology
International Nuclear Information System (INIS)
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
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Pan eLi
2013-10-01
Full Text Available Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
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…
Mathematical modelling of anisotropy of illite-rich shale
Chesnokov, E.M.; Tiwary, D.K.; Bayuk, I.O.; Sparkman, M.A.; Brown, R.L.
2009-01-01
The estimation of illite-rich shale anisotropy to account for the alignment of clays and gas- or brine-filled cracks is presented via mathematical modelling. Such estimation requires analysis to interpret the dominance of one effect over another. This knowledge can help to evaluate the permeability in the unconventional reservoir, stress orientation, and the seal capacity for the conventional reservoir. Effective media modelling is used to predict the elastic properties of the illite-rich shale and to identify the dominant contributions to the shale anisotropy. We consider two principal reasons of the shale anisotropy: orientation of clay platelets and orientation of fluid-filled cracks. In reality, both of these two factors affect the shale anisotropy. The goal of this study is, first, to separately analyse the effect of these two factors to reveal the specific features in P- and S-wave velocity behaviour typical of each of the factors, and, then, consider a combined effect of the factors when the cracks are horizontally or vertically aligned. To do this, we construct four models of shale. The behaviour of P- and S-wave velocities is analysed when gas- and water-filled cracks embedded in a host matrix are randomly oriented, or horizontally or vertically aligned. The host matrix can be either isotropic or anisotropic (of VTI symmetry). In such a modelling, we use published data on mineralogy and clay platelet alignment along with other micromechanical measurements. In the model, where the host matrix is isotropic, the presence of a singularity point (when the difference VS1 - VS2 changes its sign) in shear wave velocities is an indicator of brine-filled aligned cracks. In the model with the VTI host matrix and horizontally aligned cracks filled with gas, an increase in their volume concentration leads to that the azimuth at which the singularity is observed moves toward the symmetry axis. In this case, if the clay content is small (around 20 per cent), the
Application of Mathematical Modeling Activities in Costarican High School Education
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Karen Porras-Lizano
2015-01-01
Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.
Mathematical Modeling of Linear and Non-Linear Aircraft Structures.
1980-07-01
7 A-A OBO 439 LISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT--ETC F IG 1/2 MATHENATICAL MODELING OF LINEAR AND NON-LINEAR AIRCRAFT STRUCTu...theoretical model. (see Fig.1): Continuum Physical Model Mathematical Model Numerical computation ] Analytical treatment (Discretization)Ft Fig.: 1...this model neglecting unessential details. This "Mathematical Model" is usually solved by numerical computation , which means that a discretization of
Logistics of Mathematical Modeling-Focused Projects
Harwood, R. Corban
2018-01-01
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche
2012-01-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…
MODELS FOR MATHEMATICS IN THE SCHOOL.
KENNEDY, LEONARD M.
THE PURPOSE OF THIS BOOK IS TO DESCRIBE LEARNING AIDS THAT MAY BE MADE BY A TEACHER OR CHILDREN FOR USE IN MATHEMATICS PROGRAMS IN THE ELEMENTARY SCHOOL. THESE AIDS ARE OF TWO TYPES--MANIPULATIVE AND VISUAL. DESCRIPTIONS IN THIS BOOK INCLUDE (1) THE PURPOSE OF THE TEACHING AID IN A MODERN MATHEMATICS PROGRAM, (2) EXAMPLES OF ITS USE, AND (3) ITS…
Mathematical rainfall model for hydrographic demarcation of Manabi ...
African Journals Online (AJOL)
... systems (GIS), a mathematical model to estimate very accurately the values of rainfall based only on the geographical coordinates. To achieve this objective, the basins of the Hydrographic Demarcation of Manabí have been chosen to develop the indicated mathematical model, which can be applied to other basins in the ...
Mathematical programming model for the optimization of nutritional ...
African Journals Online (AJOL)
The use of a mathematical programming model for determining optimal nutritional strategy for a dairy cow is described. Mixed Integer Programming (MIP) may be used to fit curvilinear functions, such as the changes in the nutrient requirements of the cow, into a standard mathematical programme. The model determines the.
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
iSTEM: Promoting Fifth Graders' Mathematical Modeling
Yanik, H. Bahadir; Karabas, Celil
2014-01-01
Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…
An Integrated Approach to Mathematical Modeling: A Classroom Study.
Doerr, Helen M.
Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…
Mathematical modeling of dissolved oxygen in fish ponds ...
African Journals Online (AJOL)
Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...
Mathematical Modeling of Tuberculosis Granuloma Activation
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Steve M. Ruggiero
2017-12-01
Full Text Available Tuberculosis (TB is one of the most common infectious diseases worldwide. It is estimated that one-third of the world’s population is infected with TB. Most have the latent stage of the disease that can later transition to active TB disease. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb. Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in latent TB. The bacteria can be perturbed from latency to active TB disease in a process called granuloma activation when the granulomas are compromised by other immune response events in a host, such as HIV, cancer, or aging. Dysregulation of matrix metalloproteinase 1 (MMP-1 has been recently implicated in granuloma activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational model is developed to fill this gap. This dynamic mathematical model focuses specifically on the latent to active transition after the initial immune response has successfully formed a granuloma. Bacterial leakage from latent granulomas is successfully simulated in response to the MMP-1 dynamics under several scenarios for granuloma activation.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
A mathematical model of embodied consciousness.
Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth
2017-09-07
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical model I. Electron and quantum mechanics
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Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
A mathematical model of forgetting and amnesia
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Jaap M. J. Murre
2013-02-01
Full Text Available We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time-scales share two fundamental properties: (1 representations in a store decline in strength (2 while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i the temporal gradient of retrograde amnesia (Ribot's Law, (ii forgetting curves with and without anterograde amnesia, and (iii learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff's Disease, Alzheimer's Dementia, Huntington's Disease, and other disorders.
Mathematical modeling of Chikungunya fever control
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical Model of Pipeline Abandonment and Recovery in Deepwater
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Xia-Guang Zeng
2014-01-01
Full Text Available In offshore oil and gas engineering the pipeline abandonment and recovery is unavoidable and its mechanical analysis is necessary and important. For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. A novel technique for the handling of the moving boundary condition is proposed, which can tackle the moving boundary condition without contact analysis. Based on a traditional numerical method, the problem is solved directly by the proposed technique. The results of the presented method are in good agreement with the results of the traditional finite element method coupled with contact analysis. Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting.
Mathematical modeling of phase interaction taking place in materials processing
International Nuclear Information System (INIS)
Zinigrad, M.
2002-01-01
The quality of metallic products depends on their composition and structure. The composition and the structure are determined by various physico-chemical and technological factors. One of the most important and complicated problems in the modern industry is to obtain materials with required composition, structure and properties. For example, deep refining is a difficult task by itself, but the problem of obtaining the material with the required specific level of refining is much more complicated. It will take a lot of time and will require a lot of expanses to solve this problem empirically and the result will be far from the optimal solution. The most effective way to solve such problems is to carry out research in two parallel direction. Comprehensive analysis of thermodynamics, kinetics and mechanisms of the processes taking place at solid-liquid-gaseous phase interface and building of the clear well-based physico-chemical model of the above processes taking into account their interaction. Development of mathematical models of the specific technologies which would allow to optimize technological processes and to ensure obtaining of the required properties of the products by choosing the optimal composition of the raw materials. We apply the above unique methods. We developed unique methods of mathematical modeling of phase interaction at high temperatures. These methods allows us to build models taking into account: thermodynamic characteristics of the processes, influence of the initial composition and temperature on the equilibrium state of the reactions, kinetics of homogeneous and heterogeneous processes, influence of the temperature, composition, speed of the gas flows, hydrodynamic and thermal factors on the velocity of the chemical and diffusion processes. The models can be implemented in optimization of various metallurgical processes in manufacturing of steels and non-ferrous alloys as well as in materials refining, alloying with special additives
Is there Life after Modelling? Student conceptions of mathematics
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
2010-09-01
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Development of the CCP-200 mathematical model for Syzran CHPP using the Thermolib software package
Usov, S. V.; Kudinov, A. A.
2016-04-01
Simplified cycle diagram of the CCP-200 power generating unit of Syzran CHPP containing two gas turbines PG6111FA with generators, two steam recovery boilers KUP-110/15-8.0/0.7-540/200, and one steam turbine Siemens SST-600 (one-cylinder with two variable heat extraction units of 60/75 MW in heatextraction and condensing modes, accordingly) with S-GEN5-100 generators was presented. Results of experimental guarantee tests of the CCP-200 steam-gas unit are given. Brief description of the Thermolib application for the MatLab Simulink software package is given. Basic equations used in Thermolib for modeling thermo-technical processes are given. Mathematical models of gas-turbine plant, heat-recovery steam generator, steam turbine and integrated plant for power generating unit CCP-200 of Syzran CHPP were developed with the help of MatLab Simulink and Thermolib. The simulation technique at different ambient temperature values was used in order to get characteristics of the developed mathematical model. Graphic comparison of some characteristics of the CCP-200 simulation model (gas temperature behind gas turbine, gas turbine and combined cycle plant capacity, high and low pressure steam consumption and feed water consumption for high and low pressure economizers) with actual characteristics of the steam-gas unit received at experimental (field) guarantee tests at different ambient temperature are shown. It is shown that the chosen degrees of complexity, characteristics of the CCP-200 simulation model, developed by Thermolib, adequately correspond to the actual characteristics of the steam-gas unit received at experimental (field) guarantee tests; this allows considering the developed mathematical model as adequate and acceptable it for further work.
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
Directory of Open Access Journals (Sweden)
S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Directory of Open Access Journals (Sweden)
Alexandros Sotirios Anifantis
2018-02-01
Full Text Available Nowadays, the traditional energy sources used for greenhouse heating are fossil fuels such as LPG, diesel and natural gas. The global energy demand will continue to grow and alternative technologies need to be developed in order to improve the sustainability of crop production in protected environments. Innovative solutions are represented by renewable energy plants such as photovoltaic, wind and geothermal integrated systems, however, these technologies need to be connected to the power grid in order to store the energy produced. On agricultural land, power grids are not widespread and stand-alone renewable energy systems should be investigated especially for greenhouse applications. The aim of this research is to analyze, by means of a mathematical model, the energy efficiency of a photovoltaic (8.2 kW, hydrogen (2.5 kW and ground source gas heat pump (2.2 kW integrated in a stand-alone system used for heating an experimental greenhouse tunnel (48 m2 during the winter season. A yearlong energy performance analysis was conducted for three different types of greenhouse cover materials, a single layer polyethylene film, an air inflated-double layer polyethylene film, and a double acrylic or polycarbonate. The results of one year showed that the integrated system had a total energy efficiency of 14.6%. Starting from the electric energy supplied by the photovoltaic array, the total efficiency of the hydrogen and ground source gas heat pump system was 112% if the coefficient of the performance of the heat pump is equal to 5. The heating system increased the greenhouse air temperatures by 3–9 °C with respect to the external air temperatures, depending on the greenhouse cover material used.
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Cytochrome C Biosensor—A Model for Gas Sensing
Directory of Open Access Journals (Sweden)
Gabriele Nelles
2011-06-01
Full Text Available This work is about gas biosensing with a cytochrome c biosensor. Emphasis is put on the analysis of the sensing process and a mathematical model to make predictions about the biosensor response. Reliable predictions about biosensor responses can provide valuable information and facilitate biosensor development, particularly at an early development stage. The sensing process comprises several individual steps, such as phase partition equilibrium, intermediate reactions, mass-transport, and reaction kinetics, which take place in and between the gas and liquid phases. A quantitative description of each step was worked out and finally combined into a mathematical model. The applicability of the model was demonstrated for a particular example of methanethiol gas detection by a cytochrome c biosensor. The model allowed us to predict the optical readout response of the biosensor from tabulated data and data obtained in simple liquid phase experiments. The prediction was experimentally verified with a planar three-electrode electro-optical cytochrome c biosensor in contact with methanethiol gas in a gas tight spectroelectrochemical measurement cell.
Perspectives on instructor modeling in mathematics teacher education
Brown, Cassondra
2009-01-01
Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...
Novel mathematical neural models for visual attention
DEFF Research Database (Denmark)
Li, Kang
Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive eld, described by either a response-aver...... system, supported by simulation study. Finally, we present the decoding of multiple temporal stimuli under these visual attention theories, also in a realistic biophysical situation with simulations.......Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive eld, described by either a response......-averaging or a probability-mixing model. Second, we discuss how stimuli are processed during visual search, explained by either a serial or a parallel mechanism. Here we present novel mathematical methods to answer the psychology questions from a neural perspective, combining the formulation of neural explanations...
Ion source mathematical modeling and optimization
International Nuclear Information System (INIS)
Egorov, N.V.; Vinogradova, E.M.
2004-01-01
Full text: The system of beam formation and control in the ion gun is under investigation. The calculation of the ion gun must take into account the field ion cathode influence on the beam focusing and transport conditions and the other electrodes influence both on the field cathode emission ability and on the characteristics of the formation and control systems. It's considered a mathematical model of the gun as a axially symmetrical ion-optical system which consists of a cathode, i.e. axially symmetrical thin tip on a flat substrate and a system of round apertures as the focusing electrodes. The tip shape may be various. The number of the apertures may be various too. The potential of the tip is equal to the substrate potential and is assumed to be zero without the loss of general character of the problem. A method is proposed for the determination the potential distribution. lt is calculated the distribution of potentials for whole region of the ion-optical system. All geometrical dimensions of the system and the electrodes' potentials are the parameters of this method. The problem of the optimal geometrical parameters and electrodes potentials is solved to have the required emission current. (author)
Symmetrization of mathematical model of charge transport in semiconductors
Directory of Open Access Journals (Sweden)
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
Directory of Open Access Journals (Sweden)
Hamideh Jafari Koshkouei
2016-09-01
Full Text Available The present study was carried out to investigate the influence of mathematics self-concept (MSC, motivation to learn mathematics (SMOT and self-regulation learning (SRL on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measured by mathematics scores in the first semester of 1393-94 education year. Results obtained by data analysis indicated that the primary conceptual model of the research was an appropriate model and possesses good fitness. Therefore, influence of mathematics self-concept, motivation to learn mathematics and self-regulation learning on mathematics academic achievement was confirmed. On the other hand, it was revealed that mathematics self-concept had influence on motivation to learn mathematics, and motivation to learn mathematics had effect on self-regulation learning. Compared to motivation to learn mathematics and self-regulation learning, mathematics self-concept was a stronger predictor for mathematics academic achievement. Detailed analysis of variables' direct effects showed that mathematics self-concept had considerable direct influence on motivation to learn mathematics.
Quantum Gravity Mathematical Models and Experimental Bounds
Fauser, Bertfried; Zeidler, Eberhard
2007-01-01
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Handayani, I.; Januar, R. L.; Purwanto, S. E.
2018-01-01
This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.
Development of mathematic model for coffee decaffeination with leaching method
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Sukrisno Widyotomo
2011-08-01
Full Text Available A simple mathematic model for caffeine kinetic description during the extraction process (leaching of coffee bean was developed. A nonsteady diffusion equation coupled with a macroscopic mass transfer equation for solvent was developed and them solved analytically. The kinetic of caffeine extraction from coffee bean is depend on initial caffeine content, final caffeine content, caffeine content at certain time, masstransfer coefficient, solvent volume, surface area of coffee beans, process time, radius of coffee bean, leaching rate of caffeine, caffeine diffusivity and a are constan, solvent concentration, activation energy, temperature absolute and gas constant. Caffeine internal mass diffusivity was estimated by fitting the model to an experiment using acetic acid and liquid waste of cocoa beans fermentation. The prediction equation for leaching rate of caffeine in coffee beans has been found. It was found that Dk (m2/sec=1.345x107—4.1638x107, and kL (m/sec=2.445x105—5.551x105 by acetic acid as solvent depended on temperature and solvent concentration. The prediction equation for length of time to reduce initial caffeine content to certain concentration in coffee beans has been developed, Caffeine diffusivity (Dk and masstransfer coefficient (kL was found respectively 1.591x 107—2.122x107 m2/sec and 4.897x105—6.529x105 m/sec using liquid waste of cocoa bean fermentation as solvent which depend on temperature and solvent concentration. Key words: Coffee, caffeine, decaffeination, leaching, mathematic model.
Mathematical Modelling of Coal Gasification Processes
Sundararajan, T.; Raghavan, V.; Ajilkumar, A.; Vijay Kumar, K.
2017-07-01
experimental and modelling work has been undertaken to investigate the gasification characteristics of high ash Indian coals and compare the yield with those of high grade Australian and Japanese coals. A 20 kW capacity entrained flow gasifier has been constructed and the gasification characteristics have been studied for Indian coals for different particle sizes, system pressures and air flow rates. The theoretical model incorporates the effects of Knudsen diffusion, devolatilization and various heterogenous and homogenous kinetic steps as well as two-phase flow interactions involving the gaseous and particle phases. Output parameters such as carbon conversion, cold gas efficiency and syngas composition have been compared for different grades of coals under a wide range of operating conditions. The model developed for the entrained flow gasifier predicts the gasification characteristics of both Indian and foreign coals well. Apart from the entrained flow gasifier, a bubbling bed gasifier of 100 kW capacity has also been studied. A pilot plant for the gasification of Indian coals has been set up for this capacity and its performance has been investigated experimentally as well as theoretically at different air and steam flow rates. Carbon conversion efficiency of more than 80% has been achieved.
Mathematical modeling and computational intelligence in engineering applications
Silva Neto, Antônio José da; Silva, Geraldo Nunes
2016-01-01
This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.
Teaching Writing and Communication in a Mathematical Modeling Course
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Mathematical models for drug diffusion through the compartments of ...
African Journals Online (AJOL)
M.A. Khanday
2016-07-26
Jul 26, 2016 ... quadratic shape function.10. Moreover, Khanday and. Najar11,12 established the mathematical models on oxygen transport in biological tissues through capillary bed using both analytical and numerical methods. In this study, we extended the diffusion of drug in blood and tissue using three mathemat-.
Mathematical modeling in population dynamics: the case of single ...
African Journals Online (AJOL)
... equations are tailored to describing the essential features of a continuous process. The trust of this paper is the application of mathematical models in helping to unravel the underlying mechanisms involved in biological and ecological processes. African Journal of Educational Studies in Mathematics and Sciences Vol.
Mathematical Modeling, Sense Making, and the Common Core State Standards
Schoenfeld, Alan H.
2013-01-01
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…
Mathematical Manipulative Models: In Defense of “Beanbag Biology”
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
Mathematical Model of Nicholson’s Experiment
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Sergey D. Glyzin
2017-01-01
Full Text Available Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.
Physical vs. Mathematical Models in Rock Mechanics
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
Atmosphere behavior in gas-closed mouse-algal systems - An experimental and modelling study
Averner, M. M.; Moore, B., III; Bartholomew, I.; Wharton, R.
1984-01-01
A NASA-sponsored research program initiated using mathematical modelling and laboratory experimentation aimed at examining the gas-exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere is studied. The development of control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels is considered. A mathematical model simulating the behavior of a gas-closed mouse-algal system under varying environmental conditions is described. To verify and validate the model simulations, an analytical system with which algal growth and gas exchange characteristics can be manipulated and measured is designed, fabricated, and tested. The preliminary results are presented.
Fedorov, A. V.; Tropin, D. A.
2017-10-01
The physical and mathematical models for the description of the processes of ignition, combustion and propagation of detonation in mixtures of hydrogen-oxygen, methane-oxygen and silane-air in the presence of inert micro- and nanoparticles were proposed. On the basis of these models the dependencies of detonation velocity deficit vs the size and concentration of inert micro- and nanoparticles were found. Two modes of detonation flows in gas suspensions of reactive gases and inert nanoparticles were revealed: - propagation of weak detonation wave in the gas suspension, - destruction of the detonation process. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lies in the splitting of a detonation wave to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that in the transition from microparticles to nanoparticles the detonation suppression efficiency does not increase.
Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani
2017-05-01
The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
Directory of Open Access Journals (Sweden)
Леонид Михайлович Замиховский
2015-04-01
Full Text Available The necessity of technical state control of regenerators during operation of gas pumping unit was proved in the article. Іt was proposed to develop a new method based on the use of methods of mathematical modeling of heat distribution on the surface of the regenerator and hardware methods to determine its temperature. It is considered the regularization algorithm of incorrect inverse problem of heat conduction in the material of regenerator design using values of temperature fields, which were defined experimentally
Mathematical model of gluconic acid fermentation by Aspergillus niger
Energy Technology Data Exchange (ETDEWEB)
Takamatsu, T.; Shioya, S.; Furuya, T.
1981-11-01
A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).
MODELLING OF THE GAS DIFFUSION IN FLEXIBLE PIPELINES FOR OIL & GAS PRODUCTION
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Marius STAN
2017-05-01
Full Text Available This presentation describes a model used to study gas diffusion through layers of flexible pipes by time. The temperature gradient pipe is considered as temperature dependent permeability rates. This model is coupled with a calculation that indicate changes in pressure and volume of vapors resulting in the annular space. Associated mathematical models and methods for solving the results obtained are presented in Math Soft with a user-friendly interface that helps in data entry and processing results. In this presentation will show the possibilities of this software.
The possibilities of a modelling perspective for school mathematics
Directory of Open Access Journals (Sweden)
Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
Mathematical modelling of the MAP kinase pathway using proteomic datasets.
Tian, Tianhai; Song, Jiangning
2012-01-01
The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.
Mathematics of tsunami: modelling and identification
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Mathematical modelling of MSW incineration on a travelling bed.
Yang, Y B; Goh, Y R; Zakaria, R; Nasserzadeh, V; Swithenbank, J
2002-01-01
The rising popularity of incineration of municipal solid waste (MSW) calls for detailed mathematical modelling and understanding of the incineration process. In this paper, governing equations for mass, momentum and heat transfer for both solid and gaseous phases in a moving bed in a solid-waste incineration furnace are described and relevant sub-models are presented. The burning rates of volatile hydrocarbons in the moving bed of solids are limited not only by the reaction kinetics but also the mixing of the volatile fuels with the under-fire air. The mixing rate is averaged across a computation cell and correlated to a number of parameters including local void fraction of the bed, gas velocity and a length scale comparable to the particle size in the bed. A correlation equation is also included to calculate the mixing in the freeboard area immediately next to the bed surface. A small-scale fixed bed waste incinerator was built and test runs were made in which total mass loss from the bed, temperature and gas composition at different locations along the bed height were measured. A 2-D bed-modelling program (FLIC) was developed which incorporates the various sub-process models and solves the governing equations for both gases and solids. Thermal and chemical processes are mainly confined within a layer about 5-9 times in thickness of the averaged particle size in the burning bed. For a large part of the burning process, the total mass loss rate was constant until the solid waste was totally dried out and a period of highly rising CO emission followed. The maximum bed temperature was around 1200 K. The whole burning process ended within 60 min. Big fluctuations in species concentration were observed due to channelling and subsequent 'catastrophic' changes in the local bed conditions. Reasonably good agreement between modelling and measurements has been achieved. Yet the modelling work is complicated by the channelling phenomenon in the bed. Numerical simulations
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
Directory of Open Access Journals (Sweden)
Zoran Benić
2016-01-01
Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.
Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity
Stohlmann, Micah S.
2017-01-01
Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…
Key Concept Mathematics and Management Science Models
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Modeling Students' Interest in Mathematics Homework
Xu, Jianzhong; Yuan, Ruiping; Xu, Brian; Xu, Melinda
2016-01-01
The authors examine the factors influencing mathematics homework interest for Chinese students and compare the findings with a recent study involving U.S. students. The findings from multilevel analyses revealed that some predictors for homework interest functioned similarly (e.g., affective attitude toward homework, learning-oriented reasons,…
Mathematical modelling with case studies using Maple and Matlab
Barnes, B
2014-01-01
Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-
Schwerdtfeger, Sara
2017-01-01
This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…
Mathematical modeling of electromechanical processes in a brushless DC motor
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V.I. Tkachuk
2014-03-01
Full Text Available On the basis of initial assumptions, a mathematical model that describes electromechanical processes in a brushless DC electric motor with a salient-pole stator and permanent-magnet excitation is created.
Mathematical and numerical foundations of turbulence models and applications
Chacón Rebollo, Tomás
2014-01-01
With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...
Mathematical modelling of water radiolysis kinetics under reactor conditions
International Nuclear Information System (INIS)
Khodulev, L.B.; Shapova, E.A.
1989-01-01
Experimental data on coolant radiolysis (RBMK-1000 reactor) were used to construct mathematical model of water radiolysis kinetics under reactor conditions. Good agreement of calculation results with the experiment is noted
Mechanical-mathematical modeling for landslide process
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
A Mathematical Approach to Establishing Constitutive Models for Geomaterials
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Guang-hua Yang
2013-01-01
Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.
Mathematical Modeling of Neuro-Vascular Coupling in Rat Cerebellum
DEFF Research Database (Denmark)
Rasmussen, Tina
Activity in the neurons called climbing fibers causes blood flow changes. But the physiological mechanisms which mediate the coupling are not well understood. This PhD thesis investigates the mechanisms of neuro-vascular coupling by means of mathematical methods. In experiments, the extracellularly...... measured field potential is used as an indicator of neuronal activity, and the cortical blood flow is measured by means of laser-Doppler flowmetry. Using system identification methods, these measurements have been used to construct and validate parametric mathematical models of the neuro-vascular system....... Mathematical arguments as well as hypotheses about the physiological system have been used to construct the models....
2nd Tbilisi-Salerno Workshop on Modeling in Mathematics
Ricci, Paolo; Tavkhelidze, Ilia
2017-01-01
This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Mathematical modeling of a process the rolling delivery
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.
Problems of modeling and optimal stabilization of the gas-lift process
Aliev, F. A.; Il'yasov, M. Kh.; Nuriev, N. B.
2010-11-01
The problems of motion of fluids, gases and gas-liquid mixtures in pipes related to gas-lift oil recovery are mathematically formulated as systems of nonlinear hyperbolic partial differential equations. Optimal-control problems are posed based on the proposed models and some real assumptions. These problems can be used to design programmed paths and controls, which underlie the controllers that stabilize the pressure or volume of injected gas. That the mathematical models agree with available field and laboratory data is demonstrated by examples
Mathematical modeling of a V-stack piezoelectric aileron actuation
Directory of Open Access Journals (Sweden)
Ioan URSU
2016-12-01
Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.
Partial sum approaches to mathematical parameters of some growth models
Korkmaz, Mehmet
2016-04-01
Growth model is fitted by evaluating the mathematical parameters, a, b and c. In this study, the method of partial sums were used. For finding the mathematical parameters, firstly three partial sums were used, secondly four partial sums were used, thirdly five partial sums were used and finally N partial sums were used. The purpose of increasing the partial decomposition is to produce a better phase model which gives a better expected value by minimizing error sum of squares in the interval used.
Mathematical modeling creation for curriculum based on ontology. Part 1
PIYAVSKY S.A.; LARUKHIN V.B.
2012-01-01
This article delivers a mathematical optimal formation model of curriculum based on the solution of multi-criteria optimization problem. A mathematical model of optimal curriculum shaping based on the solution of multi-criteria optimization. In combination with the previously developed ontology of the educational process, it allows us to offer information technology of forming curriculum at various levels of training in universities personalized for each students
Classical and Weak Solutions for Two Models in Mathematical Finance
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
Mathematical modelling and numerical simulation of oil pollution problems
2015-01-01
Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics, together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems. The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...
The World gas model. A multi-period mixed complementarity model for the global natural gas market
International Nuclear Information System (INIS)
Egging, Ruud; Holz, Franziska; Gabriel, Steven A.
2010-01-01
We provide the description, mathematical formulation and illustrative results of the World Gas Model, a multi-period complementarity model for the global natural gas market with explicit consideration of market power in the upstream market. Market players include producers, traders, pipeline and storage operators, LNG (liquefied natural gas) liquefiers and regasifiers as well as marketers. The model data set contains more than 80 countries and regions and covers 98% of world wide natural gas production and consumption. We also include a detailed representation of cross-border natural gas pipelines and constraints imposed by long-term contracts in the LNG market. The model is calibrated to match production and consumption projections from the PRIMES [EC. European energy and transport: trends to 2030-update 2007. Brussels: European Commission; 2008] and POLES models [EC. World energy technology outlook - 2050 (WETO-H2). Brussels: European Commission; 2006] up to 2030. The results of our numerical simulations illustrate how the supply shares of pipeline and LNG in various regions in the world develop very differently over time. LNG will continue to play a major role in the Asian market, also for new importers like China and India. Europe will expand its pipeline import capacities benefiting from its relative proximity to major gas suppliers. (author)
Modelling and interpretation of gas detection using remote laser pointers.
Hodgkinson, J; van Well, B; Padgett, M; Pride, R D
2006-04-01
We have developed a quantitative model of the performance of laser pointer style gas leak detectors, which are based on remote detection of backscattered radiation. The model incorporates instrumental noise limits, the reflectivity of the target background surface and a mathematical description of gas leak dispersion in constant wind speed and turbulence conditions. We have investigated optimum instrument performance and limits of detection in simulated leak detection situations. We predict that the optimum height for instruments is at eye level or above, giving an operating range of 10 m or more for most background surfaces, in wind speeds of up to 2.5 ms(-1). For ground based leak sources, we find laser pointer measurements are dominated by gas concentrations over a short distance close to the target surface, making their readings intuitive to end users in most cases. This finding is consistent with the results of field trials.
Application of mathematical modeling in sustained release delivery systems.
Grassi, Mario; Grassi, Gabriele
2014-08-01
This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.
Mathematical Modeling of Biofilm Structures Using COMSTAT Data
DEFF Research Database (Denmark)
Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.
2017-01-01
in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided......Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...
Michelsen, Claus
2015-01-01
Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…
A continuum model for metabolic gas exchange in pear fruit.
Directory of Open Access Journals (Sweden)
Q Tri Ho
2008-03-01
Full Text Available Exchange of O(2 and CO(2 of plants with their environment is essential for metabolic processes such as photosynthesis and respiration. In some fruits such as pears, which are typically stored under a controlled atmosphere with reduced O(2 and increased CO(2 levels to extend their commercial storage life, anoxia may occur, eventually leading to physiological disorders. In this manuscript we have developed a mathematical model to predict the internal gas concentrations, including permeation, diffusion, and respiration and fermentation kinetics. Pear fruit has been selected as a case study. The model has been used to perform in silico experiments to evaluate the effect of, for example, fruit size or ambient gas concentration on internal O(2 and CO(2 levels. The model incorporates the actual shape of the fruit and was solved using fluid dynamics software. Environmental conditions such as temperature and gas composition have a large effect on the internal distribution of oxygen and carbon dioxide in fruit. Also, the fruit size has a considerable effect on local metabolic gas concentrations; hence, depending on the size, local anaerobic conditions may result, which eventually may lead to physiological disorders. The model developed in this manuscript is to our knowledge the most comprehensive model to date to simulate gas exchange in plant tissue. It can be used to evaluate the effect of environmental stresses on fruit via in silico experiments and may lead to commercial applications involving long-term storage of fruit under controlled atmospheres.
Mathematical modeling of physiological systems: an essential tool for discovery.
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.
Velocity of detonation-a mathematical model.
Türker, Lemi
2010-06-01
Based on the principles of conservation of energy and momentum, a mathematical formula has been derived for the squares of detonation velocities of a large set of explosives. The equation is a function of the total energy and molecular weight of an explosive compound considered. A regressed equation has been obtained for a pool of explosives of various types including nitramines, aliphatic and aromatic nitro compounds. Also another regressed equation for nitramines only is given. For the regression, the total energies are obtained using DFT (UB3LYP/6-31G(d)). The regression statistics are given and discussed.
Mathematical Models for Camouflage Pattern Assessment
2013-04-01
Matemático Facultad de Ciencias F́ısicas y Matemáticas http://www.cmm.uchile.cl DISTRIBUTION A: Distribution approved for public release University of Chile...Centro de Modelamiento Matemático Facultad de Ciencias Físicas y Matemáticas Final Report: Camouage Assessment January 2013 Abstract The main...mathematical details are to be foun in Appendix B and the summaries of the some state-of-the- art work involving non-local segmentation considering the
A mathematical model for the leukocyte filtration process
Bruil, A.; Bruil, Anton; Beugeling, T.; Beugeling, Tom; Feijen, Jan
1995-01-01
Leukocyte filters are applied clinically to remove leukocytes from blood. In order to optimize leukocyte filters, a mathematical model to describe the leukocyte filtration process was developed by modification of a general theoretical model for depth filtration. The model presented here can be used
Mathematical model for water quality (portable water): a case study ...
African Journals Online (AJOL)
A water quality model for water-use-goal is proposed. The model is tested with a treatment schedule at a water works for portable water. It was observed that at least a 25 per cent savings can be achieved if the model is employed. Mathematics Connection Vol. 4 2004: 27-30 ...
Mathematical model for bird flu disease transmission with no bird ...
African Journals Online (AJOL)
In this paper a mathematical model for the transmission dynamics of bird flu among birds and humans is presented. The model assumes that there is no migration of birds in the susceptible bird population immediately the disease starts. The model formulated is analyzed using dynamical systems theory . The analysis of the ...
Potential of mathematical modeling in fruit quality | Vazquez-Cruz ...
African Journals Online (AJOL)
Potential of mathematical modeling in fruit quality. ... important for flavor and aroma. These models have demonstrated their ability to generate relationships between physiological variables and quality attributes (allometric relations). This new kind of hybrid models has sufficient complexity to predict quality traits behavior.
A mathematical model on germinal center kinetics andtermination
DEFF Research Database (Denmark)
Kesmir, Can; De Boer, R.J.
1999-01-01
We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics areextended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes,and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we...
mathematical model for bird flu disease transmission with no bird ...
African Journals Online (AJOL)
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In this paper a mathematical model for the transmission dynamics of bird flu among birds and humans is presented. The model assumes that there is no migration of birds in the susceptible bird population immediately the disease starts. The model formulated is analyzed using dynamical systems theory. The analysis of the ...
Mathematical model comparing of the multi-level economics systems
Brykalov, S. M.; Kryanev, A. V.
2017-12-01
The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.
A mathematical model for camera calibration based on straight lines
Directory of Open Access Journals (Sweden)
Antonio M. G. Tommaselli
2005-12-01
Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.
A Mathematical Model of Heat Transfer in Spheroplastic
Directory of Open Access Journals (Sweden)
V. S. Zarubin
2016-01-01
Full Text Available Spheroplastics are composite materials composed of a polymer or organosilicate binder and hollow spherical inclusions (mostly, of glass, but there are also of carbon, phenol, and epoxy, which are called microspheres and have a diameter within a millimeter with the wall thickness of several micrometers. To reduce the material density in watercraft constructions sometimes are used so called macrospheres of up to 40 mm in diameter and shell thickness of 0,5--1,5 mm from spheroplastic with microspheres.Microspheres may contain inert gases such as nitrogen. Many countries have commercialised quartz microspheres. The USA, in particular, produces Q-Gel microspheres with density of 300 kg / m3, the bulk density - 100 kg / m3 and the average diameter of 75 microns,characterized by a high mechanical strength and low cost. Carbon microspheres having low mechanical properties can absorb radio waves in certain frequency ranges. Spheroplastic with silicone microspheres combine relatively high mechanical and dielectric properties.In virtue of low thermal conductivity spheroplastics are used in various heat-insulating structures. As the thermal insulation coatings, the spheroplastic covers the outer surface of the pipes, in particular oil and gas pipelines in the permafrost zones, regions of swampy ground, and underwater. The effective heat conductivity factor, primarily, determines the specific application of spheroplastic as a thermal insulation material. To quantify the value of this factor is necessary to have a mathematical model describing heat ransfer in spheroplastic.The paper presents a four-phase mathematical model of the heat transfer in a representative element of a spheroplastic structure placed in an unlimited array of homogeneous material, the thermal conductivity of which is to be determined as desired characteristics of spheroplastic. This model in combination with a dual variational formulation of stationary heat conduction problem in the
A mathematical model for composting kinetics
Hamelers, H.V.M.
2001-01-01
Composting plays an important role in waste management schemes and organic farming, as the compost produced enables reuse of organic matter and nutrients. Modern composting plants must comply with strict environmental regulations, including gas emissions such as nuisance odors. Designing
Biological-Mathematical Modeling of Chronic Toxicity.
1981-07-22
Papper, E. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents. McGraw-Hill, New York, p. 59 7. Mapleson , W.W. (1964) Inert gas...exchange theory using an electric analogue. J. Appl. Physiol. 19: 1193-1199 8. Mapleson , W.W.(1963) An electric analogue for uptake and exchange of inert
Directory of Open Access Journals (Sweden)
Elena Chorukova
2015-04-01
Full Text Available Anaerobic digestion is an effective biotechnological process for treatment of different agricultural, municipal and industrial wastes. Use of mathematical models is a powerful tool for investigations and optimisation of the anaerobic digestion. In this paper a simple mathematical model of the anaerobic digestion of wasted fruits and vegetables was developed and verified experimentally and by computer simulations using Simulink. A three-step mass-balance model was considered including the gas phase. The parameter identification was based on a set of 150 days of dynamical experiments in a laboratory bioreactor. Two step identification procedure to estimate 4 model parameters is presented. The results of 15 days of experiment in a pilot-scale bioreactor were then used to validate the model.
An Equilibrium-Based Model of Gas Reaction and Detonation
International Nuclear Information System (INIS)
Trowbridge, L.D.
2000-01-01
During gaseous diffusion plant operations, conditions leading to the formation of flammable gas mixtures may occasionally arise. Currently, these could consist of the evaporative coolant CFC-114 and fluorinating agents such as F2 and ClF3. Replacement of CFC-114 with a non-ozone-depleting substitute is planned. Consequently, in the future, the substitute coolant must also be considered as a potential fuel in flammable gas mixtures. Two questions of practical interest arise: (1) can a particular mixture sustain and propagate a flame if ignited, and (2) what is the maximum pressure that can be generated by the burning (and possibly exploding) gas mixture, should it ignite? Experimental data on these systems, particularly for the newer coolant candidates, are limited. To assist in answering these questions, a mathematical model was developed to serve as a tool for predicting the potential detonation pressures and for estimating the composition limits of flammability for these systems based on empirical correlations between gas mixture thermodynamics and flammability for known systems. The present model uses the thermodynamic equilibrium to determine the reaction endpoint of a reactive gas mixture and uses detonation theory to estimate an upper bound to the pressure that could be generated upon ignition. The model described and documented in this report is an extended version of related models developed in 1992 and 1999
The Concept of Model. What is Remarkable in Mathematical Models
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
Lattice Model for Production of Gas
Marder, M.
2017-12-01
We define a lattice model for rock, absorbers, and gas that makes it possible to examine the flow of gas to a complicated absorbing boundary over long periods of time. The motivation is to deduce the geometry of the boundary from the time history of gas absorption. We find a solution to this model using Green\\'s function techniques, and apply the solution to three absorbing networks of increasing complexity.
A Simple Mathematical Model of Cyclic Circadian Learning
Directory of Open Access Journals (Sweden)
J. Šimon
2014-01-01
Full Text Available This paper deals with the derivation of a simple mathematical model of cyclic learning with a period of 24 hours. Various requirements are met with an emphasis and approach which relies on simple mathematical operations, the prediction of measurable quantities, and the creation of uncomplicated processes of calibration. The presented model can be used to answer questions such as the following. Will I be able to memorize a given set of information? How long will it take to memorize information? How long will I remember the information that was memorized? The model is based on known memory retention functions that are in good agreement with experimental results. By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. The usability of this model is limited to scenarios where logical bonds (connections to prior learning are not created and mnemonic devices cannot be utilized during the learning process.
Effectiveness of discovery learning model on mathematical problem solving
Herdiana, Yunita; Wahyudin, Sispiyati, Ririn
2017-08-01
This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Mathematical modeling for novel cancer drug discovery and development.
Zhang, Ping; Brusic, Vladimir
2014-10-01
Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.
Mathematical modeling of the working cycle of oil injected rotary twin screw compressor
International Nuclear Information System (INIS)
Seshaiah, N.; Ghosh, Subrata Kr.; Sahoo, R.K.; Sarangi, Sunil Kr.
2007-01-01
Oil injected twin-screw air and gas compressors are widely used for medium pressure applications in many industries. Low cost air compressors can be adopted for compression of helium and special gases, leading to significant cost saving. Mathematical analysis of oil injected twin-screw compressor is carried out on the basis of the laws of perfect gas and standard thermodynamic relations. Heat transfer coefficient required for computer simulation is experimentally obtained and used in performance prediction, when the working medium being air or helium. A mathematical model has been developed for calculating the compressor performance and for validating the results with experimental data. The flow coefficients required for numerical simulation to calculate leakage flow rates are obtained from efficiency verses clearance curves. Effect of some of the compressor operating and design parameters on power and volumetric efficiencies have been analyzed and presented
Nonlinear mathematical model for a biaxial MOEMS scanning mirror
Ma, Yunfei; Davis, Wyatt O.; Ellis, Matt; Brown, Dean
2010-02-01
In this paper, a nonlinear mathematic model for Microvision's MOEMS scanning mirror is presented. The pixel placement accuracy requirement for scanned laser spot displays translates into a roughly 80dB signal to noise ratio, noise being a departure from the ideal trajectory. To provide a tool for understanding subtle nonidealities, a detailed nonlinear mathematical model is derived, using coefficients derived from physics, finite element analysis, and experiments. Twelve degrees of freedom parameterize the motion of a gimbal plate and a suspended micromirror; a thirteenth is the device temperature. Illustrations of the application of the model to capture subtleties about the device dynamics and transfer functions are presented.
Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
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.
Solutions manual to accompany finite mathematics models and applications
Morris, Carla C
2015-01-01
A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr
Mathematical models of human cerebellar development in the fetal period.
Dudek, Krzysztof; Nowakowska-Kotas, Marta; Kędzia, Alicja
2018-04-01
The evaluation of cerebellar growth in the fetal period forms a part of a widely used examination to identify any features of abnormalities in early stages of human development. It is well known that the development of anatomical structures, including the cerebellum, does not always follow a linear model of growth. The aim of the study was to analyse a variety of mathematical models of human cerebellar development in fetal life to determine their adequacy. The study comprised 101 fetuses (48 males and 53 females) between the 15th and 28th weeks of fetal life. The cerebellum was exposed and measurements of the vermis and hemispheres were performed, together with statistical analyses. The mathematical model parameters of fetal growth were assessed for crown-rump length (CRL) increases, transverse cerebellar diameter and ventrodorsal dimensions of the cerebellar vermis in the transverse plane, and rostrocaudal dimensions of the cerebellar vermis and hemispheres in the frontal plane. A variety of mathematical models were applied, including linear and non-linear functions. Taking into consideration the variance between models and measurements, as well as correlation parameters, the exponential and Gompertz models proved to be the most suitable for modelling cerebellar growth in the second and third trimesters of pregnancy. However, the linear model gave a satisfactory approximation of cerebellar growth, especially in older fetuses. The proposed models of fetal cerebellar growth constructed on the basis of anatomical examination and objective mathematical calculations could be useful in the estimation of fetal development. © 2018 Anatomical Society.
Animal models of cerebral arterial gas embolism
Weenink, Robert P.; Hollmann, Markus W.; van Hulst, Robert A.
2012-01-01
Cerebral arterial gas embolism is a dreaded complication of diving and invasive medical procedures. Many different animal models have been used in research on cerebral arterial gas embolism. This review provides an overview of the most important characteristics of these animal models. The properties
MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM
Directory of Open Access Journals (Sweden)
Olha Sushchenko
2017-07-01
Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.
comparative analysis of two mathematical models for prediction
African Journals Online (AJOL)
Abstract. A mathematical modeling for prediction of compressive strength of sandcrete blocks was performed using statistical analysis for the sandcrete block data ob- tained from experimental work done in this study. The models used are Scheffes and Osadebes optimization theories to predict the compressive strength of ...
Mathematical Model for the Optimization of Compressive Strength of ...
African Journals Online (AJOL)
These mathematical models are adopted for optimization of strength of sandcrete block in compression. With the model, any desired strength of sandcrete block, given any mix proportions, is easily evaluated. Basic Language is used in the development of the computer program. The maximum compressive strength ...
Mathematical models of ABE fermentation: review and analysis.
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.
Mathematical Model for Prediction of Flexural Strength of Mound ...
African Journals Online (AJOL)
The mound soil-cement blended proportions were mathematically optimized by using scheffe's approach and the optimization model developed. A computer program predicting the mix proportion for the model was written. The optimal proportion by the program was used prepare beam samples measuring 150mm x 150mm ...
Mathematical modeling of potentially hazardous nuclear objects with time shifts
International Nuclear Information System (INIS)
Gharakhanlou, J.; Kazachkov, I.V.
2012-01-01
The aggregate models for potentially hazardous objects with time shifts are used for mathematical modeling and computer simulation. The effects of time delays are time forecasts are analyzed. The influence of shift arguments on the nonlinear differential equations is discussed. Computer simulation has established the behavior of potentially hazardous nuclear object
Stability Analysis of a Mathematical Model for Onchocerciaisis ...
African Journals Online (AJOL)
ADOWIE PERE
Stability Analysis of a Mathematical Model for Onchocerciaisis. 668. BAKO, DU; AKINWANDE, NI; ENAGI, AI; KUTA, FA; ABDULRAHMAN, S. Table 1: Values of Parameters of the model. S/N. Parameters. Value. Source. 1 ω. 0.019. Estimated. 2 h. Λ. 3,449,679. Estimated. 3 h. µ. 0.019. CIA 2016. 4. 1 α. 2.12. Shuaib 2015. 5.
A Mathematical Model for Analysis on Ships Collision Avoidance ...
African Journals Online (AJOL)
This study develops a mathematical model for analysis on collision avoidance of ships. The obtained model provides information on the quantitative effect of the ship's engine's response and the applied reversing force on separation distance and stopping abilities of the ships. Appropriate evasive maneuvers require the ...
A mathematical model of combustion kinetics of municipal solid ...
African Journals Online (AJOL)
Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the ...
The Interval Market Model in Mathematical Finance : Game Theoretic Methods
Bernhard, P.; Engwerda, J.C.; Roorda, B.; Schumacher, J.M.; Kolokoltsov, V.; Saint-Pierre, P.; Aubin, J.P.
2013-01-01
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous
Mathematical modelling in blood coagulation : simulation and parameter estimation
W.J.H. Stortelder (Walter); P.W. Hemker (Piet); H.C. Hemker
1997-01-01
textabstractThis paper describes the mathematical modelling of a part of the blood coagulation mechanism. The model includes the activation of factor X by a purified enzyme from Russel's Viper Venom (RVV), factor V and prothrombin, and also comprises the inactivation of the products formed. In this
Mathematical modelling and its impact on open channel flow | Eyo ...
African Journals Online (AJOL)
Mathematical model for dredging (excavating) an open channel, namely, a river has been developed using the conditions for best hydraulic performances for the channel. Applying the model to a numerical example we determine new dimensions for the new open channel for two-channel sections, viz: the trapezoidal and ...
Mechanistic mathematical models: An underused platform for HPV research.
Ryser, Marc D; Gravitt, Patti E; Myers, Evan R
2017-06-01
Health economic modeling has become an invaluable methodology for the design and evaluation of clinical and public health interventions against the human papillomavirus (HPV) and associated diseases. At the same time, relatively little attention has been paid to a different yet complementary class of models, namely that of mechanistic mathematical models. The primary focus of mechanistic mathematical models is to better understand the intricate biologic mechanisms and dynamics of disease. Inspired by a long and successful history of mechanistic modeling in other biomedical fields, we highlight several areas of HPV research where mechanistic models have the potential to advance the field. We argue that by building quantitative bridges between biologic mechanism and population level data, mechanistic mathematical models provide a unique platform to enable collaborations between experimentalists who collect data at different physical scales of the HPV infection process. Through such collaborations, mechanistic mathematical models can accelerate and enhance the investigation of HPV and related diseases. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.
Mathematical model of epidemics with intermediate classes | Inyama ...
African Journals Online (AJOL)
In this paper we present a Mathematical model for diseases that place some new recruits from the susceptible class into an “exposed but not yet infectious” class which we denote by E. The rest of the susceptible class can be infected directly. The model is developed and its steady state determined. The stability of the steady ...
Mathematical modelling informs HIV prevention policy in China ...
International Development Research Centre (IDRC) Digital Library (Canada)
2016-04-27
Apr 27, 2016 ... IDRC-funded research is using mathematical modelling to influence local and national policies in China to reduce HIV transmission. Treatment as prevention Earlier research conducted under Modelling and controlling infectious diseases project showed that providing antiretroviral therapy (ART) to ...
A mathematical model for Lassa fever | Okuonghae | Journal of the ...
African Journals Online (AJOL)
A mathematical model for the dynamics of Lassa fever is presented. Contributions from regular contact with the species of rats that carry the virus that cause Lassa fever and infectious contact with those suffering from the disease is seen as significant in the spread of the disease. Steady states of the model are examined for ...
Development of a mathematical model for managing magnitude and ...
African Journals Online (AJOL)
A mathematical model was developed for managing m~gnitude and risk · factors of injuries in a manufacturing industry employing System Dynamics (SD) approach. Data were collected using an injury and illness investigation register. These were used to estimate and validate the parameters of the model. The principle of ...
Mathematical modelling as basis for efficient enterprise management
Directory of Open Access Journals (Sweden)
Kalmykova Svetlana
2017-01-01
Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.
Mathematical model of the bacteria-nutrient dynamics | Inyama ...
African Journals Online (AJOL)
In this paper we developed a Mathematical Model of bacteria-nutrient dynamics which results in a system of first order ordinary differential equations. The analysis of the model was done using dynamical systems. It was found out that the product of the maximum nutrient uptake per cel; and the number of cells produced per ...
Mathematical modelling of zirconium salicylate solvent extraction process
International Nuclear Information System (INIS)
Smirnova, N.S.; Evseev, A.M.; Fadeeva, V.I.; Kochetkova, S.K.
1979-01-01
Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built
Mathematical models to simulate the East African trypanosomiasis ...
African Journals Online (AJOL)
This paper presents mathematical models for the East African trypanosomiasis or sleeping sickness. It is aimed at modelling the population dynamics for the human and domestic animal victims as well as the dynamics of the tsetse fly population that acts as the vector that spreads the parasite causing this disease.
Mathematical model of glucose-insulin homeostasis in healthy rats.
Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo
2013-10-01
According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.
Mathematical Model for Direct Evaporative Space Cooling Systems ...
African Journals Online (AJOL)
This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have ...
Mathematical Analysis of a Model for Human Immunodeficiency ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: The objective of this paper is to present a mathematical model formulated to investigate the dynamics of human immunodeficiency virus (HIV). The disease free equilibrium of the model was found to be locally and globally asymptotically stable. The endemic equilibrium point exists and it was discovered that the ...
Mathematical and computational modeling simulation of solar drying Systems
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
Simple mathematical models for housing allocation to a homeless ...
African Journals Online (AJOL)
We present simple mathematical models for modelling a homeless population and housing allocation. We look at a situation whereby the local authority makes temporary accommodation available for some of the homeless for a while and we examine how this affects the number of families homeless at any given time.
Applicability of mathematical modeling to problems of environmental physiology
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.
Invention software support by integrating function and mathematical modeling
Chechurin, L.S.; Wits, Wessel Willems; Bakker, H.M.
2015-01-01
New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a
Fuzzy Control Technique Applied to Modified Mathematical Model ...
African Journals Online (AJOL)
In this paper, fuzzy control technique is applied to the modified mathematical model for malaria control presented by the authors in an earlier study. Five Mamdani fuzzy controllers are constructed to control the input (some epidemiological parameters) to the malaria model simulated by 9 fully nonlinear ordinary differential ...
Comparative Analysis of Two Mathematical Models for Prediction of ...
African Journals Online (AJOL)
A mathematical modeling for prediction of compressive strength of sandcrete blocks was performed using statistical analysis for the sandcrete block data obtained from experimental work done in this study. The models used are Scheffe's and Osadebe's optimization theories to predict the compressive strength of sandcrete ...
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Mathematical Modeling of Biofilm Structures Using COMSTAT Data
Directory of Open Access Journals (Sweden)
Davide Verotta
2017-01-01
Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.
Mathematical model of two-phase flow in accelerator channel
Directory of Open Access Journals (Sweden)
О.Ф. Нікулін
2010-01-01
Full Text Available The problem of two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in counter jet mill accelerator channel design.
IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS
Directory of Open Access Journals (Sweden)
L. V. Ursulyak
2017-12-01
Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity
Thermodynamic modelling of acid gas removal from natural gas using the Extended UNIQUAC model
DEFF Research Database (Denmark)
Sadegh, Negar; Stenby, Erling Halfdan; Thomsen, Kaj
2017-01-01
Thermodynamics of natural gas sweetening process needs to be known for proper design of natural gas treating plants. Absorption with aqueous N-Methyldiethanolamine is currently the most commonly used process for removal of acid gas (CO2 and H2S) impurities from natural gas. Model parameters...... for the Extended UNIQUAC model have already been determined by the same authors to calculate single acid gas solubility in aqueous MDEA. In this study, the model is further extended to estimate solubility of CO2 and H2S and their mixture in aqueous MDEA at high pressures with methane as a makeup gas....
MATHEMATICAL MODELING OF BATCH ADSORPTION OF MANGANESE ONTO BONE CHAR
Maria, M. E.; Mansur, M. B.
2016-01-01
Abstract The present study investigated the dynamics of batch adsorption of manganese onto bone char by using two distinct mathematical formulations: the diffusion model and the shrinking core model. Both models assumed spherical particles and adequately described the transient behavior of metal adsorption under changing operating conditions. Comparatively, the diffusion model described the manganese adsorption better at distinct particle sizes even when small particles were used (dp ≤ 0.147 ...
Mathematical model of transmission network static state estimation
Directory of Open Access Journals (Sweden)
Ivanov Aleksandar
2012-01-01
Full Text Available In this paper the characteristics and capabilities of the power transmission network static state estimator are presented. The solving process of the mathematical model containing the measurement errors and their processing is developed. To evaluate difference between the general model of state estimation and the fast decoupled state estimation model, the both models are applied to an example, and so derived results are compared.
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
A dynamic mathematical model for packed columns in carbon capture plants
DEFF Research Database (Denmark)
Gaspar, Jozsef; Jørgensen, John Bagterp; Fosbøl, Philip Loldrup
2015-01-01
is suitable for gas-liquid packed columns, e.g. for CO2 absorption and desorption. The model is based on rigorous thermodynamic and conservation principles and it is set up to preserve these properties upon numerical integration in time. The developed model is applied for CO2 absorption and desorption......In this paper, we present a dynamic mathematical model for the absorption and desorption columns in a carbon capture plant. Carbon capture plants must be operated in synchronization with the operation of thermal power plants. Dynamic and flexible operation of the carbon capture plant is important...
Software for Mathematical Modeling of Plastic Deformation in FCC Metals
Petelin, A. E.; Eliseev, A. S.
2017-08-01
The question on the necessity of software implementation in the study of plastic deformation in FCC metals with the use of mathematical modeling methods is investigated. This article describes the implementation features and the possibility of using the software Dislocation Dynamics of Crystallographic Slip (DDCS). The software has an advanced user interface and is designed for users without an extensive experience in IT-technologies. Parameter values of the mathematical model, obtained from field experiments and accumulated in a special database, are used in DDCS to carry out computational experiments. Moreover, the software is capable of accumulating bibliographic information used in research.
Methodology and Results of Mathematical Modelling of Complex Technological Processes
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.
Mathematical modelling of dropwise condensation on textured ...
Indian Academy of Sciences (India)
The model includes formation of drops at the atomistic scale, droplet growth, coalescence, instability, slide off and fall-off, followed by fresh nucleation of liquid droplets. The model shows that the largest stable cluster size in the atomic model matches the minimum drop radius estimated from thermodynamic considerations.
A mathematical model of salmonid spawning habitat
Robert N. Havis; Carlos V. Alonzo; Keith E Woeste; Russell F. Thurow
1993-01-01
A simulation model [Salmonid Spawning Analysis Model (SSAM)I was developed as a management tool to evaluate the relative impacts of stream sediment load and water temperature on salmonid egg survival. The model is usefi.il for estimating acceptable sediment loads to spawning habitat that may result from upland development, such as logging and agriculture. Software in...
Tracer kinetic modelling of receptor data with mathematical metabolite correction
International Nuclear Information System (INIS)
Burger, C.; Buck, A.
1996-01-01
Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabilites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabilite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K 1 -k 4 ) were refitted with reasonable identifiability when using mathematical metabolite correciton. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the 11 C iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. (orig./MG)
Mathematical model for spreading dynamics of social network worms
International Nuclear Information System (INIS)
Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin
2012-01-01
In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks
Incorporating neurophysiological concepts in mathematical thermoregulation models
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Mathematical model II. Basic particle and special relativity
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we try to find out the requirements of the special relativity and suggest a mathematical particle model which can satisfy these requirements. The basic presumption is that the particle should have some structural characteristics which make the particle obey the postulates of these theories. As it is experimentally ‘difficult’ to find the structure of basic particle electron we make a mathematical attempt. We call this model as logically and mathematically probable structure of the basic particle, electron.
International Workshop on Mathematical Modeling of Tumor-Immune Dynamics
Kim, Peter; Mallet, Dann
2014-01-01
This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction betwe...
MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS
Directory of Open Access Journals (Sweden)
Daniele Penteado Rosa
2015-06-01
Full Text Available Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol
A mathematical model of Phospholipid Biosynthesis
Behzadi, Mahsa
2011-01-01
When measuring high-throughput data of cellular metabolism and its evolution, it is imperative to use appropriate models. These models allow the incorporation of these data into a coherent set. They also allow interpretation of the relevant metabolic variations and the key regulatory steps. Finally, they make contradictions apparent that question the basis on which the model itself is constructed. I use the experimental data of the metabolism of tumor cells in response to an anti-cancer treat...
Mathematical Modeling of Vegetable-Oil Crystallization
DEFF Research Database (Denmark)
Hjorth, Jeppe Lindegaard
the transient model can describe the course of crystallization for a number of oil blends and accommodates the effect of varying the cooling rate. Section 4 refines the model behavior by introducing a population balance (PB), keeping track of the chord-length distribution (CLD) (derived from particle....... Good results are obtained taking only nucleation and growth into account and disregarding aggregation. The model describes the experimental CLDs well, not only in terms of the overall shape but also with respect to trends. The model correctly describes broader distributions as the concentration...
Molecular modeling: An open invitation for applied mathematics
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.
Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław
2015-07-22
A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.
Development of a revised mathematical model of the gastrointestinal tract
International Nuclear Information System (INIS)
Barker, A.
1991-01-01
The objectives of this research are as follows. First, to incorporate new biological data into a revised mathematical adult gastrointestinal tract model that includes: ingestion in both liquid and solid forms; consideration of absorption in the stomach, small intestine, ascending colon, transverse colon or not at all; gender and age of the adult; and whether the adult is a smoker or not. Next, to create a computer program in basic language for calculating residence times in each anatomical section of the GI tract for commonly used radionuclides. Also, to compare and contrast the new model with the ICRP 30 GI tract model in terms of physiological concepts, mathematical concepts, and revised residence times for several commonly used radionuclides. Finally, to determine whether the new model is sufficiently better than the current model to warrant its use as a replacement for the Eve model