Mathematical modelling of a steam boiler room to research thermal efficiency
International Nuclear Information System (INIS)
Bujak, J.
2008-01-01
This paper introduces a mathematical model of a boiler room to research its thermal efficiency. The model is regarded as an open thermodynamic system exchanging mass, energy, and heat with the atmosphere. On those grounds, the energy and energy balance were calculated. Here I show several possibilities concerning how this model may be applied. Test results of the coefficient of thermal efficiency were compared to a real object, i.e. a steam boiler room of the Provincial Hospital in Wloclawek (Poland). The tests were carried out for 18 months. The results obtained in the boiler room were used for verification of the mathematical model
Mathematical modeling of thermal runaway in semiconductor laser operation
Smith, W.R.
2000-01-01
A mathematical model describing the coupling of electrical, optical and thermal effects in semiconductor lasers is introduced. Through a systematic asymptotic expansion, the governing system of differential equations is reduced to a single second-order boundary value problem. This highly nonlinear
Correlation of spacecraft thermal mathematical models to reference data
Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier
2018-03-01
Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.
Mathematical modelling of pasta dough dynamic viscosity, thermal conductivity and diffusivity
Directory of Open Access Journals (Sweden)
Andrei Ionuţ SIMION
2015-08-01
Full Text Available This work aimed to study the mathematical variation of three main thermodynamic properties (dynamic viscosity, thermal conductivity and thermal diffusivity of pasta dough obtained by mixing wheat semolina and water with dough humidity and deformation speed (for dynamic viscosity, respectively with dough humidity and temperature (for thermal diffusivity and conductivity. The realized regression analysis of existing graphical data led to the development of mathematical models with a high degree of accuracy. The employed statistical tests (least squares, relative error and analysis of variance revealed that the obtained equations are able to describe and predict the tendency of the dough thermodynamic properties.
Mathematical modelling of thermal storage systems for the food industry
Energy Technology Data Exchange (ETDEWEB)
Lopez, A.; Lacarra, G. [Universidad Publica de Navarra Campus Arrosadia, Pamplona (Spain). Area de Tecnologia de Alimentos
1999-07-01
Dynamic mathematical models of two thermal storage systems used in the food industry to produce chilled water are presented; an ice-bank system and a holding tank system. The variability of the refrigeration demand with time was taken into account in the model. A zoned approach using mass and energy balances was applied. Heat transfer phenomena in the evaporator were modelled using empirical correlations. The experimental validation of the mathematical models on an ice-bank system at pilot plant scale, and a centralized refrigeration system with a holding tank in a winery, showed accurate prediction. Simple models are adequate to predict the dynamic behaviour of these refrigeration systems under variable heat loads. (Author)
Physical and mathematical models for diffusion of thermal pollutants in water
International Nuclear Information System (INIS)
Pires, E.C.; Giorgetti, M.F.; Carajilescov, P.
1983-01-01
Mathematical models, such as the Fickian model and the model at PAILY and SAYRE, have been used in the analysis of thermal pollution. In the present work, experimental simulations of thermal dispersion were made using an artificial channel with injection of hat water and measurements of the temperature field were taken. The results were compared with the results given by the mentioned models, applying the image sources method. Due to the limitations of the model of PAILY and SAYRE, it was generalized for thermal sources posicioned at any place in the channel. The model of PAILY and SAYRE proved to be more satisfactory than the Fickian model and the image sources method was considered adequate. (Author) [pt
Aziz, Asim; Jamshed, Wasim; Aziz, Taha
2018-04-01
In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The non-Newtonian Maxwell nanofluid model is utilized for the working fluid along with slip and convective boundary conditions and comprehensive analysis of entropy generation in the system is also observed. The effect of thermal radiation and variable thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for Cu-water and TiO2-water nanofluids. Results are presented for the velocity, temperature and entropy generation profiles, skin friction coefficient and Nusselt number. The discussion is concluded on the effect of various governing parameters on the motion, temperature variation, entropy generation, velocity gradient and the rate of heat transfer at the boundary.
International Nuclear Information System (INIS)
Beck, T.; Bieler, A.; Thomas, N.
2012-01-01
We present structural and thermal model (STM) tests of the BepiColombo laser altimeter (BELA) receiver baffle with emphasis on the correlation of the data with a thermal mathematical model. The test unit is a part of the thermal and optical protection of the BELA instrument being tested under infrared and solar irradiation at University of Bern. An iterative optimization method known as particle swarm optimization has been adapted to adjust the model parameters, mainly the linear conductivity, in such a way that model and test results match. The thermal model reproduces the thermal tests to an accuracy of 4.2 °C ± 3.2 °C in a temperature range of 200 °C after using only 600 iteration steps of the correlation algorithm. The use of this method brings major benefits to the accuracy of the results as well as to the computational time required for the correlation. - Highlights: ► We present model correlations of the BELA receiver baffle to thermal balance tests. ► Adaptive particle swarm optimization has been adapted for the correlation. ► The method improves the accuracy of the correlation and the computational time.
Mathematical modeling and simulation of a thermal system
Toropoc, Mirela; Gavrila, Camelia; Frunzulica, Rodica; Toma, Petrica D.
2016-12-01
The aim of the present paper is the conception of a mathematical model and simulation of a system formed by a heatexchanger for domestic hot water preparation, a storage tank for hot water and a radiator, starting from the mathematical equations describing this system and developed using Scilab-Xcos program. The model helps to determine the evolution in time for the hot water temperature, for the return temperature in the primary circuit of the heat exchanger, for the supply temperature in the secondary circuit, the thermal power for heating and for hot water preparation to the consumer respectively. In heating systems, heat-exchangers have an important role and their performances influence the energy efficiency of the systems. In the meantime, it is very important to follow the behavior of such systems in dynamic regimes. Scilab-Xcos program can be utilized to follow the important parameters of the systems in different functioning scenarios.
Directory of Open Access Journals (Sweden)
Asif Mahmood
Full Text Available Solar energy is the cleanest, renewable and most abundant source of energy available on earth. The main use of solar energy is to heat and cool buildings, heat water and to generate electricity. There are two types of solar energy collection system, the photovoltaic systems and the solar thermal collectors. The efficiency of any solar thermal system depend on the thermophysical properties of the operating fluids and the geometry/length of the system in which fluid is flowing. In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The flow is induced by a non-uniform stretching of the porous sheet and the uniform magnetic field is applied in the transverse direction to the flow. The non-Newtonian Maxwell fluid model is utilized for the working fluid along with slip boundary conditions. Moreover the high temperature effect of thermal radiation and temperature dependent thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for cu-water and TiO2-water nanofluids. Results are presented for the velocity and temperature profiles as well as the skin friction coefficient and Nusselt number and the discussion is concluded on the effect of various governing parameters on the motion, temperature variation, velocity gradient and the rate of heat transfer at the boundary. Keywords: Solar energy, Thermal collectors, Maxwell-nanofluid, Thermal radiation, Partial slip, Variable thermal conductivity
International Nuclear Information System (INIS)
Torres, Alejandro; Mishkinis, Donatas; Kaya, Tarik
2014-01-01
A novel satellite thermal architecture connecting the east and west radiators of a geostationary telecommunication satellite via loop heat pipes (LHPs) is flight tested on board the satellite Hispasat 1E. The LHP operating temperature is regulated by using pressure regulating valves (PRVs). The flight data demonstrated the successful operation of the proposed concept. A transient numerical model specifically developed for the design of this system satisfactorily simulated the flight data. The validated mathematical model can be used to design and analyze the thermal behavior of more complex architectures. - Highlights: •A novel spacecraft thermal control architecture is presented. •The east–west radiators of a GEO communications satellite are connected using LHPs. •A transient mathematical model is validated with flight data. •The space flight data proved successful in-orbit operation of the novel architecture. •The model can be used to design/analyze LHP based complex thermal architectures
Directory of Open Access Journals (Sweden)
V. S. Zarubin
2016-01-01
Full Text Available A temperature state of the solid body may depend both on the conditions of heat exchange with external environment surrounding its surface and on the energy release within the body volume, caused, for example, by the processes in nuclear reactor elements or exothermic chemical reactions, absorption of penetrating radiation energy or transformation of a part of the electrical power into heat with flowing electric current (so-called Joule heat.If with growing temperature the intensity of bulk power density increases, a limited steady temperature state can emerge at which heat extracted to the body surface and released within its volume reaches maximum. Thus, small increments of temperature lead to an increase of heat release, which can not be extracted to the body surface by conduction without further temperature increase. As a result, the steady temperature distribution in the body becomes impossible that determines the state of the thermal explosion, so named due to the fact that in this case the appropriate mathematical model predicts an unlimited temperature increase.A lot of published papers and monographs concerning the study of the combustion and explosion processes in a stationary medium analyse the thermal explosion state. The most famous papers consider a mathematical model to describe a temperature distribution in the case when heat release is because of exothermic chemical reactions the rate of which increases with temperature growth. The dependence of the chemical reaction rate on temperature is usually described by the exponential Arrhenius law, which makes it necessary to consider an essentially nonlinear mathematical model containing differential equation, which includes the term, nonlinearly rising with increasing temperature. Even with simplifying assumptions, this model allows an exact closed form solution only in the case of one-dimensional temperature distributions in the two areas of the canonical form: in the plate, infinite
Mathematical modeling of photovoltaic thermal PV/T system with v-groove collector
Zohri, M.; Fudholi, A.; Ruslan, M. H.; Sopian, K.
2017-07-01
The use of v-groove in solar collector has a higher thermal efficiency in references. Dropping the working heat of photovoltaic panel was able to raise the electrical efficiency performance. Electrical and thermal efficiency were produced by photovoltaic thermal (PV/T) system concurrently. Mathematical modeling based on steady-state thermal analysis of PV/T system with v-groove was conducted. With matrix inversion method, the energy balance equations are explained by means of the investigative method. The comparison results show that in the PV/T system with the V-groove collector is higher temperature, thermal and electrical efficiency than other collectors.
Mahmood, Asif; Aziz, Asim; Jamshed, Wasim; Hussain, Sajid
Solar energy is the cleanest, renewable and most abundant source of energy available on earth. The main use of solar energy is to heat and cool buildings, heat water and to generate electricity. There are two types of solar energy collection system, the photovoltaic systems and the solar thermal collectors. The efficiency of any solar thermal system depend on the thermophysical properties of the operating fluids and the geometry/length of the system in which fluid is flowing. In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The flow is induced by a non-uniform stretching of the porous sheet and the uniform magnetic field is applied in the transverse direction to the flow. The non-Newtonian Maxwell fluid model is utilized for the working fluid along with slip boundary conditions. Moreover the high temperature effect of thermal radiation and temperature dependent thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for cu-water and TiO2 -water nanofluids. Results are presented for the velocity and temperature profiles as well as the skin friction coefficient and Nusselt number and the discussion is concluded on the effect of various governing parameters on the motion, temperature variation, velocity gradient and the rate of heat transfer at the boundary.
Mathematical and physical modeling of thermal stratification phenomena in steel ladles
Putan, V.; Vilceanu, L.; Socalici, A.; Putan, A.
2018-01-01
By means of CFD numerical modeling, a systematic analysis of the similarity between steel ladles and hot-water model regarding natural convection phenomena was studied. The key similarity criteria we found to be dependent on the dimensionless numbers Fr and βΔT. These similarity criteria suggested that hot-water models with scale in the range between 1/5 and 1/3 and using hot water with temperature of 45 °C or higher are appropriate for simulating natural convection in steel ladles. With this physical model, thermal stratification phenomena due to natural convection in steel ladles were investigated. By controlling the cooling intensity of water model to correspond to the heat loss rate of steel ladles, which is governed by Fr and βΔT, the temperature profiles measured in the water bath of the model were to deduce the extent of thermal stratification in liquid steel bath in the ladles. Comparisons between mathematically simulated temperature profiles in the prototype steel ladles and those physically simulated by scaling-up the measured temperatures profiles in the water model showed good agreement. This proved that it is feasible to use a 1/5 scale water model with 45 °C hot water to simulate natural convection in steel ladles. Therefore, besides mathematical CFD models, the physical hot-water model provided an additional means of studying fluid flow and heat transfer in steel ladles.
International Nuclear Information System (INIS)
Torres, Alejandro; Mishkinis, Donatas; Kaya, Tarik
2014-01-01
An entirely novel satellite thermal architecture, connecting the east and west radiators of a geostationary telecommunications satellite via loop heat pipes (LHPs), is proposed. The LHP operating temperature is regulated by using pressure regulating valves (PRVs). A transient numerical model is developed to simulate the thermal dynamic behavior of the proposed system. The details of the proposed architecture and mathematical model are presented. The model is used to analyze a set of critical design cases to identify potential failure modes prior to the qualification and in-orbit tests. The mathematical model results for critical cases are presented and discussed. The model results demonstrated the robustness and versatility of the proposed architecture under the predicted worst-case conditions. - Highlights: •We developed a mathematical model of a novel satellite thermal architecture. •We provided the dimensioning cases to design the thermal architecture. •We provided the failure mode cases to verify the thermal architecture. •We provided the results of the corresponding dimensioning and failure cases
VIPRE-01. a thermal-hydraulic analysis code for reactor cores. Volume 1. Mathematical modeling
International Nuclear Information System (INIS)
Stewart, C.W.; Cuta, J.M.; Koontz, A.S.; Kelly, J.M.; Basehore, K.L.; George, T.L.; Rowe, D.S.
1983-04-01
VIPRE (Versatile Internals and Component Program for Reactors; EPRI) has been developed for nuclear power utility thermal-hydraulic analysis applications. It is designed to help evaluate nuclear reactor core safety limits including minimum departure from nucleate boiling ratio (MDNBR), critical power ratio (CPR), fuel and clad temperatures, and coolant state in normal operation and assumed accident conditions. This volume (Volume 1: Mathematical Modeling) explains the major thermal hydraulic models and supporting correlations in detail
Directory of Open Access Journals (Sweden)
K. M. Vasyliv
2017-06-01
Full Text Available Purpose. Development of a model-software complex (MSC for computer analysis of modes of the system of induction motors (IM of smoke exhausters of thermal power plant (TPP, the basic elements of which are mathematical models and corresponding software written in the programming language FORTRAN. Methodology. Mathematical model serves as a system of differential equations of electrical and mechanical condition. The equation of electric state is written in phase coordinates based on Kirchhoff's laws, and mechanical condition described by the d'Alembert equation. Mathematical model focuses on explicit numerical integration methods. Scientific novelty. The equation of state of electrical connections takes into account the mutual electromagnetic circuits for transformer of own needs (TON and induction motors and interdependence (in all possible combinations between: TON (from which motors powered and each of the two IM and blood pressure between themselves. The complex allows to simulate electromagnetic and electromechanical processes in transitional and steady, symmetric and asymmetric modes including modes of self-induction motors. Results. Complex is used for computer analysis of electromagnetic and electromechanical processes and established the basic laws of motion modes of starting, stopping and self-start of IM of smoke exhausters of the TPP unit. Practical value. The complex is suitable for computer analysis of modes of other similar units of own needs of thermal power plants.
Energy Technology Data Exchange (ETDEWEB)
Sousa, Ronaldo Martins de
1996-01-01
A thermal and electrical dynamic mathematical model for squirrel cage induction motors is presented. The electrical model is described by Park equation and the torque equation, while the thermal model is described by a system of four first order differential equations that represent the motor heat transfer process. The model presented can be used to determine thermal and electrical performance for any operation condition. However, it is suitable mainly for machines operating under continuously transient condition. The presented mathematical model also incorporate variation of rotor winding electrical parameters due to skin effect. (author)
Mathematical modelling of thermal and flow processes in vertical ground heat exchangers
Directory of Open Access Journals (Sweden)
Pater Sebastian
2017-12-01
Full Text Available The main task of mathematical modelling of thermal and flow processes in vertical ground heat exchanger (BHE-Borehole Heat Exchanger is to determine the unit of borehole depth heat flux obtainable or transferred during the operation of the installation. This assignment is indirectly associated with finding the circulating fluid temperature flowing out from the U-tube at a given inlet temperature of fluid in respect to other operational parameters of the installation.
Mathematical modelling of two-phase flows
International Nuclear Information System (INIS)
Komen, E.M.J.; Stoop, P.M.
1992-11-01
A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs
Review on mathematical basis for thermal conduction equation
Energy Technology Data Exchange (ETDEWEB)
Park, D. G.; Kim, H. M
2007-10-15
In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation.
Review on mathematical basis for thermal conduction equation
International Nuclear Information System (INIS)
Park, D. G.; Kim, H. M.
2007-10-01
In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation
Directory of Open Access Journals (Sweden)
Sayantan Nath
2015-09-01
Full Text Available In this paper, integration between multiple functions of image processing and its statistical parameters for intelligent alarming series based fire detection system is presented. The proper inter-connectivity mapping between processing elements of imagery based on classification factor for temperature monitoring and multilevel intelligent alarm sequence is introduced by abstractive canonical approach. The flow of image processing components between core implementation of intelligent alarming system with temperature wise area segmentation as well as boundary detection technique is not yet fully explored in the present era of thermal imaging. In the light of analytical perspective of convolutive functionalism in thermal imaging, the abstract algebra based inter-mapping model between event-calculus supported DAGSVM classification for step-by-step generation of alarm series with gradual monitoring technique and segmentation of regions with its affected boundaries in thermographic image of coal with respect to temperature distinctions is discussed. The connectedness of the multifunctional operations of image processing based compatible fire protection system with proper monitoring sequence is presently investigated here. The mathematical models representing the relation between the temperature affected areas and its boundary in the obtained thermal image defined in partial derivative fashion is the core contribution of this study. The thermal image of coal sample is obtained in real-life scenario by self-assembled thermographic camera in this study. The amalgamation between area segmentation, boundary detection and alarm series are described in abstract algebra. The principal objective of this paper is to understand the dependency pattern and the principles of working of image processing components and structure an inter-connected modelling technique also for those components with the help of mathematical foundation.
Mathematical Models of IABG Thermal-Vacuum Facilities
Doring, Daniel; Ulfers, Hendrik
2014-06-01
IABG in Ottobrunn, Germany, operates thermal-vacuum facilities of different sizes and complexities as a service for space-testing of satellites and components. One aspect of these tests is the qualification of the thermal control system that keeps all onboard components within their save operating temperature band. As not all possible operation / mission states can be simulated within a sensible test time, usually a subset of important and extreme states is tested at TV facilities to validate the thermal model of the satellite, which is then used to model all other possible mission states. With advances in the precision of customer thermal models, simple assumptions of the test environment (e.g. everything black & cold, one solar constant of light from this side) are no longer sufficient, as real space simulation chambers do deviate from this ideal. For example the mechanical adapters which support the spacecraft are usually not actively cooled. To enable IABG to provide a model that is sufficiently detailed and realistic for current system tests, Munich engineering company CASE developed ESATAN models for the two larger chambers. CASE has many years of experience in thermal analysis for space-flight systems and ESATAN. The two models represent the rather simple (and therefore very homogeneous) 3m-TVA and the extremely complex space simulation test facility and its solar simulator. The cooperation of IABG and CASE built up extensive knowledge of the facilities thermal behaviour. This is the key to optimally support customers with their test campaigns in the future. The ESARAD part of the models contains all relevant information with regard to geometry (CAD data), surface properties (optical measurements) and solar irradiation for the sun simulator. The temperature of the actively cooled thermal shrouds is measured and mapped to the thermal mesh to create the temperature field in the ESATAN part as boundary conditions. Both models comprise switches to easily
Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated
Trujillo Arredondo, Mariana
2014-05-01
A mathematical model for drying potato cylinders using solar radiation is proposed and solved analytically. The model incorporates the energy balance for the heat capacity of the potato, the radiation heat transfer from the potato toward the drying chamber and the solar radiation absorbed by the potato during the drying process. Potato cylinders are assumed to exhibit a thermal conductivity which is radially modulated. The method of the Laplace transform, with integral Bromwich and residue theorem will be applied and the analytic solutions for the temperature profiles in the potato cylinder will be derived in the form of an infinite series of Bessel functions, when the thermal conductivity is constant; and in the form of an infinite series of Heun functions, when the thermal conductivity has a linear radial modulation. All computations are performed using computer algebra, specifically Maple. It is expected that the analytical results obtained will be useful in food engineering and industry. Our results suggest some lines for future investigations such as the adoption of more general forms of radial modulation for the thermal conductivity of potato cylinders; and possible applications of other computer algebra software such as Maxima and Mathematica.
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.
Directory of Open Access Journals (Sweden)
Alibek Issakhov
2014-01-01
Full Text Available This paper presents the mathematical model of the thermal process from thermal power plant to aquatic environment of the reservoir-cooler, which is located in the Pavlodar region, 17 Km to the north-east of Ekibastuz town. The thermal process in reservoir-cooler with different hydrometeorological conditions is considered, which is solved by three-dimensional Navier-Stokes equations and temperature equation for an incompressible flow in a stratified medium. A numerical method based on the projection method, divides the problem into three stages. At the first stage, it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm. Finally, at the third stage, it is expected that the transfer is only due to the pressure gradient. Numerical method determines the basic laws of the hydrothermal processes that qualitatively and quantitatively are approximated depending on different hydrometeorological conditions.
A mathematical model for the simulation of thermal transients in the water loop of IPEN
International Nuclear Information System (INIS)
Pontedeiro, A.C.
1980-01-01
A mathematical model for simulation of thermal transients in the water loop at the Instituto de Pesquisas Energeticas e Nucleares, Sao Paulo, Brasil, is developed. The model is based on energy equations applied to the components of the experimental water loop. The non-linear system of first order diferencial equations and of non-linear algebraic equations obtained through the utilization of the IBM 'System/360-Continous System Modeling Program' (CSMP) is resolved. An optimization of the running time of the computer is made and a typical simulation of the water loop is executed. (Author) [pt
Applied mathematical methods in nuclear thermal hydraulics
International Nuclear Information System (INIS)
Ransom, V.H.; Trapp, J.A.
1983-01-01
Applied mathematical methods are used extensively in modeling of nuclear reactor thermal-hydraulic behavior. This application has required significant extension to the state-of-the-art. The problems encountered in modeling of two-phase fluid transients and the development of associated numerical solution methods are reviewed and quantified using results from a numerical study of an analogous linear system of differential equations. In particular, some possible approaches for formulating a well-posed numerical problem for an ill-posed differential model are investigated and discussed. The need for closer attention to numerical fidelity is indicated
International Nuclear Information System (INIS)
Gama, R.M.S. da.
1992-05-01
The energy transfer process in a gray, opaque and rigid plate, heated by an external thermal radiant source, is considered. The source is regarded as a spherical black body, with radius a (a → 0) and uniform heat generation, placed above the plate. A mathematical model is constructed, assuming that the heat transfer from/to the plate takes place by thermal radiation. The obtained mathematical model is nonlinear. Is presented a suitable variational principle which is employed for simulating some particular cases. (author)
Directory of Open Access Journals (Sweden)
Kryukov Igor Yu.
2017-01-01
Full Text Available Present article is devoted to the development of the mathematical model, which describes thermal state and crystallization process of the rectangular cross-section blank while continious process of extraction from a horysontal continious casting machine (HCCM.The developed model took cue for the heat-transfer properties of non-iron metal teeming; its temperature on entry to the casting mold; cooling conditions of blank in the carbon molds in the presence of a copper water cooler. Besides, has been considered the asymmetry of heat interchange from blank`s head and drag at mold, coming out from fluid contraction and features of the horizontal casting mold. The developed mathematical model allows to determine alterations in crystallizing blank of the following factors with respect to time: temperature pattern of crystallizing blank under different technical working regimes of HCCM; boundaries of solid two-phase field and liquid two-phase filed; blank`s thickness variation under shrinkage of the ingot`s material
Directory of Open Access Journals (Sweden)
Mančić Marko V.
2014-01-01
Full Text Available Buildings with indoor swimming pools have a large energy footprint. The source of major energy loss is the swimming pool hall where air humidity is increased by evaporation from the pool water surface. This increases energy consumption for heating and ventilation of the pool hall, fresh water supply loss and heat demand for pool water heating. In this paper, a mathematical model of the swimming pool was made to assess energy demands of an indoor swimming pool building. The mathematical model of the swimming pool is used with the created multi-zone building model in TRNSYS software to determine pool hall energy demand and pool losses. Energy loss for pool water and pool hall heating and ventilation are analyzed for different target pool water and air temperatures. The simulation showed that pool water heating accounts for around 22%, whereas heating and ventilation of the pool hall for around 60% of the total pool hall heat demand. With a change of preset controller air and water temperatures in simulations, evaporation loss was in the range 46-54% of the total pool losses. A solar thermal sanitary hot water system was modelled and simulated to analyze it's potential for energy savings of the presented demand side model. The simulation showed that up to 87% of water heating demands could be met by the solar thermal system, while avoiding stagnation. [Projekat Ministarstva nauke Republike Srbije, br. III 42006: Research and development of energy and environmentally highly effective polygeneration systems based on using renewable energy sources
Model-based analysis of thermal insulation coatings
DEFF Research Database (Denmark)
Kiil, Søren
2014-01-01
Thermal insulation properties of coatings based on selected functional filler materials are investigated. The underlying physics, thermal conductivity of a heterogeneous two-component coating, and porosity and thermal conductivity of hollow spheres (HS) are quantified and a mathematical model for...
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
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
Directory of Open Access Journals (Sweden)
G. Lebedeva
2004-06-01
Full Text Available In the publication the methodical aspects of a mathematical model of the combined parametrical analysis of an indicator process and thermal loading on the diesel engine piston have been considered. A thermodynamic model of a diesel engine cycle is developed. The executed development is intended for use during researches and on the initial stages of design work. Its realization for high revolution diesel engines of perspective type CHN15/15 allowed to choose rational variants for the organization of an indicator process and to prove power ranges of application for not cooled and created cooled oil welded pistons.
Mathematical Safety Assessment Approaches for Thermal Power Plants
Directory of Open Access Journals (Sweden)
Zong-Xiao Yang
2014-01-01
Full Text Available How to use system analysis methods to identify the hazards in the industrialized process, working environment, and production management for complex industrial processes, such as thermal power plants, is one of the challenges in the systems engineering. A mathematical system safety assessment model is proposed for thermal power plants in this paper by integrating fuzzy analytical hierarchy process, set pair analysis, and system functionality analysis. In the basis of those, the key factors influencing the thermal power plant safety are analyzed. The influence factors are determined based on fuzzy analytical hierarchy process. The connection degree among the factors is obtained by set pair analysis. The system safety preponderant function is constructed through system functionality analysis for inherence properties and nonlinear influence. The decision analysis system is developed by using active server page technology, web resource integration, and cross-platform capabilities for applications to the industrialized process. The availability of proposed safety assessment approach is verified by using an actual thermal power plant, which has improved the enforceability and predictability in enterprise safety assessment.
Energy Technology Data Exchange (ETDEWEB)
Buscheck, T., LLNL
1998-04-29
This chapter describes the physical processes and natural and engineered system conditions that affect thermal-hydrological (T-H) behavior in the unsaturated zone (UZ) at Yucca Mountain and how these effects are represented in mathematical and numerical models that are used to predict T-H conditions in the near field, altered zone, and engineered barrier system (EBS), and on waste package (WP) surfaces.
Mathematical model for temperature change of a journal bearing
Directory of Open Access Journals (Sweden)
Antunović Ranko
2018-01-01
Full Text Available In this work, a representative mathematical model has been developed, which reliably describes the heating and cooling of a journal bearing as a result of its malfunctioning, and the model has been further confirmed on a test bench. The bearing model was validated by using analytical modeling methods, i. e. the experimental results were compared to the data obtained by analytical calculations. The regression and variance analysis techniques were applied to process the recorded data, to test the mathematical model and to define mathematical functions for the heating/cooling of the journal bearing. This investigation shows that a representative model may reliably indicate the change in the thermal field, which may be a consequence of journal bearing damage.
Thermal sensation models: a systematic comparison.
Koelblen, B; Psikuta, A; Bogdan, A; Annaheim, S; Rossi, R M
2017-05-01
Thermal sensation models, capable of predicting human's perception of thermal surroundings, are commonly used to assess given indoor conditions. These models differ in many aspects, such as the number and type of input conditions, the range of conditions in which the models can be applied, and the complexity of equations. Moreover, the models are associated with various thermal sensation scales. In this study, a systematic comparison of seven existing thermal sensation models has been performed with regard to exposures including various air temperatures, clothing thermal insulation, and metabolic rate values after a careful investigation of the models' range of applicability. Thermo-physiological data needed as input for some of the models were obtained from a mathematical model for human physiological responses. The comparison showed differences between models' predictions for the analyzed conditions, mostly higher than typical intersubject differences in votes. Therefore, it can be concluded that the choice of model strongly influences the assessment of indoor spaces. The issue of comparing different thermal sensation scales has also been discussed. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
A REFINED MATHEMATICAL MODEL OF MULTIPHYSICS PROCESSES FOR MAGNETIC PULSE TREATMENT OF MATERIALS
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E.I. Baida
2015-04-01
Full Text Available Introduction. The complexity of the theoretical description of the magnetic pulse treatment of the material is in the mutual coupled processes of electromagnetic and thermal fields with plastic deformation of the material and processes in an electrical circuit. The paper deals with the combined transient mathematical model of the system of equations of the electromagnetic field, theory of elasticity, thermal conductivity and electrical circuit. Purpose. Research and testing of the developed mathematical model and assess the impact of various parameters on the process of deformation of the work piece. Methodology. Investigation of nonlinear mathematical model is carried out by the finite element method using a special software package. Results. The resulting solution of the transient mathematical model allows studying the influence of parameters of the circuit, the speed and the characteristics of the material to plastic deformation and heating of the work piece, which allows to select the optimum process parameters. Originality. This is an integrated approach to the development of a mathematical model, which includes the electromagnetic field equations, the theory of elasticity, thermal conductivity and electrical circuit equations with a storage capacitor. Conclusions. A comprehensive mathematical model and its solution are obtained. It is established a small effect of heating temperature on the amount of strain. Currents caused by movement of the work piece must be taken into account in the calculations. Inertial forces significantly affect the nature of the deformation. During the deformation it is necessary to consider the nonlinearity of elasticity modulus. Thermal deformation of the work piece is much less mechanical strain and opposite in sign to them, but the surface temperature stresses due to the high temperature gradient equal to 20 % of the yield strength of the work piece.
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…
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…
A MATHEMATICAL MODEL OF THE ROASTING CHESTNUTS PROCESS BY SUPERHEATED STEAM
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A. N. Ostrikov
2013-01-01
Full Text Available The mathematic modeling for chestnuts roasting process by superheated steam is conducted. Diffusion and thermal diffusion coefficients are used for process description. Initial conditions and boundary conditions of the third kind for thermal conductivity and mass transfer equations are set.
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.
Mathematical modelling of the combustion of a single wood particle
Energy Technology Data Exchange (ETDEWEB)
Porteiro, J.; Miguez, J.L.; Granada, E.; Moran, J.C. [Departamento de Ingenieria Mecanica, Maquinas y Motores Termicos y Fluidos. Universidad de Vigo, Lagoas Marcosende 9 36200 Vigo (Spain)
2006-01-15
A mathematical model describing the thermal degradation of densified biomass particles is presented here. The model uses a novel discretisation scheme and combines intra-particle combustion processes with extra-particle transport processes, thereby including thermal and diffusional control mechanisms. The influence of structural changes on the physical-thermal properties of wood in its different stages is studied together with shrinkage of the particle during its degradation. The model is used to compare the predicted data with data on the mass loss dynamics and internal temperature of several particles from previous works and relevant literature, with good agreement. (author)
Development and evaluation of thermal model reduction algorithms for spacecraft
Deiml, Michael; Suderland, Martin; Reiss, Philipp; Czupalla, Markus
2015-05-01
This paper is concerned with the topic of the reduction of thermal models of spacecraft. The work presented here has been conducted in cooperation with the company OHB AG, formerly Kayser-Threde GmbH, and the Institute of Astronautics at Technische Universität München with the goal to shorten and automatize the time-consuming and manual process of thermal model reduction. The reduction of thermal models can be divided into the simplification of the geometry model for calculation of external heat flows and radiative couplings and into the reduction of the underlying mathematical model. For simplification a method has been developed which approximates the reduced geometry model with the help of an optimization algorithm. Different linear and nonlinear model reduction techniques have been evaluated for their applicability in reduction of the mathematical model. Thereby the compatibility with the thermal analysis tool ESATAN-TMS is of major concern, which restricts the useful application of these methods. Additional model reduction methods have been developed, which account to these constraints. The Matrix Reduction method allows the approximation of the differential equation to reference values exactly expect for numerical errors. The summation method enables a useful, applicable reduction of thermal models that can be used in industry. In this work a framework for model reduction of thermal models has been created, which can be used together with a newly developed graphical user interface for the reduction of thermal models in industry.
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…
International Nuclear Information System (INIS)
Baldi, G.; Borsetto, M.; Hueckel, T.
1987-01-01
This report presents results of research on the verification of the validity of a generalized thermo-elastoplastic-hydraulic mathematical model elaborated at Ismes for description of the behaviour of boom clay. The model is described in Section 2. Experimental results performed at Ismes for the identification of the material constants in athermal and thermal drained conditions are then presented. Procedures for the identification are described in Section 4. The undrained consolidated constant total stress heating test is then discussed. The undrained test shows the possibility of clay yielding due to effective pressure decrease during heating, caused by water pressure growth. The test has been simulated numerically, confirming the interpretation of the experiment. Further simulation of plane strain and plane stress central heating axisymmetric problem shows again a formation of a yielded clay zone around the heater. Interpretation of the results and recommendations for further research are given
Mathematical model of heat transfer to predict distribution of hardness through the Jominy bar
International Nuclear Information System (INIS)
Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.
2013-01-01
The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)
MATHEMATICAL MODEL OF UNSTEADY HEAT TRANSFER OF PASSENGER CAR WITH HEATING SYSTEM
E. V. Biloshytskyi
2018-01-01
Purpose. The existing mathematical models of unsteady heat processes in a passenger car do not fully reflect the thermal processes, occurring in the car wits a heating system. In addition, unsteady heat processes are often studied in steady regime, when the heat fluxes and the parameters of the thermal circuit are constant and do not depend on time. In connection with the emergence of more effective technical solutions to the life support system there is a need for creating a new mathematical...
Akhmetova, I. G.; Chichirova, N. D.
2017-11-01
Currently the actual problem is a precise definition of the normative and actual heat loss. Existing methods - experimental, on metering devices, on the basis of mathematical modeling methods are not without drawbacks. Heat losses establishing during the heat carrier transport has an impact on the tariff structure of heat supply organizations. This quantity determination also promotes proper choice of main and auxiliary equipment power, temperature chart of heat supply networks, as well as the heating system structure choice with the decentralization. Calculation of actual heat loss and their comparison with standard values justifies the performance of works on improvement of the heat networks with the replacement of piping or its insulation. To determine the cause of discrepancies between normative and actual heat losses thermal tests on the magnitude of the actual heat losses in the 124 sections of heat networks in Kazan. As were carried out the result mathematical model of the regulatory definition of heat losses is developed and tested. This model differ from differs the existing according the piping insulation type. The application of this factor will bring the value of calculative normative losses heat energy to their actual value. It is of great importance for enterprises operating distribution networks and because of the conditions of their configuration and extensions do not have the technical ability to produce thermal testing.
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.
Berrios, William M.
1992-01-01
The Long Duration Exposure Facility (LDEF) postflight thermal model predicted temperatures were matched to flight temperature data recorded by the Thermal Measurement System (THERM), LDEF experiment P0003. Flight temperatures, recorded at intervals of approximately 112 minutes for the first 390 days of LDEF's 2105 day mission were compared with predictions using the thermal mathematical model (TMM). This model was unverified prior to flight. The postflight analysis has reduced the thermal model uncertainty at the temperature sensor locations from +/- 40 F to +/- 18 F. The improved temperature predictions will be used by the LDEF's principal investigators to calculate improved flight temperatures experienced by 57 experiments located on 86 trays of the facility.
Features of Functioning the Integrated Building Thermal Model
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Morozov Maxim N.
2017-01-01
Full Text Available A model of the building heating system, consisting of energy source, a distributed automatic control system, elements of individual heating unit and heating system is designed. Application Simulink of mathematical package Matlab is selected as a platform for the model. There are the specialized application Simscape libraries in aggregate with a wide range of Matlab mathematical tools allow to apply the “acausal” modeling concept. Implementation the “physical” representation of the object model gave improving the accuracy of the models. Principle of operation and features of the functioning of the thermal model is described. The investigations of building cooling dynamics were carried out.
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 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 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
Mathematical models in Slowpoke reactor internal irradiation site
International Nuclear Information System (INIS)
Raza, J.
2007-01-01
The main objective is to build representative mathematical models of neutron activation analysis in a Slowpoke internal irradiation site. Another significant objective is to correct various elements neutron activation analysis measured mass using these models. The neutron flux perturbation is responsible for the measured under-estimation of real masses. We supposed that neutron flux perturbation measurements taken during the Ecole Polytechnique de Montreal Slowpoke reactor first fuel loading were still valid after the second fuelling. .We also supposed that the thermal neutrons spatial and kinetic energies distributions as well as the absorption microscopic cross section dependence on the neutrons kinetic energies were important factors to satisfactorily represent neutron activation analysis results. In addition, we assumed that the neutron flux is isotropic in the laboratory system. We used experimental results from the Slowpoke reactor internal irradiation sites, in order to validate our mathematical models. Our models results are in close agreement with these experimental results..We established an accurate global mathematical correlation of the neutron flux perturbation in function of samples volumes and macroscopic neutron absorption cross sections. It is applicable to sample volumes ranging from 0,1 to 1,3 ml and macroscopic neutron absorption cross section up to 5 moles-b for seven (7) elements with atomic numbers (Z) ranging from 5 to 79. We first came up with a heuristic neutron transport mathematical semi-analytical model, in order to better understand neutrons behaviour in presence of one of several different nuclei samples volumes and mass. In order to well represent the neutron flux perturbation, we combined a neutron transport solution obtained from the spherical harmonics method of a finite cylinder and a mathematical expression combining two cylindrical harmonic functions..With the help of this model and the least squares method, we made extensive
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
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 MODEL MANIPULATOR ROBOTS
Directory of Open Access Journals (Sweden)
O. N. Krakhmalev
2015-12-01
Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.
Evaluation and verification of thermal stratification models for was
African Journals Online (AJOL)
USER
prediction of the condition of thermal stratification in WSPs under different hydraulic conditions and ... off coefficient. The models are verified with data collected from the full scale waste .... comparing two mathematical models based ..... 2 Comparison of measured and predicted effluent coliform bacteria (N) againsty depth.
Modelling of Thermal Behavior of Borehole Heat Exchangers of Geothermal Heat Pump Heating Systems
Directory of Open Access Journals (Sweden)
Gornov V.F.
2016-01-01
Full Text Available This article reports results of comparing the accuracy of the software package “INSOLAR.GSHP.12”, modeling non-steady thermal behavior of geothermal heat pump heating systems (GHCS and of the similar model “conventional” using finite difference methods for solving spatial non-steady problems of heat conductivity. The software package is based on the method of formulating mathematical models of thermal behavior of ground low-grade heat collection systems developed by INSOLAR group of companies. Equations of mathematical model of spatial non-steady thermal behavior of ground mass of low-grade heat collection system obtained by the developed method have been solved analytically that significantly reduced computing time spent by the software complex “INSOLAR.GSHP.12” for calculations. The method allows to turn aside difficulties associated with information uncertainty of mathematical models of the ground thermal behavior and approximation of external factors affecting the ground. Use of experimentally obtained information about the ground natural thermal behavior in the software package allows to partially take into account the whole complex of factors (such as availability of groundwater, their velocity and thermal behavior, structure and arrangement of ground layers, the Earth’s thermal background, precipitation, phase transformations of moisture in the pore space, and more, significantly influencing the formation of thermal behavior of the ground mass of a low-grade geothermal heat collection system. Numerical experiments presented in the article confirmed the high convergence of the results obtained through the software package “INSOLAR.GSHP.12” with solutions obtained by conventional finite-difference methods.
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....
International Nuclear Information System (INIS)
Dikij, N.P.; Rudychev, Y.V.; Fedorchenko, D.V.; Khazhmuradov, M.A.
2014-01-01
This paper considers a method for 67 Cu isotope production using electron bremsstrahlung by the 68 Zn(gamma, p) 67 Cu reaction. The facility for 67 Cu isotope production contains an electron accelerator, electron-gamma converter and zinc target. To optimize this facility we developed three-dimensional model of the converter and the target. Using this model, we performed the mathematical modeling of zinc target irradiation and thermal-hydraulic processes inside the target for various parameters of the electron beam and converter configurations. For mathematical modeling of radiation processes we used the MCNPX software. Thermal-hydraulic simulation utilized the commercial SolidWorks software with Flow Simulation module. Mathematical modeling revealed that efficient 67 Cu isotope production needs smaller beam diameter and higher electron energy. Under these conditions target heat power also increases, thus additional cooling is necessary. If the beam diameter and the electron energy are fixed the most effective method to satisfy the operating parameters and retain an efficient isotope yield is to optimize photonuclear spectra of the target by variation of converter thickness. We developed an algorithm for multicriterion optimization and performed the optimization of the facility with account to coupled radiation and heat transfer processes.
Mathematical modelling of thermal-plume interaction at Waterford Nuclear Power Station
International Nuclear Information System (INIS)
Tsai, S.Y.H.
1981-01-01
The Waldrop plume model was used to analyze the mixing and interaction of thermal effluents in the Mississippi River resulting from heated-water discharges from the Waterford Nuclear Power Station Unit 3 and from two nearby fossil-fueled power stations. The computer program of the model was modified and expanded to accommodate the multiple intake and discharge boundary conditions at the Waterford site. Numerical results of thermal-plume temperatures for individual and combined operation of the three power stations were obtained for typical low river flow (200,000 cfs) and maximum station operating conditions. The predicted temperature distributions indicated that the surface jet discharge from Waterford Unit 3 would interact with the thermal plumes produced by the two fossil-fueled stations. The results also showed that heat recirculation between the discharge of an upstream fossil-fueled plant and the intake of Waterford Unit 3 is to be expected. However, the resulting combined temperature distributions were found to be well within the thermal standards established by the state of Louisiana
International Nuclear Information System (INIS)
Sundberg, Jan
2003-04-01
Site investigations are in progress for the siting of a deep repository for spent nuclear fuel. As part of the planning work, strategies are developed for site descriptive modelling regarding different disciplines, amongst them the thermal conditions. The objective of the strategy for a thermal site descriptive model is to guide the practical implementation of evaluating site specific data during the site investigations. It is understood that further development may be needed. The model describes the thermal properties and other thermal parameters of intact rock, fractures and fracture zones, and of the rock mass. The methodology is based on estimation of thermal properties of intact rock and discontinuities, using both empirical and theoretical/numerical approaches, and estimation of thermal processes using mathematical modelling. The methodology will be used and evaluated for the thermal site descriptive modelling at the Aespoe Hard Rock Laboratory
Mathematical modeling of laser linear thermal effects on the anterior layer of the human eye
Rahbar, Sahar; Shokooh-Saremi, Mehrdad
2018-02-01
In this paper, mathematical analysis of thermal effects of excimer lasers on the anterior side of the human eye is presented, where linear effect of absorption by the human eye is considered. To this end, Argon Fluoride (ArF) and Holmium:Yttrium-Aluminum-Garent (Ho:YAG) lasers are utilized in this investigation. A three-dimensional model of the human eye with actual dimensions is employed and finite element method (FEM) is utilized to numerically solve the governing (Penne) heat transfer equation. The simulation results suggest the corneal temperature of 263 °C and 83.4 °C for ArF and Ho:YAG laser radiations, respectively, and show less heat penetration depth in comparison to the previous reports. Moreover, the heat transfer equation is solved semi-analytically in one-dimension. It is shown that the exploited simulation results are also consistent with those derived from the semi-analytical solution of the Penne heat transfer equation for both types of laser radiations.
MATHEMATICAL MODEL OF UNSTEADY HEAT TRANSFER OF PASSENGER CAR WITH HEATING SYSTEM
Directory of Open Access Journals (Sweden)
E. V. Biloshytskyi
2018-02-01
Full Text Available Purpose. The existing mathematical models of unsteady heat processes in a passenger car do not fully reflect the thermal processes, occurring in the car wits a heating system. In addition, unsteady heat processes are often studied in steady regime, when the heat fluxes and the parameters of the thermal circuit are constant and do not depend on time. In connection with the emergence of more effective technical solutions to the life support system there is a need for creating a new mathematical apparatus, which would allow taking into account these features and their influence on the course of unsteady heat processes throughout the travel time. The purpose of this work is to create a mathematical model of the heat regime of a passenger car with a heating system that takes into account the unsteady heat processes. Methodology. To achieve this task the author composed a system of differential equations, describing unsteady heat processes during the heating of a passenger car. For the solution of the composed system of equations, the author used the method of elementary balances. Findings. The paper presents the developed numerical algorithm and computer program for simulation of transitional heat processes in a locomotive traction passenger car, which allows taking into account the various constructive solutions of the life support system of passenger cars and to simulate unsteady heat processes at any stage of the trip. Originality. For the first time the author developed a mathematical model of heat processes in a car with a heating system, that unlike existing models, allows to investigate the unsteady heat engineering performance in the cabin of the car under different operating conditions and compare the work of various life support systems from the point of view their constructive solutions. Practical value. The work presented the developed mathematical model of the unsteady heat regime of the passenger car with a heating system to estimate
Mathematical model of thermal and mechanical steady state fuel element behaviour TEDEF
International Nuclear Information System (INIS)
Dinic, N.; Kostic, Z.; Josipovic, M.
1987-01-01
In this paper a numerical model of thermal and thermomechanical behaviour of a cylindrical metal uranium fuel element is described. Presented are numerical method and computer program for solving the stationary temperature field and thermal stresses of a fuel element. The model development is a second phase of analysis of these phenomena, and may as well be used for analysing power nuclear reactor fuel elements behaviour. (author)
International Nuclear Information System (INIS)
Yassin, Jamal S.; Eljrushi, Gibril S.
2006-01-01
This paper presents a mathematical model for thermal desalination plant operating with solar energy and hydrogen. This plant is composed of two main systems, the heating system and the distillation system. The distillation system is composed of multi-cells; each cell is using the humidification-dehumidification (H-D) process in the distillation unit and getting the required amount of heat from feed seawater heater. The feed seawater heater is a heat exchanger used to raise the temperature of the preheated seawater coming from the condensation chamber (Dehumidifier) of each cell to about 85 degree centigrade. The heating amount in the heat exchangers is obtained from the thermal storage tank, which gets its energy from solar thermal system and is coupled with a hydrogen-fired backup system to guaranty necessary operating conditions and permit 24 hours solar H-D desalination plant to enhance the performance of this system. The mathematical model studies the performance of the proposed desalination system using thermal solar energy and hydrogen as fuel. Other pertinent variable in the heating and distillation system are also studied. The outcomes of this study are analyzed to enhance the used solar desalination process and make commercial.(Author)
Alifanov, O. M.; Paleshkin, A. V.; Terent‧ev, V. V.; Firsyuk, S. O.
2016-01-01
A methodological approach to determination of the thermal state at a point on the surface of an isothermal element of a small spacecraft has been developed. A mathematical model of heat transfer between surfaces of intricate geometric configuration has been described. In this model, account was taken of the external field of radiant fluxes and of the differentiated mutual influence of the surfaces. An algorithm for calculation of the distribution of the density of the radiation absorbed by surface elements of the object under study has been proposed. The temperature field on the lateral surface of the spacecraft exposed to sunlight and on its shady side has been calculated. By determining the thermal state of magnetic controls of the orientation system as an example, the authors have assessed the contribution of the radiation coming from the solar-cell panels and from the spacecraft surface.
Mathematical model predicts the elastic behavior of composite materials
Directory of Open Access Journals (Sweden)
Zoroastro de Miranda Boari
2005-03-01
Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.
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...
Robust multi-model predictive control of multi-zone thermal plate system
Directory of Open Access Journals (Sweden)
Poom Jatunitanon
2018-02-01
Full Text Available A modern controller was designed by using the mathematical model of a multi–zone thermal plate system. An important requirement for this type of controller is that it must be able to keep the temperature set-point of each thermal zone. The mathematical model used in the design was determined through a system identification process. The results showed that when the operating condition is changed, the performance of the controller may be reduced as a result of the system parameter uncertainties. This paper proposes a weighting technique of combining the robust model predictive controller for each operating condition into a single robust multi-model predictive control. Simulation and experimental results showed that the proposed method performed better than the conventional multi-model predictive control in rise time of transient response, when used in a system designed to work over a wide range of operating conditions.
Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.
2018-05-01
The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the
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…
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…
Modeling and simulation of thermally actuated bilayer plates
Bartels, Sören; Bonito, Andrea; Muliana, Anastasia H.; Nochetto, Ricardo H.
2018-02-01
We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be discretized with standard plate elements. We devise a fully practical iterative scheme and apply it to the simulation of folding of several practically useful compliant structures comprising of thin elastic layers.
Directory of Open Access Journals (Sweden)
Bondarenko V.I.
2015-03-01
Full Text Available The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.
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.
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…
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
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…
Mathematical Model of Induction Heating Processes in Axial Symmetric Inductor-Detail Systems
Directory of Open Access Journals (Sweden)
Maik Streblau
2014-05-01
Full Text Available The wide variety of models for analysis of processes in the inductor-detail systems makes it necessary to summarize them. This is a difficult task because of the variety of inductor-detail system configurations. This paper aims to present a multi physics mathematical model for complex analysis of electromagnetic and thermal fields in axial symmetric systems inductor-detail.
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...
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…
Mathematical modeling and the two-phase constitutive equations
International Nuclear Information System (INIS)
Boure, J.A.
1975-01-01
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr
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.
Mathematical Modeling of Dual Intake Transparent Transpired Solar Collector
Directory of Open Access Journals (Sweden)
Thomas Semenou
2015-01-01
Full Text Available Nowadays, in several types of commercial or institutional buildings, a significant rise of transpired solar collectors used to preheat the fresh air of the building can be observed. Nevertheless, when the air mass flow rate is low, the collector efficiency collapses and a large amount of energy remains unused. This paper presents a simple yet effective mathematical model of a transparent transpired solar collector (TTC with dual intake in order to remove stagnation problems in the plenum and ensure a better thermal efficiency and more heat recovery. A thermal model and a pressure loss model were developed. Then, the combined model was validated with experimental data from the Solar Rating and Certification Corporation (SRCC. The results show that the collector efficiency can be up to 70% and even 80% regardless of operating conditions. The temperature gain is able to reach 20°K when the solar irradiation is high.
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…
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
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…
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.
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…
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…
Mathematical Model of Piston Ring Sealing in Combustion Engine
Directory of Open Access Journals (Sweden)
Koszałka Grzegorz
2015-01-01
Full Text Available This paper presents a mathematical model of piston-rings-cylinder sealing (TPC of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The paper contains descriptions of: assumptions used for developing the model, the model itself, its numerical solution as well as its computer application for carrying out simulation tests.
Solar thermal energy as a topic in secondary mathematics classrooms
Energy Technology Data Exchange (ETDEWEB)
Brinkmann, A.; Brinkmann, K. [EnviPro Environmental Process Engineering Prof. Dr. Klaus Brinkmann, Iserlohn (Germany)
2004-07-01
One of the most effective methods to achieve a sustainable change of our momentary existing power supply system to a system mainly based on renewable energy conversion is the education of our children. For this purpose the compulsory school subject mathematics appears to be suitable. In order to promote renewable energy issues in mathematics classrooms, the authors have developed a special didactical concept to open this field for students, as well as for their teachers. The aim of this paper is to present firstly an overview of our concept and secondly examples of problems to the special topic of solar thermal energy, developed on the basis of our concept. (orig.)
Thermal diffusivity effect in opto-thermal skin measurements
International Nuclear Information System (INIS)
Xiao, P; Imhof, R E; Cui, Y; Ciortea, L I; Berg, E P
2010-01-01
We present our latest study on the thermal diffusivity effect in opto-thermal skin measurements. We discuss how thermal diffusivity affects the shape of opto-thermal signal, and how to measure thermal diffusivity in opto-thermal measurements of arbitrary sample surfaces. We also present a mathematical model for a thermally gradient material, and its corresponding opto-thermal signal. Finally, we show some of our latest experimental results of this thermal diffusivity effect study.
Hydrodynamic and thermal modelling of gas-particle flow in fluidized beds
International Nuclear Information System (INIS)
Abdelkawi, O.S; Abdalla, A.M.; Atwan, E.F; Abdelmonem, S.A.; Elshazly, K.M.
2009-01-01
In this study a mathematical model has been developed to simulate two dimensional fluidized bed with uniform fluidization. The model consists of two sub models for hydrodynamic and thermal behavior of fluidized bed on which a FORTRAN program entitled (NEWFLUIDIZED) is devolved. The program is used to predict the volume fraction of gas and particle phases, the velocity of the two phases, the gas pressure and the temperature distribution for two phases. Also the program calculates the heat transfer coefficient. Besides the program predicts the fluidized bed stability and determines the optimum input gas velocity for fluidized bed to achieve the best thermal behavior. The hydrodynamic model is verified by comparing its results with the computational fluid dynamic code MFIX . While the thermal model was tested and compared by the available previous experimental correlations.The model results show good agreement with MFIX results and the thermal model of the present work confirms Zenz and Gunn equations
Thermal Performance of the LHC External Auxiliary Bus-Bar Tube Mathematical Modelling
Kowalczyk, P; Sacré, P; Skoczen, Blazej
1998-01-01
The Large Hadron Collider (LHC) externally routed auxiliary bus-bar tube (EAB) will house the electrical feeders of the LHC short straight section (SSS) correcting magnets. The superconducting wires w ill be contained in a stainless steel tube and immersed in a quasi-static helium bath. The EAB thermal performance during the cooling of the magnets down to the operating temperature of 1.9 K is studi ed. A 3-d finite element thermal model of the EAB during a cooling process from 293 K to 4.5 K is described. The semi-analytical model of the EAB cool-down from 4.5 K to 1.9 K is also presented.
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...
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics
Wickstrom, Megan H.
2017-01-01
This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
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
DEFF Research Database (Denmark)
Coman, Paul Tiberiu; Rayman, Sean; White, Ralph
2016-01-01
This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary...
Mathematical model for creep and thermal shrinkage of concrete at high temperature
International Nuclear Information System (INIS)
Bazant, Z.P.
1983-01-01
Based on the existing limited test data, it is possible to set up an approximate constitutive model for creep and shrinkage at temperatures above 100 0 C, up to about 400 0 C. The model presented here describes the effect of various constant temperatures on the creep rate and the rate of aging, similar effects of the specific water content, the creep increase caused by simultaneous changes in moisture content, the thermal volume changes as well as the volume changes caused by changes in moisture content (drying shrinkage or thermal shrinkage), and the effect of pore pressure produced by heating. Generalizations to time-variable stresses and multiaxial stresses are also given. The model should allow more realistic analysis of reactor vessels and containments for accident situations, of concrete structures subjected to fire, of vessels for coal gasification or liquefaction, etc. (orig.)
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…
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…
Modelling of thermal degradation kinetics of ascorbic acid in ...
African Journals Online (AJOL)
Ascorbic acid (vitamin C) loss in thermally treated pawpaw and potato was modelled mathematically. Isothermal experiments in the temperature range of 50 -80 oC for the drying of pawpaw and 60 -100 oC for the blanch-drying of potato were utilized to determine the kinetics of ascorbic acid loss in both fruit and vegetable.
Numerical modeling of the autumnal thermal bar
Tsydenov, Bair O.
2018-03-01
The autumnal riverine thermal bar of Kamloops Lake has been simulated using atmospheric data from December 1, 2015, to January 4, 2016. The nonhydrostatic 2.5D mathematical model developed takes into account the diurnal variability of the heat fluxes and wind on the lake surface. The average values for shortwave and longwave radiation and latent and sensible heat fluxes were 19.7 W/m2, - 95.9 W/m2, - 11.8 W/m2, and - 32.0 W/m2 respectively. Analysis of the wind regime data showed prevailing easterly winds and maximum speed of 11 m/s on the 8th and 19th days. Numerical experiments with different boundary conditions at the lake surface were conducted to evaluate effects of variable heat flux and wind stress. The results of modeling demonstrated that the variable heat flux affects the process of thermal bar evolution, especially during the lengthy night cooling. However, the wind had the greatest impact on the behavior of the autumnal thermal bar: The easterly winds contributed to an earlier appearance of the thermal bar, but the strong winds generating the intensive circulations (the velocity of the upper lake flow increased to 6 cm/s) may destroy the thermal bar front.
Modeling of the dilution of thermal discharges into the sea
International Nuclear Information System (INIS)
Boulot, F.; Hauguel, A.
1981-01-01
The report describes the differences in behaviour existing between tidal and tideless oceans with resulting consequences for mathematical modeling of thermal discharges and their dispersion off the coast where plant is located. Examples of studies performed at sites on the Channel and in the Mediterranean sea are also explained [fr
Mathematical Modelling of Predatory Prokaryotes
Wilkinson, Michael H.F.
2006-01-01
Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic
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…
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
Thermal measurements and inverse techniques
Orlande, Helcio RB; Maillet, Denis; Cotta, Renato M
2011-01-01
With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has enabled numerical simulations of most physical phenomena. In addition, recent advances in thermal instrumentation and heat transfer modeling have improved experimental procedures and indirect measurements for heat transfer research of both natural phe
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.
Directory of Open Access Journals (Sweden)
Khalid Ahmed Joudi
2017-01-01
Full Text Available This paper presents a computer simulation model of a thermally activated roof (TAR to cool a room using cool water from a wet cooling tower. Modeling was achieved using a simplified 1-D resistance-capacitance thermal network (RC model for an infinite slab. Heat transfer from the cooling pipe network was treated as 2-D heat flow. Only a limited number of nodes were required to obtain reliable results. The use of 6th order RC-thermal model produced a set of ordinary differential equations that were solved using MATLAB - R2012a. The computer program was written to cover all possible initial conditions, material properties, TAR system geometry and hourly solar radiation. The cool water supply was considered time dependent with the variation of the ambient wet bulb temperature. Results from RC-thermal modeling were compared with experimental measurements for a second story room measuring 5.5 m x 4 m x 3 m at Amarah city/ Iraq (31.865 ˚N, 47.128 ˚E for 21 July, 2013. The roof was constructed of 200 mm concrete slab, 150 mm turf and 50 mm insulation. Galvanized 13 mm steel pipe coils were buried in the roof slab with a pipe occupation ratio of 0.12. The walls were constructed of 240 mm common brick with 10mm cement plaster on the inside and outside surfaces and 20 mm Styrofoam insulation on the inside surface and covered with PVC panel. Thermistors were used to measure the indoor and outdoor temperatures, TAR system water inlet and outlet temperatures and temperature distribution inside the concrete slab. The effect of pipe spacing and water mass flow rate were evaluated. Agreement was good between the experimental and RC-thermal model. Concrete core temperature reaches the supply water temperature faster for lower pipe spacing. Heat extracted from the space increased with water mass flow rate to an optimum of 0.0088 kg/s.m².
Orion Active Thermal Control System Dynamic Modeling Using Simulink/MATLAB
Wang, Xiao-Yen J.; Yuko, James
2010-01-01
This paper presents dynamic modeling of the crew exploration vehicle (Orion) active thermal control system (ATCS) using Simulink (Simulink, developed by The MathWorks). The model includes major components in ATCS, such as heat exchangers and radiator panels. The mathematical models of the heat exchanger and radiator are described first. Four different orbits were used to validate the radiator model. The current model results were compared with an independent Thermal Desktop (TD) (Thermal Desktop, PC/CAD-based thermal model builder, developed in Cullimore & Ring (C&R) Technologies) model results and showed good agreement for all orbits. In addition, the Orion ATCS performance was presented for three orbits and the current model results were compared with three sets of solutions- FloCAD (FloCAD, PC/CAD-based thermal/fluid model builder, developed in C&R Technologies) model results, SINDA/FLUINT (SINDA/FLUINT, a generalized thermal/fluid network-style solver ) model results, and independent Simulink model results. For each case, the fluid temperatures at every component on both the crew module and service module sides were plotted and compared. The overall agreement is reasonable for all orbits, with similar behavior and trends for the system. Some discrepancies exist because the control algorithm might vary from model to model. Finally, the ATCS performance for a 45-hr nominal mission timeline was simulated to demonstrate the capability of the model. The results show that the ATCS performs as expected and approximately 2.3 lb water was consumed in the sublimator within the 45 hr timeline before Orion docked at the International Space Station.
Mathematical modeling of the energy consumption of heated swimming pools
Energy Technology Data Exchange (ETDEWEB)
Le Bel, C.; Millette, J. [LTE Shawinigan, Shawinigan, PQ (Canada)
2007-07-01
A mathematical model was developed to estimate the water temperature of a residential swimming pool. The model can compare 2 different situations and, if local climatic conditions are known, it can accurately predict energy costs of the pool relative to the total energy consumption of the house. When used with the appropriate energy transfer coefficient and weather file, the model can estimate the water temperature of a residential swimming pool having specific characteristics, such as in-ground, above-ground, heated or non-heated. The model is suitable for determining residential loads. It can be applied to different pool types and sizes, for different water heating scenarios and different climatic regions. Data obtained from the monitoring of water temperature and electricity use of 57 residential swimming pools was used to validate the model. In addition, 5 above-ground pools were installed on the property of LTE Shawinigan to allow for a more detailed study of the parameters involved in the thermal balance of a pool. The mathematical model, based on a global heat transfer coefficient, can determine the effect of a solar blanket and the effect of water volume. 14 refs., 5 tabs., 11 figs.
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2001-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR) system. This study involved mathematical modeling of CANDU PHWR major system components and the developments of software to study the thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique.The integrated CANDU-PHWR model includes the neutronic, reactivity, fuel channel heat transfer, piping and the preheater type U-tube steam generator (PUTSG). The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and reactivity feed back due to the changes in fuel temperature and coolant temperature. The complex operation of the preheater type U-tube steam generator (PUTSG) is represented by a non-linear dynamic model using a state variable, moving boundary and lumped parameter techniques. The secondary side of the PUTSG model has six separate lumps including a preheater region, a lower boiling section, a mixing region, a riser, a chimmeny section, and a down-corner. The tube side of PUTSG has three main thermal zones. The PUTSG model is based on conservation of mass, energy and momentum relation-ships. The CANDU-PHWR integrated model are coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
Yang, Yao Bin; Sharifi, Vida; Swithenbank, Jim
2008-11-01
Fluidised bed combustor (FBC) is one of the key technologies for sewage sludge incineration. In this paper, a mathematical model is developed for the simulation of a large-scale sewage sludge incineration plant. The model assumes the bed consisting of a fast-gas phase, an emulsion phase and a fuel particle phase with specific consideration for thermally-thick fuel particles. The model further improves over previous works by taking into account throughflow inside the bubbles as well as the floating and random movement of the fuel particles inside the bed. Validation against both previous lab-scale experiments and operational data of a large-scale industrial plant was made. Calculation results indicate that combustion split between the bed and the freeboard can range from 60/40 to 90/10 depending on the fuel particle distribution across the bed height under the specific conditions. The bed performance is heavily affected by the variation in sludge moisture level. The response time to variation in feeding rate is different for different parameters, from 6 min for outlet H2O, 10 min for O2, to 34 min for bed temperature.
Sabanskis, A.; Virbulis, J.
2018-05-01
Mathematical modelling is employed to numerically analyse the dynamics of the Czochralski (CZ) silicon single crystal growth. The model is axisymmetric, its thermal part describes heat transfer by conduction and thermal radiation, and allows to predict the time-dependent shape of the crystal-melt interface. Besides the thermal field, the point defect dynamics is modelled using the finite element method. The considered process consists of cone growth and cylindrical phases, including a short period of a reduced crystal pull rate, and a power jump to avoid large diameter changes. The influence of the thermal stresses on the point defects is also investigated.
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.
A review of heat transfer in human tooth--experimental characterization and mathematical modeling.
Lin, Min; Xu, Feng; Lu, Tian Jian; Bai, Bo Feng
2010-06-01
With rapid advances in modern dentistry, high-energy output instruments (e.g., dental lasers and light polymerizing units) are increasingly employed in dental surgery for applications such as laser assisted tooth ablation, bleaching, hypersensitivity treatment and polymerization of dental restorative materials. Extreme high temperature occurs within the tooth during these treatments, which may induce tooth thermal pain (TTP) sensation. Despite the wide application of these dental treatments, the underlying mechanisms are far from clear. Therefore, there is an urgent need to better understand heat transfer (HT) process in tooth, thermally induced damage of tooth, and the corresponding TTP. This will enhance the design and optimization of clinical treatment strategies. This paper presents the state-of-the-art of the current understanding on HT in tooth, with both experimental study and mathematical modeling reviewed. Limitations of the current experimental and mathematical methodologies are discussed and potential solutions are suggested. Interpretation of TTP in terms of thermally stimulated dentinal fluid flow is also discussed. Copyright (c) 2010 Academy of Dental Materials. All rights reserved.
Model of optical phantoms thermal response upon irradiation with 975 nm dermatological laser
Wróbel, M. S.; Bashkatov, A. N.; Yakunin, A. N.; Avetisyan, Yu. A.; Genina, E. A.; Galla, S.; Sekowska, A.; Truchanowicz, D.; Cenian, A.; Jedrzejewska-Szczerska, M.; Tuchin, V. V.
2018-04-01
We have developed a numerical model describing the optical and thermal behavior of optical tissue phantoms upon laser irradiation. According to our previous studies, the phantoms can be used as substitute of real skin from the optical, as well as thermal point of view. However, the thermal parameters are not entirely similar to those of real tissues thus there is a need to develop mathematical model, describing the thermal and optical response of such materials. This will facilitate the correction factors, which would be invaluable in translation between measurements on skin phantom to real tissues, and gave a good representation of a real case application. Here, we present the model dependent on the data of our optical phantoms fabricated and measured in our previous preliminary study. The ambiguity between the modeling and the thermal measurements depend on lack of accurate knowledge of material's thermal properties and some exact parameters of the laser beam. Those parameters were varied in the simulation, to provide an overview of possible parameters' ranges and the magnitude of thermal response.
Apollo telescope mount thermal systems unit thermal vacuum test
Trucks, H. F.; Hueter, U.; Wise, J. H.; Bachtel, F. D.
1971-01-01
The Apollo Telescope Mount's thermal systems unit was utilized to conduct a full-scale thermal vacuum test to verify the thermal design and the analytical techniques used to develop the thermal mathematical models. Thermal vacuum test philosophy, test objectives configuration, test monitoring, environment simulation, vehicle test performance, and data correlation are discussed. Emphasis is placed on planning and execution of the thermal vacuum test with particular attention on problems encountered in conducting a test of this maguitude.
Mathematical models in medicine: Diseases and epidemics
International Nuclear Information System (INIS)
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling
The analogic model ''RIC'' of thermal behaviour of mass concrete
International Nuclear Information System (INIS)
Gonzalez Redondo, M.; Gonzalez de Posada, F.; Plana Claver, J.
1997-01-01
In order to study the thermal field and calorific flows in heat sources (i.e. mass concrete during setting) we have conceived, built and experimented with an analogical electric model. This model, named RIC, consists of resistors (R) and capacitors (C) in which nodes an electric current (I) has been injected. Several analogical constants were used for the mathematical approximation. Thus, this paper describes the analogical RIC model, simulating heat generation, boundary and initial conditions and concreting. (Author) 4 refs
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
Directory of Open Access Journals (Sweden)
Ladeesh V. G.
2017-01-01
Full Text Available Grinding aided electrochemical discharge machining is a hybrid technique, which combines the grinding action of an abrasive tool and thermal effects of electrochemical discharges to remove material from the workpiece for producing complex contours. The present study focuses on developing fluidic channels on borosilicate glass using G-ECDM and attempts to develop a mathematical model for surface roughness of the machined channel. Preliminary experiments are conducted to study the effect of machining parameters on surface roughness. Voltage, duty factor, frequency and tool feed rate are identified as the significant factors for controlling surface roughness of the channels produced by G-ECDM. A mathematical model was developed for surface roughness by considering the grinding action and thermal effects of electrochemical discharges in material removal. Experiments are conducted to validate the model and the results obtained are in good agreement with that predicted by the model.
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…
Directory of Open Access Journals (Sweden)
Mohammad Alobaid
2018-06-01
Full Text Available Research into photovoltaic thermal systems is important in solar technologies as photovoltaic thermal systems are designed to produce both electrical and thermal energy, this can lead to improved performance of the overall system. The performance of photovoltaic thermal systems is based on several factors that include photovoltaic thermal materials, design, ambient temperature, inlet and outlet fluid temperature and photovoltaic cell temperature. The aim of this study is to investigate the effect of photovoltaic thermal outlet water temperatures and solar cell temperature on both electrical and thermal efficiency for different range of inlet water temperature. To achieve this, a mathematical model of a photovoltaic thermal system was developed to calculate the anticipated system performance. The factors that affect the efficiency of photovoltaic thermal collectors were discussed and the outlet fluid temperature from the photovoltaic thermal is investigated in order to reach the highest overall efficiency for the solar cooling system. An average thermal and electrical efficiency of 65% and 13.7%, respectively, was achieved and the photovoltaic thermal mathematical model was validated with experimental data from literature.
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…
Directory of Open Access Journals (Sweden)
Vladimir N. Vodyakov
2017-12-01
Full Text Available Introduction: Mathematical modeling allows assigning optimal parameters for the process of compression molding of plates and calculating the dimensions of the mold without costly and long-term experiments. The options ensure the required precision of pressing. The disadvantages of the known models are the assumptions about the process isothermicity and independence of the thermal-physical coefficients from temperature. The models do not take into account the dependence of the pressure in the cavity of the mold on the excess of the melt; the problem of calculating the dimensions of the mold cavity for given plate dimensions is not posed. The known models do not give a complete description of all stages of the process. The aim of this paper is to develop a perfect mathematical model without limitations for the compression molding of plates from a granulate of highly filled thermoplastic composites. Materials and Methods: The paper proposes a non-stationary mathematical model. The model takes into account the presence of physical states transitions and dependence of the thermophysical characteristics of composites on temperature. The model is based on the known equations of thermal physics and continuum mechanics. Results: Initial and boundary conditions, rheological equations, systems of equations for the material, thermal, and power balance are determined for three stages of the process. The calculation problems are determined too. A program of iterative numerical calculation has been developed because of the resulting system of equations has no analytical solution. A convergence of experimental and theoretical results with the correlation coefficient confirms the adequacy of the developed mathematical model and the calculation program. Discussion and Conclusions: The results of the study allow calculating the dimensions of the mold cavity, the initial granulate required mass, technological losses, the time functions of pressure and temperature
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…
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…
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.
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.
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...
Thermal models of pulse electrochemical machining
International Nuclear Information System (INIS)
Kozak, J.
2004-01-01
Pulse electrochemical machining (PECM) provides an economical and effective method for machining high strength, heat-resistant materials into complex shapes such as turbine blades, die, molds and micro cavities. Pulse Electrochemical Machining involves the application of a voltage pulse at high current density in the anodic dissolution process. Small interelectrode gap, low electrolyte flow rate, gap state recovery during the pulse off-times lead to improved machining accuracy and surface finish when compared with ECM using continuous current. This paper presents a mathematical model for PECM and employs this model in a computer simulation of the PECM process for determination of the thermal limitation and energy consumption in PECM. The experimental results and discussion of the characteristics PECM are presented. (authors)
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
Model-based thermal system design optimization for the James Webb Space Telescope
Cataldo, Giuseppe; Niedner, Malcolm B.; Fixsen, Dale J.; Moseley, Samuel H.
2017-10-01
Spacecraft thermal model validation is normally performed by comparing model predictions with thermal test data and reducing their discrepancies to meet the mission requirements. Based on thermal engineering expertise, the model input parameters are adjusted to tune the model output response to the test data. The end result is not guaranteed to be the best solution in terms of reduced discrepancy and the process requires months to complete. A model-based methodology was developed to perform the validation process in a fully automated fashion and provide mathematical bases to the search for the optimal parameter set that minimizes the discrepancies between model and data. The methodology was successfully applied to several thermal subsystems of the James Webb Space Telescope (JWST). Global or quasiglobal optimal solutions were found and the total execution time of the model validation process was reduced to about two weeks. The model sensitivities to the parameters, which are required to solve the optimization problem, can be calculated automatically before the test begins and provide a library for sensitivity studies. This methodology represents a crucial commodity when testing complex, large-scale systems under time and budget constraints. Here, results for the JWST Core thermal system will be presented in detail.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
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
Thermal IR exitance model of a plant canopy
Kimes, D. S.; Smith, J. A.; Link, L. E.
1981-01-01
A thermal IR exitance model of a plant canopy based on a mathematical abstraction of three horizontal layers of vegetation was developed. Canopy geometry within each layer is quantitatively described by the foliage and branch orientation distributions and number density. Given this geometric information for each layer and the driving meteorological variables, a system of energy budget equations was determined and solved for average layer temperatures. These estimated layer temperatures, together with the angular distributions of radiating elements, were used to calculate the emitted thermal IR radiation as a function of view angle above the canopy. The model was applied to a lodgepole pine (Pinus contorta) canopy over a diurnal cycle. Simulated vs measured radiometric average temperatures of the midcanopy layer corresponded with 2 C. Simulation results suggested that canopy geometry can significantly influence the effective radiant temperature recorded at varying sensor view angles.
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Method for automated building of spindle thermal model with use of CAE system
Kamenev, S. V.
2018-03-01
The spindle is one of the most important units of the metal-cutting machine tool. Its performance is critical to minimize the machining error, especially the thermal error. Various methods are applied to improve the thermal behaviour of spindle units. One of the most important methods is mathematical modelling based on the finite element analysis. The most common approach for its realization is the use of CAE systems. This approach, however, is not capable to address the number of important effects that need to be taken into consideration for proper simulation. In the present article, the authors propose the solution to overcome these disadvantages using automated thermal model building for the spindle unit utilizing the CAE system ANSYS.
Specific Type of Knowledge Map: Mathematical Model
Milan, Houška; Martina, Beránková
2005-01-01
The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.
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…
Thermal mathematical modeling of a multicell common pressure vessel nickel-hydrogen battery
Kim, Junbom; Nguyen, T. V.; White, R. E.
1992-01-01
A two-dimensional and time-dependent thermal model of a multicell common pressure vessel (CPV) nickel-hydrogen battery was developed. A finite element solver called PDE/Protran was used to solve this model. The model was used to investigate the effects of various design parameters on the temperature profile within the cell. The results were used to help find a design that will yield an acceptable temperature gradient inside a multicell CPV nickel-hydrogen battery. Steady-state and unsteady-state cases with a constant heat generation rate and a time-dependent heat generation rate were solved.
A heat mathematical model of polymer composite cylinder during microwave treatment
Directory of Open Access Journals (Sweden)
S. V. Reznik
2014-01-01
Full Text Available Traditional technologies of producing epoxy based polymer composite materials (PCM require a long-term and energy consuming thermal processing. Microwave heating could be used as an alternative technology for heating work pieces made of PCM; this would allow to reduce treatment time and energy consumption significantly. A mathematical model of temperature distribution inside a cylindrical composite system during microwave treatment was investigated in this paper. The model includes a hollow PCM cylinder made of an epoxy binder and carbon fibers and a solid cylindrical mandrel. Theoretical and experimental results on the temperature state of the system were analyzed and discussed.
International Nuclear Information System (INIS)
Huang, J H; Wang, X J; Wang, J
2016-01-01
The primary purpose of this paper is to propose a mathematical model of PLZT ceramic with coupled multi-physics fields, e.g. thermal, electric, mechanical and light field. To this end, the coupling relationships of multi-physics fields and the mechanism of some effects resulting in the photostrictive effect are analyzed theoretically, based on which a mathematical model considering coupled multi-physics fields is established. According to the analysis and experimental results, the mathematical model can explain the hysteresis phenomenon and the variation trend of the photo-induced voltage very well and is in agreement with the experimental curves. In addition, the PLZT bimorph is applied as an energy transducer for a photovoltaic–electrostatic hybrid actuated micromirror, and the relation of the rotation angle and the photo-induced voltage is discussed based on the novel photostrictive mathematical model. (paper)
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…
Thermal control of high energy nuclear waste, space option. [mathematical models
Peoples, J. A.
1979-01-01
Problems related to the temperature and packaging of nuclear waste material for disposal in space are explored. An approach is suggested for solving both problems with emphasis on high energy density waste material. A passive cooling concept is presented which utilized conduction rods that penetrate the inner core. Data are presented to illustrate the effectiveness of the rods and the limit of their capability. A computerized thermal model is discussed and developed for the cooling concept.
MATHEMATICAL MODELING OF UNSTEADY HEAT EXCHANGE IN A PASSENGER CAR
Directory of Open Access Journals (Sweden)
I. Yu. Khomenko
2013-07-01
Full Text Available Purpose.Existing mathematicalmodelsofunsteadyheatexchangeinapassengercardonotsatisfytheneedofthedifferentconstructivedecisionsofthelifesupportsystemefficiencyestimation. They also don’t allow comparing new and old life support system constructions influence on the inner environment conditions. Moreoverquite frequently unsteady heat exchange processes were studied at the initial car motion stage. Due to the new competitive engineering decisionsof the lifesupportsystemthe need of a new mathematical instrument that would satisfy the mentioned features and their influence on the unsteadyheatexchangeprocesses during the whole time of the road appeared. The purpose of this work is creation of the mathematicalmodel ofunsteadyheatexchangeinapassengercarthatcan satisfythe above-listed requirements. Methodology. Fortheassigned task realizationsystemofdifferentialequationsthatcharacterizesunsteadyheatexchangeprocessesinapassengercarwascomposed; forthesystemof equationssolution elementary balance method was used. Findings. Computational algorithm was developed andcomputer program for modeling transitional heat processes in the car was designed. It allows comparing different life support system constructions influence on the inner environment conditionsand unsteady heat exchange processes can be studied at every car motion stage. Originality.Mathematicalmodelofunsteadyheatexchangeinapassengercarwasimproved. That is why it can be used for the heat engineering studying of the inner car state under various conditions and for the operation of the different life support systems of passenger cars comparison. Mathematicalmodelingofunsteadyheatexchangeinapassengercarwas made by the elementary balance method. Practical value. Created mathematical model gives the possibility to simulate temperature changes in passenger car on unsteady thermal conditions with enough accuracy and to introduce and remove additional elements to the designed model. Thus different
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.
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mathematical models of hysteresis
International Nuclear Information System (INIS)
1998-01-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...
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…
The many faces of the mathematical modeling cycle
Perrenet, J.C.; Zwaneveld, B.
2012-01-01
In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been
Mathematical models in radiogeochronology
International Nuclear Information System (INIS)
Abril, J.M.; Garcia Leon, M.
1991-01-01
The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)
Mathematical modelling a case studies approach
Illner, Reinhard; McCollum, Samantha; Roode, Thea van
2004-01-01
Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...
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.
A mathematical model of a lithium/thionyl chloride primary cell
Evans, T. I.; Nguyen, T. V.; White, R. E.
1987-08-01
A 1-D mathematical model for the lithium/thionyl chloride primary cell was developed to investigate methods of improving its performance and safety. The model includes many of the components of a typical lithium/thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict 1-D, time dependent profiles of concentration, porosity, current, and potential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to determine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to establish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided.
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…
Pyrometer model based on sensor physical structure and thermal operation
International Nuclear Information System (INIS)
Sebastian, Eduardo; Armiens, Carlos; Gomez-Elvira, Javier
2010-01-01
This paper proposes a new simplified thermal model for pyrometers, which takes into account both their internal and external physical structure and operation. The model is experimentally tested on the REMS GTS, an instrument for measuring ground temperature, which is part of the payload of the NASA MSL mission to Mars. The proposed model is based on an energy balance equation that represents the heat fluxes exchanged between sensor elements through radiation, conduction and convection. Despite being mathematically more complex than the more commonly used model, the proposed model makes it possible to design a methodology to compensate the effects of sensor spatial thermal gradients. The paper includes a practical methodology for identifying model constants, which is part of the GTS instrument calibration plan and uses a differential approach to avoid setup errors. Experimental results of the model identification methodology and a target temperature measurement performance after identification has been made are reported. Results demonstrate the good behaviour of the model, with errors below 0.15 deg. C in target temperature estimates.
Mathematical Modeling Approaches in Plant Metabolomics.
Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas
2018-01-01
The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
Modelling of Thermal Hyperemia in the Skin of Type 2 Diabetic Patients
Directory of Open Access Journals (Sweden)
Andrea Bandini
2013-01-01
Full Text Available The microcirculatory response to thermal stimulation involves both an axon reflex and NO-mediated activation. The analysis of the microcirculatory flow following thermal stimulation may therefore enhance the detection of any impairment of the small unmyelinated fibres that are involved in the axon reflex. The aim of this work is to establish a method of non-invasive measurement of small fibre impairment. The microcirculatory flow in response to local heating is measured by using a laser Doppler instrument, and mathematically modelled to extract a set of quantitative parameters. The results confirm that there is a significant difference in the parameters modelling the axon reflex between diabetic and control subjects, while no significant difference is found in the parameters modelling the NO-mediated activation.
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…
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-01-01
This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments
Advanced Stirling Radioisotope Generator (ASRG) Thermal Power Model in MATLAB
Wang, Xiao-Yen, J.
2012-01-01
This paper presents a one-dimensional steady-state mathematical thermal power model of the ASRG. It aims to provide a guideline of understanding how the ASRG works and what can change its performance. The thermal dynamics and energy balance of the generator is explained using the thermal circuit of the ASRG. The Stirling convertor performance map is used to represent the convertor. How the convertor performance map is coupled in the thermal circuit is explained. The ASRG performance characteristics under i) different sink temperatures and ii) over the years of mission (YOM) are predicted using the one-dimensional model. Two Stirling converter control strategies, i) fixing the hot-end of temperature of the convertor by adjusting piston amplitude and ii) fixing the piston amplitude, were tested in the model. Numerical results show that the first control strategy can result in a higher system efficiency than the second control strategy when the ambient gets warmer or the general-purpose heat source (GPHS) fuel load decays over the YOM. The ASRG performance data presented in this paper doesn't pertain to the ASRG flight unit. Some data of the ASRG engineering unit (EU) and flight unit that are available in public domain are used in this paper for the purpose of numerical studies.
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…
Modeling of Thickness and Profile Uniformity of Thermally Sprayed Coatings Deposited on Cylinders
Yanjun, Zhang; Wenbo, Li; Dayu, Li; Jinkun, Xiao; Chao, Zhang
2018-02-01
In thermal spraying processes, kinematic parameters of the robot play a decisive role in the coating thickness and profile. In this regard, some achievements have been made to optimize the spray trajectory on flat surfaces. However, few reports have focused on nonholonomic or variable-curvature cylindrical surfaces. The aim of this study is to investigate the correlation between the coating profile, coating thickness, and scanning step, which is determined by the radius of curvature and scanning angle. A mathematical simulation model was developed to predict the thickness of thermally sprayed coatings. Experiments were performed on cylinders with different radiuses of curvature to evaluate the predictive ability of the model.
Directory of Open Access Journals (Sweden)
Nita Delima
2017-03-01
Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa. Kata Kunci: Comprehensive
Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc
2016-01-01
Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…
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...
Teaching Mathematical Modelling for Earth Sciences via Case Studies
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Rival approaches to mathematical modelling in immunology
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
International Nuclear Information System (INIS)
Yu, W; Choi, S.U.S.
2004-01-01
We previously developed a renovated Maxwell model for the effective thermal conductivity of nanofluids and determined that the solid/liquid interfacial layers play an important role in the enhanced thermal conductivity of nanofluids. However, this renovated Maxwell model is limited to suspensions with spherical particles. Here, we extend the Hamilton--Crosser model for suspensions of nonspherical particles to include the effect of a solid/liquid interface. The solid/liquid interface is described as a confocal ellipsoid with a solid particle. The new model for the three-phase suspensions is mathematically expressed in terms of the equivalent thermal conductivity and equivalent volume fraction of anisotropic complex ellipsoids, as well as an empirical shape factor. With a generalized empirical shape factor, the renovated Hamilton--Crosser model correctly predicts the magnitude of the thermal conductivity of nanotube-in-oil nanofluids. At present, this new model is not able to predict the nonlinear behavior of the nanofluid thermal conductivity
Mathematical manipulative models: in defense of "beanbag biology".
Jungck, John R; Gaff, Holly; Weisstein, Anton E
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
Rostampour Samarin, V.; Bloemendal, J.M.; Keviczky, T.
2017-01-01
This paper presents a complete model of a building heating and cooling equipment and a ground source heat pump (GSHP) coupled with an aquifer thermal energy storage (ATES) system. This model contains detailed
mathematical representations of building thermal dynamics, ATES system dynamics, heat
Mathematical modeling of biomass fuels formation process
International Nuclear Information System (INIS)
Gaska, Krzysztof; Wandrasz, Andrzej J.
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task
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…
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.
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.
Transient thermal hydraulic modeling and analysis of ITER divertor plate system
International Nuclear Information System (INIS)
El-Morshedy, Salah El-Din; Hassanein, Ahmed
2009-01-01
A mathematical model has been developed/updated to simulate the steady state and transient thermal-hydraulics of the International Thermonuclear Experimental Reactor (ITER) divertor module. The model predicts the thermal response of the armour coating, divertor plate structural materials and coolant channels. The selected heat transfer correlations cover all operating conditions of ITER under both normal and off-normal situations. The model also accounts for the melting, vaporization, and solidification of the armour material. The developed model is to provide a quick benchmark of the HEIGHTS multidimensional comprehensive simulation package. The present model divides the coolant channels into a specified axial regions and the divertor plate into a specified radial zones, then a two-dimensional heat conduction calculation is created to predict the temperature distribution for both steady and transient states. The model is benchmarked against experimental data performed at Sandia National Laboratory for both bare and swirl tape coolant channel mockups. The results show very good agreements with the data for steady and transient states. The model is then used to predict the thermal behavior of the ITER plasma facing and structural materials due to plasma instability event where 60 MJ/m 2 plasma energy is deposited over 500 ms. The results for ITER divertor response is analyzed and compared with HEIGHTS results.
Transient thermal hydraulic modeling and analysis of ITER divertor plate system
Energy Technology Data Exchange (ETDEWEB)
El-Morshedy, Salah El-Din [Argonne National Laboratory, Argonne, IL (United States); Atomic Energy Authority, Cairo (Egypt)], E-mail: selmorshedy@etrr2-aea.org.eg; Hassanein, Ahmed [Purdue University, West Lafayette, IN (United States)], E-mail: hassanein@purdue.edu
2009-12-15
A mathematical model has been developed/updated to simulate the steady state and transient thermal-hydraulics of the International Thermonuclear Experimental Reactor (ITER) divertor module. The model predicts the thermal response of the armour coating, divertor plate structural materials and coolant channels. The selected heat transfer correlations cover all operating conditions of ITER under both normal and off-normal situations. The model also accounts for the melting, vaporization, and solidification of the armour material. The developed model is to provide a quick benchmark of the HEIGHTS multidimensional comprehensive simulation package. The present model divides the coolant channels into a specified axial regions and the divertor plate into a specified radial zones, then a two-dimensional heat conduction calculation is created to predict the temperature distribution for both steady and transient states. The model is benchmarked against experimental data performed at Sandia National Laboratory for both bare and swirl tape coolant channel mockups. The results show very good agreements with the data for steady and transient states. The model is then used to predict the thermal behavior of the ITER plasma facing and structural materials due to plasma instability event where 60 MJ/m{sup 2} plasma energy is deposited over 500 ms. The results for ITER divertor response is analyzed and compared with HEIGHTS results.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.
2013-06-01
The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)
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...
Directory of Open Access Journals (Sweden)
M.M. Bhatti
2017-06-01
Full Text Available Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls. Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body
Modelling and Optimizing Mathematics Learning in Children
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
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.
MATHEMATICAL MODELLING OF OPERATION HEAT NETWORKS IN VIEW OF HEAT LOSS
Directory of Open Access Journals (Sweden)
ZBARAZ L. I.
2016-08-01
Full Text Available Goal. In recent years, due to a significant rise in price of energy, the reduction of direct costs for heating becomes a priority. In the utilities especially important to optimization of energy heating system equipment. During transport of thermal energy in the distribution networks thermal losses occur along the length of the hydraulic pipes and the coolant pumping losses. These loss-dependence of the particular distribution network. Changing temperature and the hydraulic regime at the source necessary to achieve the minimum cost of transport for today acting tariffs for energy. Scientific novelty. The studies received law changes head to the source at the qualitative and quantitative methods of regulation. Results. A mathematical model of an extensive network of decentralized heat source heating, which are analyzed using different methods of regulating and found the best.
Fasni, N.; Turmudi, T.; Kusnandi, K.
2017-09-01
This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.
Directory of Open Access Journals (Sweden)
Chong Peng
2015-03-01
Full Text Available Modeling thermal comfort provides quantitative evidence and parameters for effective and efficient urban planning, design, and building construction particularly in a dense and narrow inner city, which has become one of many concerns for sustainable urban development. This paper aims to develop geometric and mathematical models of wind and thermal comfort and use them to examine the impacts of six small-scale renewal strategies on the wind and thermal environment at pedestrian level in Dazhimen neighborhood, Wuhan, which is a typical case study of urban renewal project in a mega-city. The key parameters such as the solar radiation, natural convection, relative humidity, ambient crosswind have been incorporated into the mathematical models by using user-defined-function (UDF method. Detailed temperature and velocity distributions under different strategies have been compared for the optimization of local renewal strategies. It is concluded that five rules generated from the simulation results can provide guidance for building demolition and reconstruction in a neighborhood and there is no need of large-scale demolition. Particularly, combining the local demolition and city virescence can both improve the air ventilation and decrease the temperature level in the study area.
Empirical Validation of a Thermal Model of a Complex Roof Including Phase Change Materials
Directory of Open Access Journals (Sweden)
Stéphane Guichard
2015-12-01
Full Text Available This paper deals with the empirical validation of a building thermal model of a complex roof including a phase change material (PCM. A mathematical model dedicated to PCMs based on the heat apparent capacity method was implemented in a multi-zone building simulation code, the aim being to increase the understanding of the thermal behavior of the whole building with PCM technologies. In order to empirically validate the model, the methodology is based both on numerical and experimental studies. A parametric sensitivity analysis was performed and a set of parameters of the thermal model has been identified for optimization. The use of the generic optimization program called GenOpt® coupled to the building simulation code enabled to determine the set of adequate parameters. We first present the empirical validation methodology and main results of previous work. We then give an overview of GenOpt® and its coupling with the building simulation code. Finally, once the optimization results are obtained, comparisons of the thermal predictions with measurements are found to be acceptable and are presented.
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-04-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
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...
International Nuclear Information System (INIS)
1982-01-01
The progress of the work is reported under the headings: nuclide migration studies (nuclide-rock interactions; physico-chemical effects; field experiments; groundwater dating); mathematical modelling (calculation of steady groundwater flow using NAMMU; comparison of thermally and naturally driven flows near a radioactive waste repository; diffusion of radionuclides into a rock matrix; radionuclide migration). (U.K.)
International Nuclear Information System (INIS)
Eraslan, A.H.
1975-02-01
A far-field mathematical model is presented for numerical simulation of short-time (within tidal cycle) transient, two-dimensional temperature distributions in large coastal and offshore regions resulting from the condenser cooling water discharges of power plants. The Eulerian FLIDE (fluid-in-discrete-element) formulation employs the integral forms of the conservation principles for mass and thermal energy in variable-sized discrete elements that span the specific flow region. The contributions of vertical variations of the velocity components and temperature are rigorously incorporated in the development of depth-averaged, two-dimensional energy transport fluxes by spatially integrating the conservation equations over the enclosure surfaces of the discrete elements. The general mathematical formulation considers completely arbitrary, transient oceanic flow conditions, which include periodic tidal, geostrophic, and wind-induced currents, as locally specified inputs to the model. The thermal impact of a hypothetical, multiunit generating station in a coastal region is analyzed where the oceanic flow conditions are assumed to be strictly periodic tidal currents within any appreciable net drift of sufficient duration to remove the heated effluent. The numerical simulation indicates that the periodic flow conditions cause considerable variations in the temperature distributions during the day and the tidal cycles, which result in severe recirculation and re-entrainment of the heated water between the intakes and the discharges of the different units. This leads to a gradual, long-term increase of the temperatures in the immediate vicinity of the discharge structures and also in the far-field zone. (U.S.)
Differential-discrete mathematical model of two phase flow heat exchanger
International Nuclear Information System (INIS)
Debeljkovic, D.Lj.; Zitek, Pavel; Simeunovic, G.; Inard, Christian
2007-01-01
A dynamic thermal-hydraulic mathematical model of evaporator dynamics of a once - through sub critical steam generator is derived and presented. This model allows the investigation of evaporator dynamics including its transients responses. The evaporator was considered as a part of three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and is described by a set of linearized discrete - difference equations which, with some other algebraic equations, constitutes a closed system of equations possible for exact computer solution. This model has been derived upon the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach has been applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporators dynamics in an extraordinarily simple way. In current literature this approach is sometimes called physical discretization. (author)
Mathematical models and accuracy of radioisotope gauges
International Nuclear Information System (INIS)
Urbanski, P.
1989-01-01
Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)
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…
Scaffolding Mathematical Modelling with a Solution Plan
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
Estimation of thermal conductivity of short pastry biscuit at different baking stages
Cevoli, C.; Fabbri, A.; Marai, S.V.; Ferrari, E.; Guarnieri, A.
2014-01-01
Thermal conductivity of a food material is an essential physical property in mathematical modelling and computer simulation of thermal processing. Effective thermal conductivity of non-homogeneous materials, such as food matrices, can be determined experimentally or mathematically. The aim of the following research was to compare the thermal conductivity of short pastry biscuits, at different baking stages (60-160 min), measured by a line heat source thermal conductivity probe and estimated t...
Quantitative analysis of thermal insulation coatings
DEFF Research Database (Denmark)
Kiil, Søren
2014-01-01
This work concerns the development of simulation tools for mapping of insulation properties of thermal insulation coatings based on selected functional filler materials. A mathematical model, which includes the underlying physics (i.e. thermal conductivity of a heterogeneous two-component coating...
Thermal performance of a PCM thermal storage unit
Energy Technology Data Exchange (ETDEWEB)
Liu Ming; Bruno, Frank; Saman, Wasim [Sustainable Energy Centre, Inst. for Sustainable Systems and Technologies, Univ. of South Australia, Mawson Lakes, Adelaide (Australia)
2008-07-01
The thermal performance of a PCM thermal storage unit (TSU) is studied numerically and experimentally. The TSU under analysis consists of several flat slabs of phase change material (PCM) with melting temperature of -26.7 C. Liquid heat transfer fluid (HTF) passes between the slabs to charge and discharge the storage unit. A one dimensional mathematical model was employed to analyze the transient thermal behavior of the storage unit during the melting and freezing processes. The model takes into consideration the temperature variations in the wall along the flow direction of the HTF. The paper compares the experimental and numerical simulation results in terms of HTF outlet temperatures during the melting period. (orig.)
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
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…
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.
Three-dimensional modelling of thermal stress in floating zone silicon crystal growth
Plate, Matiss; Krauze, Armands; Virbulis, Jānis
2018-05-01
During the growth of large diameter silicon single crystals with the industrial floating zone method, undesirable level of thermal stress in the crystal is easily reached due to the inhomogeneous expansion as the crystal cools down. Shapes of the phase boundaries, temperature field and elastic material properties determine the thermal stress distribution in the solid mono crystalline silicon during cylindrical growth. Excessive stress can lead to fracture, generation of dislocations and altered distribution of intrinsic point defects. Although appearance of ridges on the crystal surface is the decisive factor of a dislocation-free growth, the influence of these ridges on the stress field is not completely clear. Here we present the results of thermal stress analysis for 4” and 5” diameter crystals using a quasi-stationary three dimensional mathematical model including the material anisotropy and the presence of experimentally observed ridges which cannot be addressed with axis-symmetric models. The ridge has a local but relatively strong influence on thermal stress therefore its relation to the origin of fracture is hypothesized. In addition, thermal stresses at the crystal rim are found to increase for a particular position of the crystal radiation reflector.
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…
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...
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.
Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model
Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus
2017-12-01
The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.
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...
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary
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.
Use of mathematical modeling in nuclear measurements projects
International Nuclear Information System (INIS)
Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.
2011-01-01
Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-06-01
This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)
Mathematical Modelling Plant Signalling Networks
Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.
2013-01-01
methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more
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...
Plotnitsky, Arkady
2017-06-01
The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The
FEMME, a flexible environment for mathematically modelling the environment
Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.
2002-01-01
A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model
mathematical models for estimating radio channels utilization
African Journals Online (AJOL)
2017-08-08
Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.
Mančić Marko V.; Živković Dragoljub S.; Milosavljević Peđa M.; Todorović Milena N.
2014-01-01
Buildings with indoor swimming pools have a large energy footprint. The source of major energy loss is the swimming pool hall where air humidity is increased by evaporation from the pool water surface. This increases energy consumption for heating and ventilation of the pool hall, fresh water supply loss and heat demand for pool water heating. In this paper, a mathematical model of the swimming pool was made to assess energy demands of an indoor swimming po...
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...
A time-dependent model to determine the thermal conductivity of a nanofluid
Energy Technology Data Exchange (ETDEWEB)
Myers, T. G., E-mail: tmyers@crm.cat; MacDevette, M. M., E-mail: mmacdevette@crm.cat; Ribera, H. [Centre de Recerca Matematica (Spain)
2013-07-15
In this paper, we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100 nm). Due to the complexity of the standard mathematical analysis of this problem, we employ a well-known approximate solution technique known as the heat balance integral method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately >1 %. The results suggest that the difficulty in reproducing the high values of conductivity observed experimentally may stem from the use of a static heat flow model applied over an infinite domain rather than applying a dynamic model over a finite domain.
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 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.
The simulation of transients in thermal plant. Part I: Mathematical model
International Nuclear Information System (INIS)
Morini, G.L.; Piva, S.
2007-01-01
This paper deals with the simulation of the transient behaviour of thermal plant with control systems. It is always more difficult for a designer to predict the effects on the plant of the control processes because of the increasing complexity of plants and control systems. The easiest way to obtain information about the dynamic behaviour of a thermal plant at the design-stage involves assessing the suitability of specific computer codes. To this end, the present work demonstrates that nowadays it is possible, by using the opportunities offered by some general purpose calculation systems, to obtain such significant information. It is described how a 'thermal-library' of customized blocks (one for each component of a thermal plant such as valves, boilers, and pumps) can be built and used, in an intuitive way, to study any kind of plant. As an example, the dynamic behaviour of a residential heating system will be shown in a companion paper, forming part II of the present article
Directory of Open Access Journals (Sweden)
Orlov Anton S.
2015-01-01
Full Text Available This article investigates electrolyte filtration in the bottom of the aluminum electrolyzer cathode device using the mathematical modeling. Penetration of molten electrolyte in the heat insulation part of the lining is one of the main reasons of electrolyzer premature shutdown, because it leads to bottom destruction and excessive heat loss. This problem is considered a two-phase filtration of incompressible immiscible liquids in an inhomogeneous non-deformable porous body. The verification of the model on the problem of water filtration pin a porous medium has confirmed its adequacy. With the help of the developed mathematical model the dynamics of the impregnation of the lining of the cathode and electrolyte device defined thermal balance baths. Research has identified the speed of penetration of the melt in the bottom of the bath during service of the electrolyzer.
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 model of compact type evaporator
Borovička, Martin; Hyhlík, Tomáš
2018-06-01
In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.
Mathematic Modeling for Vegetal Coal Activation in a Rotating Cylindrical Furnace
Directory of Open Access Journals (Sweden)
Carlos Zalazar-Oliva
2016-05-01
Full Text Available The activation of vegetal coal by applying physical or thermal methods is carried out under an atmosphere containing air, carbon dioxide or water vapor at temperatures ranging from 800 °C and 900 °C. This investigation was completed based on the mathematical modeling for the coal activation process in order to estimate the gas distribution and coal temperatures inside a rotating cylindrical kiln. The model consists of a system of non-lineal differential equations and equations to calculate the temperature of the cylinder internal wall and heat transfer coefficients. The 4th order Runge–Kutta method was used for the calculations. The comparison of the results obtained from modeling gas temperatures in the interior of the cylinder and the experimental data indicated that the variation is insignificant with an error margin below 5 %.
Mathematical modeling of static layer crystallization for propellant grade hydrogen peroxide
Hao, Lin; Chen, Xinghua; Sun, Yaozhou; Liu, Yangyang; Li, Shuai; Zhang, Mengqian
2017-07-01
Hydrogen peroxide (H2O2) is an important raw material widely used in many fields. In this work a mathematical model of heat conduction with a moving boundary was proposed to study the melt crystallization process of hydrogen peroxide which was carried out outside a cylindrical crystallizer. Considering the effects of the temperature of the cooling fluid on the thermal conductivity of crude crystal, the model is an improvement of Guardani's research and can be solved by analytic iteration method. An experiment was designed to measure the thickness of crystal layer with time under different conditions. A series of analysis, including the effects of different refrigerant temperature on crystal growth rate, the effects of different cooling rates on crystal layer growth rate, the effects of crystallization temperature on heat transfer and the model's application scope were conducted based on the comparison between experimental results and simulation results of the model.
Mathematical modelling and TMCP simulation for optimisation of steel behaviour
International Nuclear Information System (INIS)
Siwecki, T.
2001-01-01
Physically based mathematical models for prediction of steel behaviour and microstructure evolution in connection with thermal and thermomechanical controlled processing (TMCP) development in Swedish Institute for Metals Research are discussed. The models can be used for computer predictions of recrystallization and grain growth of austenite after deformation, precipitation or dissolution of microalloying carbonitride in austenite, flow stress during hot working, phase transformation behaviour during accelerated cooling as well as the final microstructure and mechanical properties. The database, which contains information about steel behaviour for a large number of HSLA steels, is also presented. Optimization of TMCP parameters for improving the properties of the steel are discussed in relation to the microstructure and mechanical properties. The effect of TMCP parameters (reheating temperature, rolling schedules and finish rolling temperature as well as accelerated control cooling) on steel properties was studied in laboratory scale. (author)
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
Modeling of Thermal Behavior of Raw Natural Gas Air Coolers
Scherbinin, S. V.; Prakhova, M. Yu; Krasnov, A. N.; Khoroshavina, E. A.
2018-05-01
When gas is being prepared for a long-range transportation, it passes through air cooling units (ACUs) after compressing; there, hot gas passing through finned tubes is cooled with air streams. ACU's mode of operation shall ensure a certain value of gas temperature at the ACU's outlet. At that, when cooling raw gas, temperature distribution along all the tubes shall be known to prevent local hydrate formation. The paper proposes a mathematical model allowing one to obtain a thermal field distribution inside the ACU and study influence of various factors onto it.
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.
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
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...
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.
Directory of Open Access Journals (Sweden)
V. S. Zarubin
2015-01-01
Full Text Available Liquid hydrogen and oxygen are used as the oxidizer and fuel for liquid rocket engines. Liquefied natural gas, which is based on methane, is seen as a promising motor fuel for internal combustion engines. One of the technical problems arising from the use of said cryogenic liquid is to provide containers for storage, transport and use in the propulsion system. In the design and operation of such vessels it is necessary to have reliable information about their temperature condition, on which depend the loss of cryogenic fluids due to evaporation and the stress-strain state of the structural elements of the containers.Uneven temperature distribution along the generatrix of the cylindrical thin-walled shell of rocket cryogenic tanks, in a localized zone of cryogenic liquid level leads to a curvature of the shell and reduce the permissible axle load in a hazard shell buckling in the preparation for the start of the missile in flight with an increasing acceleration. Moving the level of the cryogenic liquid during filling or emptying the tank at a certain combination of parameters results in an increase of the local temperature distribution nonuniformity.Along with experimental study of the shell temperature state of the cryogenic container, methods of mathematical modeling allow to have information needed for designing and testing the construction of cryogenic tanks. In this study a mathematical model is built taking into account features of heat transfer in a cryogenic container, including the boiling cryogenic liquid in the inner surface of the container. This mathematical model describes the temperature state of the thin-walled shell of cylindrical cryogenic tank during filling and emptying. The work also presents a quantitative analysis of this model in case of fixed liquid level, its movement at a constant speed, and harmonic oscillations relative to a middle position. The quantitative analysis of this model has allowed to find the limit options
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 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.
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)
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 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 ...
Directory of Open Access Journals (Sweden)
Andreas Melcher
2016-04-01
Full Text Available The thermal behavior of Li-ion cells is an important safety issue and has to be known under varying thermal conditions. The main objective of this work is to gain a better understanding of the temperature increase within the cell considering different heat sources under specified working conditions. With respect to the governing physical parameters, the major aim is to find out under which thermal conditions a so called Thermal Runaway occurs. Therefore, a mathematical electrochemical-thermal model based on the Newman model has been extended with a simple combustion model from reaction kinetics including various types of heat sources assumed to be based on an Arrhenius law. This model was realized in COMSOL Multiphysics modeling software. First simulations were performed for a cylindrical 18650 cell with a L i C o O 2 -cathode to calculate the temperature increase under two simple electric load profiles and to compute critical system parameters. It has been found that the critical cell temperature T crit , above which a thermal runaway may occur is approximately 400 K , which is near the starting temperature of the decomposition of the Solid-Electrolyte-Interface in the anode at 393 . 15 K . Furthermore, it has been found that a thermal runaway can be described in three main stages.
Structured Mathematical Modeling of Industrial Boiler
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Abdullah Nur Aziz
2014-04-01
Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.
The study of thermal processes in control systems of heat consumption of buildings
Tsynaeva, E.; A, Tsynaeva
2017-11-01
The article discusses the main thermal processes in the automated control systems for heat consumption (ACSHC) of buildings, schematic diagrams of these systems, mathematical models used for description of thermal processes in ACSHC. Conducted verification represented by mathematical models. It was found that the efficiency of the operation of ACSHC depend from the external and internal factors. Numerical study of dynamic modes of operation of ACSHC.
Shi, Wenwu; Pinto, Brian
2017-12-01
Melting and holding molten metals within crucibles accounts for a large portion of total energy demand in the resource-intensive nonferrous foundry industry. Multivariate mathematical modeling aided by detailed material characterization and advancements in crucible technologies can make a significant impact in the areas of cost-efficiency and carbon footprint reduction. Key thermal properties such as conductivity and specific heat capacity were studied to understand their influence on crucible furnace energy consumption during melting and holding processes. The effects of conductivity on thermal stresses and longevity of crucibles were also evaluated. With this information, accurate theoretical models using finite element analysis were developed to study total energy consumption and melting time. By applying these findings to recent crucible developments, considerable improvements in field performance were reported and documented as case studies in applications such as aluminum melting and holding.
Bogdanovich, V. I.; Giorbelidze, M. G.
2018-03-01
A problem of mathematical modelling of powder material motion and transportation in gas thermal flow core has been addressed. Undertaken studies indicate significant impact on dynamics of motion of sprayed particles of phenomenological law for drag coefficient and accounting momentum loss of a plasma jet upon acceleration of these particles and their diameter. It is determined that at great dispersion of spraying particles, they reach detail surface at different velocity and significant particles separation takes place at spraying spot. According to the results of mathematical modelling, requirements for admissible dispersion of diameters of particles used for spraying have been formulated. Research has also allowed reducing separation of particles at the spraying spot due to the selection of the method of powder feed to the anode channel of the plasma torch.
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.
Thermal modelling using discrete vasculature for thermal therapy: a review
Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.
2013-01-01
Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700
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…
Dermol, Janja; Miklavčič, Damijan
2014-12-01
High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation. Copyright © 2014 Elsevier B.V. All rights reserved.
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 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.
In vitro burn model illustrating heat conduction patterns using compressed thermal papers.
Lee, Jun Yong; Jung, Sung-No; Kwon, Ho
2015-01-01
To date, heat conduction from heat sources to tissue has been estimated by complex mathematical modeling. In the present study, we developed an intuitive in vitro skin burn model that illustrates heat conduction patterns inside the skin. This was composed of tightly compressed thermal papers with compression frames. Heat flow through the model left a trace by changing the color of thermal papers. These were digitized and three-dimensionally reconstituted to reproduce the heat conduction patterns in the skin. For standardization, we validated K91HG-CE thermal paper using a printout test and bivariate correlation analysis. We measured the papers' physical properties and calculated the estimated depth of heat conduction using Fourier's equation. Through contact burns of 5, 10, 15, 20, and 30 seconds on porcine skin and our burn model using a heated brass comb, and comparing the burn wound and heat conduction trace, we validated our model. The heat conduction pattern correlation analysis (intraclass correlation coefficient: 0.846, p < 0.001) and the heat conduction depth correlation analysis (intraclass correlation coefficient: 0.93, p < 0.001) showed statistically significant high correlations between the porcine burn wound and our model. Our model showed good correlation with porcine skin burn injury and replicated its heat conduction patterns. © 2014 by the Wound Healing Society.
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 ...
Vibratory gyroscopes : identification of mathematical model from test data
CSIR Research Space (South Africa)
Shatalov, MY
2007-05-01
Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...
Сontrol systems using mathematical models of technological objects ...
African Journals Online (AJOL)
Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...
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…
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…
Mathematical modelling of the process of quality control of construction products
Directory of Open Access Journals (Sweden)
Pogorelov Vadim
2017-01-01
Full Text Available The study presents the results of years of research in the field of quality management of industrial production construction production, based on mathematical modelling techniques, process and results of implementing the developed programme of monitoring and quality control in the production process of the enterprise. The aim of this work is the presentation of scientific community of the practical results of mathematical modelling in application programs. In the course of the research addressed the description of the applied mathematical models, views, practical results of its application in the applied field to assess quality control. The authors used this mathematical model in practice. The article presents the results of applying this model. The authors developed the experimental software management and quality assessment by using mathematical modeling methods. The authors continue research in this direction to improve the diagnostic systems and quality management systems based on mathematical modeling methods prognostic and diagnostic processes.
Mathematical modeling of rainwater runoff over catchment surface ...
African Journals Online (AJOL)
The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...
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…
Ethnophysics, Mathematical Modeling, Geometry... All in the same Manzuá
Directory of Open Access Journals (Sweden)
Ednilson Sergio Ramalho de Souza
2013-06-01
Full Text Available The objective this is paper is to show partial results of research for project of doctorate whose intention is to analyze the Ethnophysics of the amazon fisherman end to develop innovative didactic resources for the conceptual approach in Physics and Mathematics in the classroom of the high school and higher education in environment of Mathematical Modeling. The research question was: How the build the Manzuá can contextualize lessons of Physics and Mathematics in high school? The methodology used was ethnographicresearch. The theoretical foundations were Ethnomathematics (D’AMBROSIO, 2008, Mental Models (JONHSON-LAIRD, 1983, Mathematical Modeling (CHAVES e ESPÍRITO SANTO, 2008 end Conceptual Field ((VERGNAUD, 2007. The initial results suggest which the traditional physical knowledge is strongly related to mental models formed in function long years practice in the construction of the Manzuá end the operational invariants take part in the mental models. The situations lived during the construction of the Manzuá can base situations-problem in the classes of Physics and Mathematics in environment of Mathematical Modeling. We can, therefore, develop didactics resources that relate the traditional knowledge to the school knowledge
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
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)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Matoba, Y. [Sumitomo Metal Industries, Ltd., Osaka (Japan); Otsuka, K.
1998-07-01
A mathematical model and an optimal control system of hot-blast stove process are described. A precise mathematical simulation model of the hot-blast stove was developed and the accuracy of the model has been confirmed. An optimal control system of the thermal conditions of the hot-blast stoves in staggered parallel operation was also developed. By the use of the multivariable optimal regulator and the feedforward compensations for the change of the aimed blast temperature and blast volume, the system is able to control the hot blast temperature and the brick temperature efficiently. The system has been applied to Kashima works. The variations of the blast temperature and the silica brick temperature have been decreased. The ultimate low heat level operations have been realized and the thermal efficiency furthermore has been raised by about 1%. 8 refs., 14 figs., 1 tab.
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.
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 swirled flows in industrial applications
Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.
2018-03-01
Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.
A mathematical model for postirradiation immunity
International Nuclear Information System (INIS)
Smirnova, O.A.
1988-01-01
A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases
Modelling and applications in mathematics education the 14th ICMI study
Galbraith, Peter L; Niss, Mogens
2007-01-01
The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
Hybrid modelling framework by using mathematics-based and information-based methods
International Nuclear Information System (INIS)
Ghaboussi, J; Kim, J; Elnashai, A
2010-01-01
Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.
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...
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 modeling in wound healing, bone regeneration and tissue engineering.
Geris, Liesbet; Gerisch, Alf; Schugart, Richard C
2010-12-01
The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.
Thermal stability and modeling of lithium ion batteries
Botte, Gerardine Gabriela
2000-10-01
First-principles mathematical models were developed to examine the effect of the lithium-lithium ion interactions inside the anode particles on the performance of a lithium foil cell. Two different models were developed: the chemical potential model (CPM) that includes the lithium-lithium ion interactions inside the anode particles and the diffusion model (DIM) that does not include the interactions. Significant differences in the thermal and electrochemical performance of the cell were observed between the two approaches. The temperature of the cell predicted by the DFM is higher than the one predicted by the CPM at a given capacity. The discharge time of the cell predicted by the DFM is shorter than the one predicted by the CPM. The results indicate that the cell needs to be modeled using the CPM approach especially at high discharge rates. An evaluation of the numerical techniques, control volume formulation (CVF) and finite difference method (FDM), used for the models was performed. It is shown that the truncation error is the same for both methods when the boundary conditions are of the Dirichlet type, the system of equations are linear and represented in Cartesian coordinates. A new technique to analyze the accuracy of the methods is presented. The only disadvantage of the FDM is that it failed to conserve mass for a small number of nodes when both boundary conditions include a derivative term whereas the CVF did conserve mass for these cases. However, for a large number of nodes the FDM provides mass conservation. It is important to note that the CVF has only (DeltaX) order of accuracy for a Neumann type boundary condition whereas the FDM has (DeltaX) 2 order. The second topic of this dissertation presents a study of the thermal stability of LiPF6 EC:EMC electrolyte for lithium ion batteries. A differential scanning calorimeter (DSC) was used to perform the study of the electrolyte. For first time, the effect of different variables on its thermal stability
Mathematical modeling of reciprocating pump
International Nuclear Information System (INIS)
Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo
2015-01-01
A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.
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.
Directory of Open Access Journals (Sweden)
Michelle D Leach
Full Text Available Eukaryotic cells have evolved mechanisms to sense and adapt to dynamic environmental changes. Adaptation to thermal insults, in particular, is essential for their survival. The major fungal pathogen of humans, Candida albicans, is obligately associated with warm-blooded animals and hence occupies thermally buffered niches. Yet during its evolution in the host it has retained a bona fide heat shock response whilst other stress responses have diverged significantly. Furthermore the heat shock response is essential for the virulence of C. albicans. With a view to understanding the relevance of this response to infection we have explored the dynamic regulation of thermal adaptation using an integrative systems biology approach. Our mathematical model of thermal regulation, which has been validated experimentally in C. albicans, describes the dynamic autoregulation of the heat shock transcription factor Hsf1 and the essential chaperone protein Hsp90. We have used this model to show that the thermal adaptation system displays perfect adaptation, that it retains a transient molecular memory, and that Hsf1 is activated during thermal transitions that mimic fever. In addition to providing explanations for the evolutionary conservation of the heat shock response in this pathogen and the relevant of this response to infection, our model provides a platform for the analysis of thermal adaptation in other eukaryotic cells.
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
Achilles and the tortoise: Some caveats to mathematical modeling in biology.
Gilbert, Scott F
2018-01-31
Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.
Mathematical 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.
Leśko, Michał; Bujalski, Wojciech
2017-12-01
The aim of this document is to present the topic of modeling district heating systems in order to enable optimization of their operation, with special focus on thermal energy storage in the pipelines. Two mathematical models for simulation of transient behavior of district heating networks have been described, and their results have been compared in a case study. The operational optimization in a DH system, especially if this system is supplied from a combined heat and power plant, is a difficult and complicated task. Finding a global financial optimum requires considering long periods of time and including thermal energy storage possibilities into consideration. One of the most interesting options for thermal energy storage is utilization of thermal inertia of the network itself. This approach requires no additional investment, while providing significant possibilities for heat load shifting. It is not feasible to use full topological models of the networks, comprising thousands of substations and network sections, for the purpose of operational optimization with thermal energy storage, because such models require long calculation times. In order to optimize planned thermal energy storage actions, it is necessary to model the transient behavior of the network in a very simple way - allowing for fast and reliable calculations. Two approaches to building such models have been presented. Both have been tested by comparing the results of simulation of the behavior of the same network. The characteristic features, advantages and disadvantages of both kinds of models have been identified. The results can prove useful for district heating system operators in the near future.
An analytical solution for modeling thermal energy transfer in a confined aquifer system
Shaw-Yang, Yang; Hund-der, Yeh
2008-12-01
A mathematical model is developed for simulating the thermal energy transfer in a confined aquifer with different geological properties in the underlying and overlying rocks. The solutions for temperature distributions in the aquifer, underlying rock, and overlying rock are derived by the Laplace transforms and their corresponding time-domain solutions are evaluated by the modified Crump method. Field data adopted from the literature are used as examples to demonstrate the applicability of the solutions in modeling the heat transfer in an aquifer thermal energy storage (ATES) system. The results show that the aquifer temperature increases with time, injection flow rate, and water temperature. However, the temperature decreases with increasing radial and vertical distances. The heat transfer in the rocks is slow and has an effect on the aquifer temperature only after a long period of injection time. The influence distance depends on the aquifer physical and thermal properties, injection flow rate, and injected water temperature. A larger value of thermal diffusivity or injection flow rate will result in a longer influence distance. The present solution can be used as a tool for designing the heat injection facilities for an ATES system.
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.
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,...
Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories
Kim, Jong S.; Teti, Nicholas M.
2015-01-01
The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earth's magnetosphere as a laboratory to study the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10 (sup -4) pascals (10 (sup -6) torr) and the surrounding temperature achieving -180 degrees Centigrade. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperature versus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDA/FLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 degrees Centigrade of the test data using the standard deviation and mean deviation error
Field studies of submerged-diffuser thermal plumes with comparisons to predictive model results
International Nuclear Information System (INIS)
Frigo, A.A.; Paddock, R.A.; Ditmars, J.D.
1976-01-01
Thermal plumes from submerged discharges of cooling water from two power plants on Lake Michigan were studied. The system for the acquisition of water temperatures and ambient conditions permitted the three-dimensional structure of the plumes to be determined. The Zion Nuclear Power Station has two submerged discharge structures separated by only 94 m. Under conditions of flow from both structures, interaction between the two plumes resulted in larger thermal fields than would be predicted by the superposition of single non-interacting plumes. Maximum temperatures in the near-field region of the plume compared favorably with mathematical model predictions. A comparison of physical-model predictions for the plume at the D. C. Cook Nuclear Plant with prototype measurements indicated good agreement in the near-field region, but differences in the far-field occurred as similitude was not preserved there
Karatas, Ilhan
2014-01-01
This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…
Application of computer mathematical modeling in nuclear well-logging industry
International Nuclear Information System (INIS)
Cai Shaohui
1994-01-01
Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems
Mathematical Modeling Applied to Maritime Security
Center for Homeland Defense and Security
2010-01-01
Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...
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…
Thermal simulation of the magnesium thermal of metallic uranium reduction
International Nuclear Information System (INIS)
Borges, W.A.; Saliba-Silva, A.M.
2008-01-01
Metallic uranium production is vital to fabricate fuel elements for nuclear research reactors and to produce radioisotopes and radiopharmaceuticals. Metallic uranium is got via magnesiothermal reduction of UF 4 . This reaction is carried out inside a closed graphite crucible inserted in a metallic reactor adequately sealed without any outside contact. The assembled set is gradually heated up inside a pit furnace up to reach the reaction ignition temperature (between 600-650 deg C). The optimization of the reactive system depends on the mathematical modeling using simulation by finite elements and computational calculation with specialized programs. In this way, the reactants' thermal behavior is forecast until they reach the ignition temperature. The optimization of the uranium production reaction is based on minimization of thermal losses using better the exo thermal reaction heat. As lower the thermal losses, as higher would be the heat amount to raise the temperature of reaction products. This promotes the adequate melting of uranium and slag, so allowing better metal/slag separation with higher metallic yield. This work shows how the mathematical simulation is made and supplies some preliminary results. (author)
How to Introduce Mathematic Modeling in Industrial Design Education
Langereis, G.R.; Hu, J.; Feijs, L.M.G.; Stillmann, G.A.; Kaiser, G.; Blum, W.B.; Brown, J.P.
2013-01-01
With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this chapter, a model is proposed where conventional education is seen as a process from mathematics to design, while competency driven approaches
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…
Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-01-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…
The mathematics of models for climatology and environment. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Ildefonso Diaz, J. [ed.] [Universidad Complutense de Madrid (Spain). Facultad de Ciencas Matematicas
1997-12-31
This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations.
International Nuclear Information System (INIS)
Bailly, H.W.
1987-01-01
In this work, the thermal behaviour of modular reactors in cases of core heating accidents and the physical phenomena relevant for a release of radioactive materials from HTR fuel elements are explained as far as is necessary for understanding the work. The present mathematical models by which the release of radioactive materials from HTR fuel elements due to diffusion or breaking particles in cases of core heating accidents are also described, examined and evaluated with regard to their applicability to module reactors. The experiments used to verify the mathematical models are also evaluated. The mathematical models are in nearly all cases computer programs, which describe the complicated process of releasing radioactive materials quantitative mathematically. One should point out that these models are constantly being developed further, in line with the increasing amount of knowledge. To conclude the work, proposals are made for improving the certainty of information from experiments and mathematical models to determine the release behaviour of modular reactors. (orig./GL) [de
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 Formulation Requirements and Specifications for the Process Models
Energy Technology Data Exchange (ETDEWEB)
Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.
2010-11-01
naturally generates a suite of conceptual models that span a range of process complexity, potentially coupling hydrological, biogeochemical, geomechanical, and thermal processes. The Platform will use ensembles of these simulations to quantify the associated uncertainty, sensitivity, and risk. The Process Models task within the HPC Simulator focuses on the mathematical descriptions of the relevant physical processes.
Mathematical Formulation Requirements and Specifications for the Process Models
International Nuclear Information System (INIS)
Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.
2010-01-01
generates a suite of conceptual models that span a range of process complexity, potentially coupling hydrological, biogeochemical, geomechanical, and thermal processes. The Platform will use ensembles of these simulations to quantify the associated uncertainty, sensitivity, and risk. The Process Models task within the HPC Simulator focuses on the mathematical descriptions of the relevant physical processes.
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 for Micropiles Embedded in Salt Rock
Directory of Open Access Journals (Sweden)
Rădan (Toader Georgiana
2016-03-01
Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.
A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes
Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.
2018-04-01
Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.
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 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
Thermal physics of gas-thermal coatings formation processes. State of investigations
International Nuclear Information System (INIS)
Fialko, N.M.; Prokopov, V.G.; Meranova, N.O.; Borisov, Yu.S.; Korzhik, V.N.; Sherenkovskaya, G.P.; AN Ukrainskoj SSR, Kiev
1993-01-01
The analysis of state of investigations of gas-thermal coatings formation processes in presented. Classification of approaches to mathematical simulation of thermal phenomena studies is offered. The general characteristics of three main approaches to the analysis of heat transport processes is given. Some problems of mathematical simulation of single particle thermal interaction with solid surface are considered in details. The main physical assumptions are analysed
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...
Directory of Open Access Journals (Sweden)
Hafizh Nizham
2017-12-01
Full Text Available This study is a Quasi Experimental study with the design of The Pretest-Post-Test Non-Equivalent Group Design. Population in this research is all student of class X SHS in South Jakarta. Sampling is done by purposive sampling, to obtain an experimental class and control class. In the experimental class, students learn with Treffinger learning model and control, class learning with conventional learning. This study is also to examine the differences of self-efficacy improvement and students literacy skills, and decreased students' mathematical anxiety. Also, this study also examines the relevance of early mathematical abilities (high, medium, low with improving students' math literacy skills. The instrument used in this research is literacy skill test, self-efficacy scale, mathematical anxiety scale, observation sheet, and student interview. Data were analyzed by t-test, one-way ANOVA, and two lines. From the results of the data, it is found that: (1 The improvement of literacy ability of students who are learned with Treffinger model learning is not significantly higher than students who learn with conventional. (2 The self-efficacy of students who learning with the Treffinger model learning is better than the student that is learning by conventional. (3 The mathematical anxiety of students learning with Treffinger model learning reduces better than students learning with conventional. (4 There is a difference in the improvement of students' mathematical literacy skills learning by learning the Treffinger model and students learning with conventional learning based on early mathematical abilities. (5 Student response to Treffinger model learning is better than students learning with conventional learning. Therefore, learning model Treffinger can be an alternative model of learning to improve students' mathematical literacy skills, and self-efficacy students, and able to reduce mathematical anxiety.
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 models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
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-
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
Technological geological and mathematical models of petroleum stratum
International Nuclear Information System (INIS)
Zhumagulov, B.T.; Monakhov, V.N.
1997-01-01
The comparative analysis of different mathematical methods of petroleum stratum, the limit of their applicability and hydrodynamical analysis of numerical calculation's results is carried out. The problem of adaptation of the mathematical models and the identification of petroleum stratum parameters are considered. (author)
A mathematical framework for agent based models of complex biological networks.
Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2011-07-01
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.
Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.
Velichkin, Vladimir A.; Zavyalov, Vladimir A.
2018-03-01
This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.
PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE
Directory of Open Access Journals (Sweden)
N. V. Andrianov
2006-01-01
Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated
Fire suppression as a thermal implosion
Novozhilov, Vasily
2017-01-01
The present paper discusses the possibility of the thermal implosion scenario. This process would be a reverse of the well known thermal explosion (autoignition) phenomenon. The mechanism for thermal implosion scenario is proposed which involves quick suppression of the turbulent diffusion flame. Classical concept of the thermal explosion is discussed first. Then a possible scenario for the reverse process (thermal implosion) is discussed and illustrated by a relevant mathematical model. Based on the arguments presented in the paper, thermal implosion may be observed as an unstable equilibrium point on the generalized Semenov diagram for turbulent flame, however this hypothesis requires ultimate experimental confirmation.
Numerical modelling of thermal and fluid flow phenomena in the mould channel
Directory of Open Access Journals (Sweden)
L. Sowa
2007-12-01
Full Text Available In the paper, a mathematical and a numerical model of the solidification of a cylindrical slender shaped casting, which take into account the process of filling the mould cavity with molten metal, has been proposed. Pressure and velocity fields were obtained by solving the momentum equations and the continuity equation, while the thermal fields were obtained by solving the heat conduction equation containing the convection term. Next, the numerical analysis of the solidification process of metals alloy in a cylindrical mould channel has been made. In the model one takes into account interdependence the heat transfer and fluid flow phenomena. Coupling of the thermal and fluid flow phenomena has been taken into consideration by the changes of the fluidity function and thermophysical parameters of alloy with respect to the temperature. The influence of the pressure and the temperature of metal pouring on the solid phase growth kinetics were estimated. The problem has been solved by the finite element method.
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
Mathematical models to predict rheological parameters of lateritic hydromixtures
Directory of Open Access Journals (Sweden)
Gabriel Hernández-Ramírez
2017-10-01
Full Text Available The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to the Herschel-Bulkley model for real plastics. In addition, they show that for current operating conditions, even for new situations, UPD mathematical models have a greater ability to predict rheological parameters than least squares mathematical models.
Directory of Open Access Journals (Sweden)
Himmatul Afthina
2017-12-01
Full Text Available The aims of this research to determine the effect of Think Talk Write (TTW and Think Pair Share (TPS model with Realistic Mathematics Education (RME approach viewed from mathematical-logical intelligence. This research employed the quasi experimental research. The population of research was all students of the eight graders of junior high school in Karangamyar Regency in academic year 2016/2017. The result of this research shows that (1 TTW with RME approach gave better mathematics achievement than TPS with RME approach, (2 Students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one, (3 In TTW model with RME approach, students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average and low mathematical-logical intelligence gave same mathematics achievement, and in TPS model with RME approach students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one (4 In each category of mathematical-logical intelligence, TTW with RME approach and TPS with RME approach gave same mathematics achievement.
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.
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
Parallel Boltzmann machines : a mathematical model
Zwietering, P.J.; Aarts, E.H.L.
1991-01-01
A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a
Farag, Mohammed; Sweity, Haitham; Fleckenstein, Matthias; Habibi, Saeid
2017-08-01
Real-time prediction of the battery's core temperature and terminal voltage is very crucial for an accurate battery management system. In this paper, a combined electrochemical, heat generation, and thermal model is developed for large prismatic cells. The proposed model consists of three sub-models, an electrochemical model, heat generation model, and thermal model which are coupled together in an iterative fashion through physicochemical temperature dependent parameters. The proposed parameterization cycles identify the sub-models' parameters separately by exciting the battery under isothermal and non-isothermal operating conditions. The proposed combined model structure shows accurate terminal voltage and core temperature prediction at various operating conditions while maintaining a simple mathematical structure, making it ideal for real-time BMS applications. Finally, the model is validated against both isothermal and non-isothermal drive cycles, covering a broad range of C-rates, and temperature ranges [-25 °C to 45 °C].
Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J
2016-01-01
Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...
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.…
Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.
Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael
2016-11-01
Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.
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...
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 Mathematical Approach to Establishing Constitutive Models for Geomaterials
Directory of Open Access Journals (Sweden)
Guang-hua Yang
2013-01-01
Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.
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.
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.
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.
Turbofan engine mathematic model for its static and dynamic characteristics research
Directory of Open Access Journals (Sweden)
О.Є. Карпов
2004-01-01
Full Text Available Demands to mathematical model of the turbofan engine are determined in the article. The mathematical model is used for calculations static and dynamic parameters, which are required for estimation of engine technical state in operation. There are the mathematical model of the turbofan engine AИ-25 and the results of calculations static and dynamic parameters at initial condition in the article.
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)
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)
1997-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Human Thermal Model Evaluation Using the JSC Human Thermal Database
Bue, Grant; Makinen, Janice; Cognata, Thomas
2012-01-01
Human thermal modeling has considerable long term utility to human space flight. Such models provide a tool to predict crew survivability in support of vehicle design and to evaluate crew response in untested space environments. It is to the benefit of any such model not only to collect relevant experimental data to correlate it against, but also to maintain an experimental standard or benchmark for future development in a readily and rapidly searchable and software accessible format. The Human thermal database project is intended to do just so; to collect relevant data from literature and experimentation and to store the data in a database structure for immediate and future use as a benchmark to judge human thermal models against, in identifying model strengths and weakness, to support model development and improve correlation, and to statistically quantify a model s predictive quality. The human thermal database developed at the Johnson Space Center (JSC) is intended to evaluate a set of widely used human thermal models. This set includes the Wissler human thermal model, a model that has been widely used to predict the human thermoregulatory response to a variety of cold and hot environments. These models are statistically compared to the current database, which contains experiments of human subjects primarily in air from a literature survey ranging between 1953 and 2004 and from a suited experiment recently performed by the authors, for a quantitative study of relative strength and predictive quality of the models.
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...
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 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.
Aspects of Mathematical Modelling Applications in Science, Medicine, Economics and Management
Hosking, Roger J
2008-01-01
The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Jaworski, Maciej; Łapka, Piotr; Furmański, Piotr
2014-01-01
Highlights: • A new concept of heat storage in ventilation ducts is described. • Ceiling panel as a part of ventilation system is made of a composite with PCM. • A set-up for experimental investigation of heat storage unit was built. • Numerical model of heat transfer in the storage unit was developed. • Numerical code was validated on the base of experimental measurements. - Abstract: Objective: The paper presents a new concept of building integrated thermal energy storage unit and novel mathematical and numerical models of its operation. This building element is made of gypsum based composite with microencapsulated PCM. The proposed heat storage unit has a form of a ceiling panel with internal channels and is, by assumption, incorporated in a ventilation system. Its task is to reduce daily variations of ambient air temperature through the absorption (and subsequent release) of heat in PCM, without additional consumption of energy. Methods: The operation of the ceiling panel was investigated experimentally on a special set-up equipped with temperature sensors, air flow meter and air temperature control system. Mathematical and numerical models of heat transfer and fluid flow in the panel account for air flow in the panel as well as real thermal properties of the PCM composite, i.e.: thermal conductivity variation with temperature and hysteresis of enthalpy vs. temperature curves for heating and cooling. Proposed novel numerical simulator consists of two strongly coupled sub models: the first one – 1D – which deals with air flowing through the U-shaped channel and the second one – 3D – which deals with heat transfer in the body of the panel. Results: Spatial and temporal air temperature variations, measured on the experimental set-up, were used to validate numerical model as well as to get knowledge of thermal performance of the panel operating in different conditions. Conclusion: Preliminary results of experimental tests confirmed the ability of
Ordinary Mathematical Models in Calculating the Aviation GTE Parameters
Directory of Open Access Journals (Sweden)
E. A. Khoreva
2017-01-01
Full Text Available The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc. enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.
ANALYSIS OF NON-FOURIER THERMAL BEHAVIOUR FOR MULTI-LAYER SKIN MODEL
Directory of Open Access Journals (Sweden)
Kuo-Chi Liu
2011-01-01
Full Text Available This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.
Potential of mathematical modeling in fruit quality
African Journals Online (AJOL)
ONOS
2010-01-18
Jan 18, 2010 ... successful mathematical model, the modeler needs to chose what .... equations. In the SUCROS models, the rate of CO2 assimilation is .... insect ecology. ... García y García A, Ingram KT, Hatch U, Hoogenboom G, Jones JW,.
Mathematical modeling of cancer metabolism.
Medina, Miguel Ángel
2018-04-01
Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.
Thermal fatigue. Materials modelling
International Nuclear Information System (INIS)
Siegele, D.; Fingerhuth, J.; Mrovec, M.
2012-01-01
In the framework of the ongoing joint research project 'Thermal Fatigue - Basics of the system-, outflow- and material-characteristics of piping under thermal fatigue' funded by the German Federal Ministry of Education and Research (BMBF) fundamental numerical and experimental investigations on the material behavior under transient thermal-mechanical stress conditions (high cycle fatigue V HCF and low cycle fatigue - LCF) are carried out. The primary objective of the research is the further development of simulation methods applied in safety evaluations of nuclear power plant components. In this context the modeling of crack initiation and growth inside the material structure induced by varying thermal loads are of particular interest. Therefore, three scientific working groups organized in three sub-projects of the joint research project are dealing with numerical modeling and simulation at different levels ranging from atomistic to micromechanics and continuum mechanics, and in addition corresponding experimental data for the validation of the numerical results and identification of the parameters of the associated material models are provided. The present contribution is focused on the development and experimental validation of material models and methods to characterize the damage evolution and the life cycle assessment as a result of thermal cyclic loading. The individual purposes of the subprojects are as following: - Material characterization, Influence of temperature and surface roughness on fatigue endurances, biaxial thermo-mechanical behavior, experiments on structural behavior of cruciform specimens and scatter band analysis (IfW Darmstadt) - Life cycle assessment with micromechanical material models (MPA Stuttgart) - Life cycle assessment with atomistic and damage-mechanical material models associated with material tests under thermal fatigue (Fraunhofer IWM, Freiburg) - Simulation of fatigue crack growth, opening and closure of a short crack under
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...
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
Modelling and simulation of thermal power plants
Energy Technology Data Exchange (ETDEWEB)
Eborn, J.
1998-02-01
Mathematical modelling and simulation are important tools when dealing with engineering systems that today are becoming increasingly more complex. Integrated production and recycling of materials are trends that give rise to heterogenous systems, which are difficult to handle within one area of expertise. Model libraries are an excellent way to package engineering knowledge of systems and units to be reused by those who are not experts in modelling. Many commercial packages provide good model libraries, but they are usually domain-specific and closed. Heterogenous, multi-domain systems requires open model libraries written in general purpose modelling languages. This thesis describes a model database for thermal power plants written in the object-oriented modelling language OMOLA. The models are based on first principles. Subunits describe volumes with pressure and enthalpy dynamics and flows of heat or different media. The subunits are used to build basic units such as pumps, valves and heat exchangers which can be used to build system models. Several applications are described; a heat recovery steam generator, equipment for juice blending, steam generation in a sulphuric acid plant and a condensing steam plate heat exchanger. Model libraries for industrial use must be validated against measured data. The thesis describes how parameter estimation methods can be used for model validation. Results from a case-study on parameter optimization of a non-linear drum boiler model show how the technique can be used 32 refs, 21 figs
Mathematical model of polyethylene pipe bending stress state
Serebrennikov, Anatoly; Serebrennikov, Daniil
2018-03-01
Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.
Modelling as a foundation for academic forming in mathematics education
Perrenet, J.C.; Morsche, ter H.G.
2004-01-01
The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students
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 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.
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 Modeling of Biofilm Structures Using COMSTAT Data
DEFF Research Database (Denmark)
Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.
2017-01-01
Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...
Mathematics for plasma physics; Mathematiques pour la physique des plasmas
Energy Technology Data Exchange (ETDEWEB)
Sentis, R. [CEA Bruyeres-le-Chatel, 91 (France)
2011-01-15
The plasma physics is in the heart of the research of the CEA-DAM. Using mathematics in this domain is necessary, particularly for a precise statement of the partial differential equations systems which are on the basis of the numerical simulations. Examples are given concerning hydrodynamics, models for the thermal conduction and laser-plasma interaction. For the bi-temperature compressible Euler model, the mathematical study of the problem has allowed us to understand why the role of the energy equations dealing with ions on one hand and electrons on the other hand are not identical despite the symmetrical appearance of the system. The mathematical study is also necessary to be sure of the existence and uniqueness of the solution
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...
Mathematical model for solid fuel combustion in fluidized bed
International Nuclear Information System (INIS)
Kostikj, Zvonimir; Noshpal, Aleksandar
1994-01-01
A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)
Thermal conductivity model for nanofiber networks
Zhao, Xinpeng; Huang, Congliang; Liu, Qingkun; Smalyukh, Ivan I.; Yang, Ronggui
2018-02-01
Understanding thermal transport in nanofiber networks is essential for their applications in thermal management, which are used extensively as mechanically sturdy thermal insulation or high thermal conductivity materials. In this study, using the statistical theory and Fourier's law of heat conduction while accounting for both the inter-fiber contact thermal resistance and the intrinsic thermal resistance of nanofibers, an analytical model is developed to predict the thermal conductivity of nanofiber networks as a function of their geometric and thermal properties. A scaling relation between the thermal conductivity and the geometric properties including volume fraction and nanofiber length of the network is revealed. This model agrees well with both numerical simulations and experimental measurements found in the literature. This model may prove useful in analyzing the experimental results and designing nanofiber networks for both high and low thermal conductivity applications.
Thermal conductivity model for nanofiber networks
Energy Technology Data Exchange (ETDEWEB)
Zhao, Xinpeng [Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA; Huang, Congliang [Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA; School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou 221116, China; Liu, Qingkun [Department of Physics, University of Colorado, Boulder, Colorado 80309, USA; Smalyukh, Ivan I. [Department of Physics, University of Colorado, Boulder, Colorado 80309, USA; Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA; Yang, Ronggui [Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA; Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA; Buildings and Thermal Systems Center, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
2018-02-28
Understanding thermal transport in nanofiber networks is essential for their applications in thermal management, which are used extensively as mechanically sturdy thermal insulation or high thermal conductivity materials. In this study, using the statistical theory and Fourier's law of heat conduction while accounting for both the inter-fiber contact thermal resistance and the intrinsic thermal resistance of nanofibers, an analytical model is developed to predict the thermal conductivity of nanofiber networks as a function of their geometric and thermal properties. A scaling relation between the thermal conductivity and the geometric properties including volume fraction and nanofiber length of the network is revealed. This model agrees well with both numerical simulations and experimental measurements found in the literature. This model may prove useful in analyzing the experimental results and designing nanofiber networks for both high and low thermal conductivity applications.
DEFF Research Database (Denmark)
Bahman, Amir Sajjad; Ma, Ke; Blaabjerg, Frede
2018-01-01
Detailed thermal dynamics of high power IGBT modules are important information for the reliability analysis and thermal design of power electronic systems. However, the existing thermal models have their limits to correctly predict these complicated thermal behavior in the IGBTs: The typically used...... thermal model based on one-dimensional RC lumps have limits to provide temperature distributions inside the device, moreover some variable factors in the real-field applications like the cooling and heating conditions of the converter cannot be adapted. On the other hand, the more advanced three......-dimensional thermal models based on Finite Element Method (FEM) need massive computations, which make the long-term thermal dynamics difficult to calculate. In this paper, a new lumped three-dimensional thermal model is proposed, which can be easily characterized from FEM simulations and can acquire the critical...
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…
The role of mathematical models in the optimization of radiopharmaceutical therapy
International Nuclear Information System (INIS)
Divgi, C.
2001-01-01
Mathematical models have been used in radiopharmaceutical therapy for over five decades. These have served to determine the amount of radioactivity required to treat disease, as in the therapy of hyperthyroidism with iodine-131, or, more frequently, to determine the largest amount of radioactivity that can be safely administered. Mathematical models are especially useful in the determination of fractionated radiopharmaceutical therapy. This review will briefly outline the historical development and current utility of mathematical models in radiopharmaceutical therapy, including thyroid disorders and radioimmunotherapy; and describe the potential of modeling in fractionated therapy. The extended application of such models to currently used radiopharmaceutical therapy based on indices of body mass or surface area, to alleviate toxicity and increase radiation dose to tumour, will be proposed. Finally, future applications of mathematical models in radiopharmaceutical therapy will be outlined. (author)
Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience
Charpin, J. P. F.; O'Hara, S.; Mackey, D.
2013-01-01
In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…
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.
Comparison of learning models based on mathematics logical intelligence in affective domain
Widayanto, Arif; Pratiwi, Hasih; Mardiyana
2018-04-01
The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.
International Nuclear Information System (INIS)
Mistry, N.S.; Carlton, D.; Storer, G.
1992-01-01
This report concerns the mathematical modelling by the finite element method of the behaviour of concrete, one of the candidate materials for use in the backfilling and scaling of underground repositories for radioactive waste. In order to act as an assured physical barrier to ground water migration in the vicinity of the waste packages, a concrete backfill must remain intact and free from cracks. One of the risk periods during which mass concrete is susceptible to cracking is during the early days after casting when concrete undergoes rapid changes in internal temperatures and mechanical properties, including, most obviously, strength. Existing commercially available finite element codes do not have a model for concrete that can adequately represent these early age characteristics. The present study, therefore, is predominantly concerned with the development of a mathematical model for use within the ADINA finite element code to predict the time-dependent performance of concrete as a backfilling and sealing material. The evaluation of creep and shrinkage strains is based on the CEB-FIP Model Code together with Illston's approach to delayed and transitional thermal strains. The finite element material model developed is general and could be applied to various types of structure and loading. The model accounts for the ageing of concrete, multi-axial creep and creep recovery, the effect of external environmental humidity and changing internal temperatures. 32 refs., 31 figs., 1 tab
Directory of Open Access Journals (Sweden)
Dinh An Nguyen
2012-07-01
Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.
Mathematical and numerical models for eddy currents and magnetostatics with selected applications
Rappaz, Jacques
2013-01-01
This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problem
International Nuclear Information System (INIS)
Yang, Weihong; Blasiak, Wlodzimierz
2005-01-01
A study of the mathematical modelling of NO formation and emissions in a gas-fired regenerative furnace with high-preheated air was performed. The model of NO formation via N 2 O-intermediate mechanism was proposed because of the lower flame temperature in this case. The reaction rates of this new model were calculated basing on the eddy-dissipation-concept. This model accompanied with thermal-NO, prompt-NO and NO reburning models were used to predict NO emissions and formations. The sensitivity of the furnace temperature and the oxygen availability on NO generation rate has been investigated. The predicted results were compared with experimental values. The results show that NO emission formed by N 2 O-intermediate mechanism is of outstanding importance during the high-temperature air combustion (HiTAC) condition. Furthermore, it shows that NO models with N 2 O-route model can give more reasonable profile of NO formation. Additionally, increasing excess air ratio leads to increasing of NO emission in the regenerative furnace. (author)
Mathematical Modeling in Population Dynamics: The Case of Single ...
African Journals Online (AJOL)
kofimereku
Department of Mathematics, Kwame Nkrumah University of Science and Technology,. Kumasi, Ghana ... The trust of this paper is the application of mathematical models in helping to ..... Statistics and Computing, New York: Wiley. Cox, C.B and ...
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).
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.
Mathematical modeling of infectious disease dynamics
Siettos, Constantinos I.; Russo, Lucia
2013-01-01
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814
Directory of Open Access Journals (Sweden)
Melike TURAL SÖNMEZ
2017-12-01
Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide
Mathematical modeling of the mixing zone for getting bimetallic compound
Energy Technology Data Exchange (ETDEWEB)
Kim, Stanislav L. [Institute of Applied Mechanics, Ural Branch, Izhevsk (Russian Federation)
2011-07-01
A mathematical model of the formation of atomic bonds in metals and alloys, based on the electrostatic interaction between the outer electron shells of atoms of chemical elements. Key words: mathematical model, the interatomic bonds, the electron shell of atoms, the potential, the electron density, bimetallic compound.
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.
Modeling eBook acceptance: A study on mathematics teachers
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
Mathematical supply-chain modelling: Product analysis of cost and time
International Nuclear Information System (INIS)
Easters, D J
2014-01-01
Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management
Mathematical supply-chain modelling: Product analysis of cost and time
Easters, D. J.
2014-03-01
Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.
A three-dimensional thermal and electromagnetic model of whole limb heating with a MAPA.
Charny, C K; Levin, R L
1991-10-01
Previous studies by the authors have shown that if properly implemented, the Pennes assumptions can be applied to quantify bioheat transfer during extremity heating. Given its relative numerical simplicity and its ability to predict temperatures in thermoregulated tissue, the Pennes model of bioheat transfer was utilized in a three-dimensional thermal model of limb heating. While the arterial blood temperature was assumed to be radially uniform within a cross section of the limb, axial gradients in the arterial and venous blood temperatures were computed with this three-dimensional model. A realistically shaped, three-dimensional finite element model of a tumor-bearing human lower leg was constructed and was "attached" mathematically to the whole body thermal model of man described in previous studies by the authors. The central as well as local thermoregulatory feedback control mechanisms which determine blood perfusion to the various tissues and rate of evaporation by sweating were input into the limb model. In addition, the temperature of the arterial blood which feeds into the most proximal section of the lower leg was computed by the whole body thermal model. The variations in the shape of the tissues which comprise the limb were obtained from computerized tomography scans. Axial variations in the energy deposition patterns along the length of the limb exposed to a miniannular phased array (MAPA) applicator were also input into this model of limb heating. Results indicate that proper positioning of the limb relative to the MAPA is a significant factor in determining the effectiveness of the treatment. A patient-specific hyperthermia protocol can be designed using this coupled electromagnetic and thermal model.
International Nuclear Information System (INIS)
Begum, N.N.; Ahmed, J.
2006-01-01
A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)
short communication mathematical modelling for magnetite
African Journals Online (AJOL)
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The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.
Coman, Paul T.; Rayman, Sean; White, Ralph E.
2016-03-01
This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary Differential Equations) describing reaction rates and electrochemical reactions, as well as the isentropic flow equations for describing electrolyte venting. The results are validated against experimental findings from Golubkov et al. [1] [Andrey W. Golubkov, David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph Stangl, Gisela Fauler, Gernot Voitice Alexander Thaler and Viktor Hacker, RSC Advances, 4:3633-3642, 2014] for two cases - with flow and without flow. The results show that if the isentropic flow equations are not included in the model, the thermal runaway is triggered prematurely at the point where venting should occur. This shows that the heat dissipation due to ejection of electrolyte and jelly roll contents has a significant contribution. When the flow equations are included, the model shows good agreement with the experiment and therefore proving the importance of including venting.
Outlooks for mathematical modelling of the glass melting process
Energy Technology Data Exchange (ETDEWEB)
Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)
1997-12-31
Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.
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.
The prediction of epidemics through mathematical modeling.
Schaus, Catherine
2014-01-01
Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.
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
Statistical modeling of an integrated boiler for coal fired thermal power plant
Directory of Open Access Journals (Sweden)
Sreepradha Chandrasekharan
2017-06-01
Full Text Available The coal fired thermal power plants plays major role in the power production in the world as they are available in abundance. Many of the existing power plants are based on the subcritical technology which can produce power with the efficiency of around 33%. But the newer plants are built on either supercritical or ultra-supercritical technology whose efficiency can be up to 50%. Main objective of the work is to enhance the efficiency of the existing subcritical power plants to compensate for the increasing demand. For achieving the objective, the statistical modeling of the boiler units such as economizer, drum and the superheater are initially carried out. The effectiveness of the developed models is tested using analysis methods like R2 analysis and ANOVA (Analysis of Variance. The dependability of the process variable (temperature on different manipulated variables is analyzed in the paper. Validations of the model are provided with their error analysis. Response surface methodology (RSM supported by DOE (design of experiments are implemented to optimize the operating parameters. Individual models along with the integrated model are used to study and design the predictive control of the coal-fired thermal power plant. Keywords: Chemical engineering, Applied mathematics
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 human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Hobiny, Aatef D.; Abbas, Ibrahim A.
2018-01-01
The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.
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.
Mathematical model of three winding auto transformer
International Nuclear Information System (INIS)
Volcko, V.; Eleschova, Z.; Belan, A.; Janiga, P.
2012-01-01
This article deals with the design of mathematical model of three-winding auto transformer for steady state analyses. The article is focused on model simplicity for the purposes of the use in complex transmission systems and authenticity of the model taking into account different types of step-voltage regulator. (Authors)
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 ...
RADYN Simulations of Non-thermal and Thermal Models of Ellerman Bombs
Energy Technology Data Exchange (ETDEWEB)
Hong, Jie; Ding, M. D. [School of Astronomy and Space Science, Nanjing University, Nanjing 210023 (China); Carlsson, Mats, E-mail: dmd@nju.edu.cn [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo (Norway)
2017-08-20
Ellerman bombs (EBs) are brightenings in the H α line wings that are believed to be caused by magnetic reconnection in the lower atmosphere. To study the response and evolution of the chromospheric line profiles, we perform radiative hydrodynamic simulations of EBs using both non-thermal and thermal models. Overall, these models can generate line profiles that are similar to observations. However, in non-thermal models we find dimming in the H α line wings and continuum when the heating begins, while for the thermal models dimming occurs only in the H α line core, and with a longer lifetime. This difference in line profiles can be used to determine whether an EB is dominated by non-thermal heating or thermal heating. In our simulations, if a higher heating rate is applied, then the H α line will be unrealistically strong and there are still no clear UV burst signatures.
RADYN Simulations of Non-thermal and Thermal Models of Ellerman Bombs
Hong, Jie; Carlsson, Mats; Ding, M. D.
2017-08-01
Ellerman bombs (EBs) are brightenings in the Hα line wings that are believed to be caused by magnetic reconnection in the lower atmosphere. To study the response and evolution of the chromospheric line profiles, we perform radiative hydrodynamic simulations of EBs using both non-thermal and thermal models. Overall, these models can generate line profiles that are similar to observations. However, in non-thermal models we find dimming in the Hα line wings and continuum when the heating begins, while for the thermal models dimming occurs only in the Hα line core, and with a longer lifetime. This difference in line profiles can be used to determine whether an EB is dominated by non-thermal heating or thermal heating. In our simulations, if a higher heating rate is applied, then the Hα line will be unrealistically strong and there are still no clear UV burst signatures.
Parental modelling of mathematical affect: self-efficacy and emotional arousal
Bartley, Sarah R.; Ingram, Naomi
2017-12-01
This study explored the relationship between parents' mathematics self-efficacy and emotional arousal to mathematics and their 12- and 13-year-old children's mathematics self-efficacy and emotional arousal to mathematics. Parental modelling of affective relationships during homework was a focus. Eighty-four parent and child pairings from seven schools in New Zealand were examined using embedded design methodology. No significant correlations were found when the parents' mathematics self-efficacy and emotional arousal to mathematics were compared with the children's mathematics self-efficacy and emotional arousal to mathematics. However, the parents' level of emotional arousal to mathematics was found to have affected their willingness to assist with mathematics homework. For those parents who assisted, a significant positive correlation was found between their mathematics self-efficacy and their children's emotional arousal to mathematics. Parents who did assist were generally reported as being calm, and used techniques associated with positive engagement. Fathers were calmer and more likely to express readiness to assist with mathematics homework than mothers. A further significant positive correlation was found between fathers' emotional arousal to mathematics and children's mathematics self-efficacy. Implications from the study suggest directions for future research.
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
Modeling and Optimization of the Medium-Term Units Commitment of Thermal Power
Directory of Open Access Journals (Sweden)
Shengli Liao
2015-11-01
Full Text Available Coal-fired thermal power plants, which represent the largest proportion of China’s electric power system, are very sluggish in responding to power system load demands. Thus, a reasonable and feasible scheme for the medium-term optimal commitment of thermal units (MOCTU can ensure that the generation process runs smoothly and minimizes the start-up and shut-down times of thermal units. In this paper, based on the real-world and practical demands of power dispatch centers in China, a flexible mathematical model for MOCTU that uses equal utilization hours for the installed capacity of all thermal power plants as the optimization goal and that considers the award hours for MOCTU is developed. MOCTU is a unit commitment (UC problem with characteristics of large-scale, high dimensions and nonlinearity. For optimization, an improved progressive optimality algorithm (IPOA offering the advantages of POA is adopted to overcome the drawback of POA of easily falling into the local optima. In the optimization process, strategies of system operating capacity equalization and single station operating peak combination are introduced to move the target solution from the boundary constraints along the target isopleths into the feasible solution’s interior to guarantee the global optima. The results of a case study consisting of nine thermal power plants with 27 units show that the presented algorithm can obtain an optimal solution and is competent in solving the MOCTU with high efficiency and accuracy as well as that the developed simulation model can be applied to practical engineering needs.
Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling
Gould, Heather; Wasserman, Nicholas H.
2014-01-01
With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…
Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry
Jacobs, Gerrie J.; Durandt, Rina
2017-01-01
This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2003-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR). This study involved mathematical modeling of CANDU-PHWR to study its thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique. The reactor model includes the neutronic, reactivity, and fuel channel heat transfer. The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and the reactivity feed back due to the changes in the fuel temperature and coolant temperature. The CANDU-PHWR model was coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
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...
Local Stability Analysis of an Infection-Age Mathematical Model for ...
African Journals Online (AJOL)
Timothy
1Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, Makurdi, ... ABSTRACT: An infection age structured mathematical model for tuberculosis disease ...... its applications to optimal vaccination strategies.
Cooking Potatoes: Experimentation and Mathematical Modeling.
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
A Mathematical Model, Implementation and Study of a Swarm System
Varghese, Blesson; McKee, Gerard
2013-01-01
The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...
Edwin Musdi
2016-01-01
This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...
Energy Technology Data Exchange (ETDEWEB)
Sundberg, Jan; Wrafter, John; Laendell, Maerta (Geo Innova AB (Sweden)); Back, Paer-Erik; Rosen, Lars (Sweco AB (Sweden))
2008-11-15
This report present the results of thermal modelling work for the Forsmark area carried out during modelling stage 2.3. The work complements the main modelling efforts carried out during modelling stage 2.2. A revised spatial statistical description of the rock mass thermal conductivity for rock domain RFM045 is the main result of this work. Thermal modelling of domain RFM045 in Forsmark model stage 2.2 gave lower tail percentiles of thermal conductivity that were considered to be conservatively low due to the way amphibolite, the rock type with the lowest thermal conductivity, was modelled. New and previously available borehole data are used as the basis for revised stochastic geological simulations of domain RFM045. By defining two distinct thermal subdomains, these simulations have succeeded in capturing more of the lithological heterogeneity present. The resulting thermal model for rock domain RFM045 is, therefore, considered to be more realistic and reliable than that presented in model stage 2.2. The main conclusions of modelling efforts in model stage 2.3 are: - Thermal modelling indicates a mean thermal conductivity for domain RFM045 at the 5 m scale of 3.56 W/(mK). This is slightly higher than the value of 3.49 W/(mK) derived in model stage 2.2. - The variance decreases and the lower tail percentiles increase as the scale of observation increases from 1 to 5 m. Best estimates of the 0.1 percentile of thermal conductivity for domain RFM045 are 2.24 W/(mK) for the 1 m scale and 2.36 W/(mK) for the 5 m scale. This can be compared with corresponding values for domain RFM029 of 2.30 W/(mK) for the 1 m scale and 2.87 W/(mK)for the 5 m scale. - The reason for the pronounced lower tail in the thermal conductivity distribution for domain RFM045 is the presence of large bodies of the low-conductive amphibolite. - The modelling results for domain RFM029 presented in model stage 2.2 are still applicable. - As temperature increases, the thermal conductivity decreases
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 of Column-Base Connections under Monotonic Loading
Directory of Open Access Journals (Sweden)
Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
Science modelling in pre-calculus: how to make mathematics problems contextually meaningful
Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen
2011-04-01
'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization
Mathematical Model for the Control of measles 1*PETER, OJ ...
African Journals Online (AJOL)
PROF HORSFALL
2018-04-16
Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.
Klein, Cornel; Rumpe, Bernhard; Broy, Manfred
2014-01-01
In the SysLab project we develop a software engineering method based on a mathematical foundation. The SysLab system model serves as an abstract mathematical model for information systems and their components. It is used to formalize the semantics of all used description techniques such as object diagrams state automata sequence charts or data-flow diagrams. Based on the requirements for such a reference model, we define the system model including its different views and their relationships.
SOME TRENDS IN MATHEMATICAL MODELING FOR BIOTECHNOLOGY
Directory of Open Access Journals (Sweden)
O. M. Klyuchko
2018-02-01
Full Text Available The purpose of present research is to demonstrate some trends of development of modeling methods for biotechnology according to contemporary achievements in science and technique. At the beginning the general approaches are outlined, some types of classifications of modeling methods are observed. The role of mathematic methods modeling for biotechnology in present époque of information computer technologies intensive development is studied and appropriate scheme of interrelation of all these spheres is proposed. Further case studies are suggested: some mathematic models in three different spaces (1D, 2D, 3D models are described for processes in living objects of different levels of hierarchic organization. In course of this the main attention was paid to some processes modeling in neurons as well as in their aggregates of different forms, including glioma cell masses (1D, 2D, 3D brain processes models. Starting from the models that have only theoretical importance for today, we describe at the end a model which application may be important for the practice. The work was done after the analysis of approximately 250 current publications in fields of biotechnology, including the authors’ original works.
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.
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.
Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program
DEFF Research Database (Denmark)
Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni
2018-01-01
Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...
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 modeling of optical glazing performance
Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.
1994-01-01
Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like
Introduction to mathematical models and methods
Energy Technology Data Exchange (ETDEWEB)
Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
Performance study of heat-pipe solar photovoltaic/thermal heat pump system
International Nuclear Information System (INIS)
Chen, Hongbing; Zhang, Lei; Jie, Pengfei; Xiong, Yaxuan; Xu, Peng; Zhai, Huixing
2017-01-01
Highlights: • The testing device of HPS PV/T heat pump system was established by a finished product of PV panel. • A detailed mathematical model of heat pump was established to investigate the performance of each component. • The dynamic and static method was combined to solve the mathematical model of HPS PV/T heat pump system. • The HPS PV/T heat pump system was optimized by the mathematical model. • The influence of six factors on the performance of HPS PV/T heat pump system was analyzed. - Abstract: A heat-pipe solar (HPS) photovoltaic/thermal (PV/T) heat pump system, combining HPS PV/T collector with heat pump, is proposed in this paper. The HPS PV/T collector integrates heat pipes with PV panel, which can simultaneously generate electricity and thermal energy. The extracted heat from HPS PV/T collector can be used by heat pump, and then the photoelectric conversion efficiency is substantially improved because of the low temperature of PV cells. A mathematical model of the system is established in this paper. The model consists of a dynamic distributed parameter model of the HPS PV/T collection system and a quasi-steady state distributed parameter model of the heat pump. The mathematical model is validated by testing data, and the dynamic performance of the HPS PV/T heat pump system is discussed based on the validated model. Using the mathematical model, a reasonable accuracy in predicting the system’s dynamic performance with a relative error within ±15.0% can be obtained. The capacity of heat pump and the number of HPS collectors are optimized to improve the system performance based on the mathematical model. Six working modes are proposed and discussed to investigate the effect of solar radiation, ambient temperature, supply water temperature in condenser, PV packing factor, heat pipe pitch and PV backboard absorptivity on system performance by the validated model. It is found that the increase of solar radiation, ambient temperature and PV
Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki
2014-01-01
This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
Thermal modeling of cylindrical lithium ion battery during discharge cycle
International Nuclear Information System (INIS)
Jeon, Dong Hyup; Baek, Seung Man
2011-01-01
Highlights: → Transient and thermo-electric finite element analysis (FEA) of cylindrical lithium ion (Li-ion) battery was presented. → This model provides the thermal behavior of Li-ion battery during discharge cycle. → A LiCoO 2 /C battery at various discharge rates was investigated. → The contribution of heat source due to joule heating was significant at a high discharge rate. → The contribution of heat source due to entropy change was dominant at a low discharge rate. - Abstract: Transient and thermo-electric finite element analysis (FEA) of cylindrical lithium ion (Li-ion) battery was presented. The simplified model by adopting a cylindrical coordinate was employed. This model provides the thermal behavior of Li-ion battery during discharge cycle. The mathematical model solves conservation of energy considering heat generations due to both joule heating and entropy change. A LiCoO 2 /C battery at various discharge rates was investigated. The temperature profile from simulation had similar tendency with experiment. The temperature profile was decomposed with contributions of each heat sources and was presented at several discharge rates. It was found that the contribution of heat source due to joule heating was significant at a high discharge rate, whereas that due to entropy change was dominant at a low discharge rate. Also the effect of cooling condition and the LiNiCoMnO 2 /C battery were analyzed for the purpose of temperature reduction.
Directory of Open Access Journals (Sweden)
Y. A. Perminov
2014-01-01
Full Text Available The paper substantiates the need for profile training in mathematical modeling for pedagogical students, caused by the total penetration of mathematics into different sciences, including the humanities; fast development of the information communications technologies; and growing importance of mathematical modeling, combining the informal scientific and formal mathematical languages with the unique opportunities of computer programming. The author singles out the reasons for mastering and using the mathematical apparatus by teaches in every discipline. Indeed, among all the modern mathematical methods and ideas, mathematical modeling retains its priority in all professional spheres. Therefore, the discipline of “Mathematical Modeling” can play an important role in integrating different components of specialists training in various profiles. By mastering the basics of mathematical modeling, students acquire skills of methodological thinking; learn the principles of analysis, synthesis, generalization of ideas and methods in different disciplines and scientific spheres; and achieve general culture competences. In conclusion, the author recommends incorporating the “Methods of Profile Training in Mathematical Modeling” into the pedagogical magistracy curricula.
Mathematical modelling and numerical simulation of forces in milling process
Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.
2018-04-01
Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.
Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.
Yates, James W T
2008-07-03
One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.
Identification of Chemical Reactor Plant’s Mathematical Model
Pyakullya, Boris Ivanovich; Kladiev, Sergey Nikolaevich
2015-01-01
This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
Solar thermal power plants simulation using the TRNSYS software
Energy Technology Data Exchange (ETDEWEB)
Popel, O.S.; Frid, S.E.; Shpilrain, E.E. [Institute for High Temperatures, Russian Academy of Sciences (IVTAN), Moscow (Russian Federation)
1999-03-01
The paper describes activity directed on the TRNSYS software application for mathematical simulation of solar thermal power plants. First stage of developments has been devoted to simulation and thermodynamic analysis of the Hybrid Solar-Fuel Thermal Power Plants (HSFTPP) with gas turbine installations. Three schemes of HSFTPP, namely: Gas Turbine Regenerative Cycle, Brayton Cycle with Steam Injection and Combined Brayton-Rankine Cycle,- have been assembled and tested under the TRNSYS. For this purpose 18 new models of the schemes components (gas and steam turbines, compressor, heat-exchangers, steam generator, solar receiver, condenser, controllers, etc) have been elaborated and incorporated into the TRNSYS library of 'standard' components. The authors do expect that this initiative and received results will stimulate experts involved in the mathematical simulation of solar thermal power plants to join the described activity to contribute to acceleration of development and expansion of 'Solar Thermal Power Plants' branch of the TRNSYS. The proposed approach could provide an appropriate basis for standardization of analysis, models and assumptions for well-founded comparison of different schemes of advanced solar power plants. (authors)
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
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 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.
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...
Global thermal models of the lithosphere
Cammarano, F.; Guerri, M.
2017-12-01
Unraveling the thermal structure of the outermost shell of our planet is key for understanding its evolution. We obtain temperatures from interpretation of global shear-velocity (VS) models. Long-wavelength thermal structure is well determined by seismic models and only slightly affected by compositional effects and uncertainties in mineral-physics properties. Absolute temperatures and gradients with depth, however, are not well constrained. Adding constraints from petrology, heat-flow observations and thermal evolution of oceanic lithosphere help to better estimate absolute temperatures in the top part of the lithosphere. We produce global thermal models of the lithosphere at different spatial resolution, up to spherical-harmonics degree 24, and provide estimated standard deviations. We provide purely seismic thermal (TS) model and hybrid models where temperatures are corrected with steady-state conductive geotherms on continents and cooling model temperatures on oceanic regions. All relevant physical properties, with the exception of thermal conductivity, are based on a self-consistent thermodynamical modelling approach. Our global thermal models also include density and compressional-wave velocities (VP) as obtained either assuming no lateral variations in composition or a simple reference 3-D compositional structure, which takes into account a chemically depleted continental lithosphere. We found that seismically-derived temperatures in continental lithosphere fit well, overall, with continental geotherms, but a large variation in radiogenic heat is required to reconcile them with heat flow (long wavelength) observations. Oceanic shallow lithosphere below mid-oceanic ridges and young oceans is colder than expected, confirming the possible presence of a dehydration boundary around 80 km depth already suggested in previous studies. The global thermal models should serve as the basis to move at a smaller spatial scale, where additional thermo-chemical variations
International Nuclear Information System (INIS)
Dunn, W.E.; Policastro, A.J.; Paddock, R.A.
1975-05-01
This report evaluates mathematical models that may be used to predict the flow and temperature distributions resulting from heated surface discharges from power-plant outfalls. Part One discusses the basic physics of surface-plume dispersion and provides a critical review of 11 of the most popular and promising plume models developed to predict the near- and complete-field plume. The principal conclusion of the report is that the available models, in their present stage of development, may be used to give only general estimates of plume characteristics; precise predictions are not currently possible. The Shirazi-Davis and Pritchard (No. 1) models appear superior to the others tested and are capable of correctly predicting general plume characteristics. (The predictions show roughly factor-of-two accuracy in centerline distance to a given isotherm, factor-of-two accuracy in plume width, and factor-of-five accuracy in isotherm areas.) The state of the art can best be improved by pursuing basic laboratory studies of plume dispersion along with further development of numerical-modeling techniques
A novel mathematical model for controllable near-field electrospinning
Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun
2014-01-01
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
A novel mathematical model for controllable near-field electrospinning
International Nuclear Information System (INIS)
Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun
2014-01-01
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers
A novel mathematical model for controllable near-field electrospinning
Energy Technology Data Exchange (ETDEWEB)
Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)
Winda, A.; Sufyani, P.; Elah, N.
2018-05-01
Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.
International Nuclear Information System (INIS)
Gao, Junling; Du, Qungui; Chen, Min; Li, Bo; Zhang, Dongwen
2015-01-01
An accurate mathematical model of thermoelectric modules (TEMs) provides the basis for the analysis and design of thermoelectric conversion system. TEM models from the literature are only valid for the heat transfer of N-type and P-type thermoelectric couples without considering air around the actual thermoelectric couples of TEMs. In fact, air space imposes significant influence on the model computational accuracy, especially for a TEM with large air space inside. In this study, heat transfer analyses of air between the TEM cold and hot plates were carried out in order to propose a new mathematical model that minimises simulation errors. This model was applied to analyse characteristic parameters of two typical TEMs, and the ratio of cross-sectional area of air space to thermocouples were 48.2% and 80.0%, respectively. The average relative errors in simulation decreased from 5.2% to 2.8% and from 12.8% to 3.7%, respectively. It is noted that our new model gives result more accurate than models from the literature provided that higher temperature difference occurs between hot side and cold side of TEM. Thus, the proposed model is of theoretical significance in guiding future design of TEMs for high-power or large-temperature-difference thermoelectric conversion systems. - Highlights: • Built a new accurate model for thermoelectric modules with inner air heat transfer. • Analysed the influence on heat transfer of the air within the TEM ∗ . • Reduced simulation errors for high-power thermoelectric conversion systems. • Two typical TEMs were measured with a good agreement with theoretical results. • ∗ TEM is the abbreviation of thermoelectric module
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
Mathematical modeling of thermal stresses in basic oxygen furnace hood tubes
Samarasekera, I. V.
1985-06-01
The stress-strain history of Basic Oxygen Furnace hood tubes during thermal cycling has been computed using heat flow and stress analyses. The steady-state temperature distribution in a transverse section of the tube was computed at a location where gas temperature in the hood could be expected to be a maximum. Calculations were performed for peak gas temperatures in the range 1950 to 2480 °C (3500 to 4500 °F). The stress-strain history of an element of material located at the center of the tube hot face was traced for three consecutive cycles using elasto-plastic finite-element analysis. It has been shown that the state of stress in the element alternates between compression and tension as the tube successively heats and cools. Yielding and plastic flow occurs at the end of each half of a given cycle. It was postulated that owing to repctitive yielding, plastic strain energy accumulates causing failure of the tubes by fatigue in the low cycle region. Using fatigue theory a conservative estimate for tube life was arrived at. In-plant observations support this mechanism of failure, and the number of cycles within which tube cracking was observed compares reasonably with model predictions. Utilizing the heat flow and stress models it was recommended that tube life could be enhanced by changing the tube material to ARMCO 17-4 pH or AISI 405 steel or alternatively reconstructing hoods with AISI 316L tubes of reduced thickness. These recommendations were based on the criterion that low-cycle fatigue failure could be averted if the magnitude of the cyclic strain could be reduced or if macroscopic plastic flow could be prevented.
Mathematical modelling of tissue formation in chondrocyte filter cultures.
Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J
2011-12-17
In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.
Investigation of seasonal thermal flow in a real dam reservoir using 3-D numerical modeling
Directory of Open Access Journals (Sweden)
Üneş Fatih
2015-03-01
Full Text Available Investigations indicate that correct estimation of seasonal thermal stratification in a dam reservoir is very important for the dam reservoir water quality modeling and water management problems. The main aim of this study is to develop a hydrodynamics model of an actual dam reservoir in three dimensions for simulating a real dam reservoir flows for different seasons. The model is developed using nonlinear and unsteady continuity, momentum, energy and k-ε turbulence model equations. In order to include the Coriolis force effect on the flow in a dam reservoir, Coriolis force parameter is also added the model equations. Those equations are constructed using actual dimensions, shape, boundary and initial conditions of the dam and reservoir. Temperature profiles and flow visualizations are used to evaluate flow conditions in the reservoir. Reservoir flow’s process and parameters are determined all over the reservoir. The mathematical model developed is capable of simulating the flow and thermal characteristics of the reservoir system for seasonal heat exchanges. Model simulations results obtained are compared with field measurements obtained from gauging stations for flows in different seasons. The results show a good agreement with the field measurements.
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…
The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study
Mischo, Christoph; Maaß, Katja
2013-01-01
This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…
Influence of mathematical models in design of PV-Diesel systems
International Nuclear Information System (INIS)
Dufo-Lopez, Rodolfo; Bernal-Agustin, Jose L.
2008-01-01
This paper presents a study of the influence of mathematical models in the optimal design of PV-Diesel systems. For this purpose, a design tool developed by the authors, which allows obtaining the most cost effective design of a PV-Diesel system through the genetic algorithm technique, has been used. The mathematical models of some elements of the hybrid system have been improved in comparison to those usually employed in hybrid systems design programs. Furthermore, a more complete general control strategy has been developed, one that also takes into account more characteristics than those usually considered in this kind of design. Several designs have been made, evaluating the effect on the results of the different mathematical models and the novel strategy that can be considered
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 and simulations of radiation fluxes from buried radionuclides
International Nuclear Information System (INIS)
Ahmad Saat
1999-01-01
A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)
The mathematical model of thread unrolling from a bobbin
Directory of Open Access Journals (Sweden)
S. M. Tenenbaum
2014-01-01
Full Text Available I. Introduction The subject of research in this work is a process of thread unrolling from a bobbin. The mathematical model of this process considering motion of thread peace on a bobbin and unrolled peace is proposed. The dimension of system of differential equations for this model is constant during deploying.The relevance to simulate this process for design of Heliogyro-like solar sails (Heliogyro [1], BMSTU-Sail [2] is proved. The paper briefly characterizes a blade for such solar sail as a simulation object. It proves the possibility for using a flexible thread model for a long blade because of very small blade thickness (less than 10 μm [3] relative to blade width and the phenomena of Koriolis forces [4] that lead to buckling failure of blade flatness.The major features of the proposed model are:-- simulated as a motion of the thread piece both being on a bobbin and its unrolled peace;-- splitting a thread length into nodes does not depend on the demand to ensure a sufficient number of nodes on a single thread turn on the coil;-- because of avoiding a problem of contact between the thread and bobbin a stable integration of motion equations is provided by the conventional Runge-Kutta method of fourth order with a constant step [5];-- in the course of solution the number of freedom degrees (number of motion equation is constant, thereby simplifying a calculation algorithm.The closest mathematical model is proposed in [6].The scientific novelty of this research is the approach to solving the problem of unrolling thread from a bobbin using a constant number of motion equations while preserving real kinematics coiling process.II. Problem formulationIn this section the problem of unrolling thread with length L from a bobbin of radius r is posed while any kind of forces are acting on the unrolled peace of thread. Moreover, the law of bobbin rotation φ(t assumed to be known with the proviso that the model can be modified if φ(t is the result of
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.
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
2017-01-01
The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…
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.
Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian
2018-01-01
In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…
Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course
Ludwig, Patrice; Tongen, Anthony; Walton, Brian
2018-01-01
James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…
Identification of Chemical Reactor Plant’s Mathematical Model
Directory of Open Access Journals (Sweden)
Pyakillya Boris
2015-01-01
Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
2017-01-01
The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...
Mathematical models of granular matter
Mariano, Paolo; Giovine, Pasquale
2008-01-01
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Thermal processes identification using virtual instrumentation
Directory of Open Access Journals (Sweden)
Iosif OLAH
2007-12-01
Full Text Available In this paper the experimental identification problem of thermal processes is presented, in order to establish their mathematical models which permit the adoption of the automation solutions, respectively the specification of a suitable control law. With this aim in view, the authors resorted to use Virtual Instrumentation with the aid of the LabVIEW development medium. In order to solve the problem of acquisition and processing data from physical real processes, Virtual Instruments which provide at the end a mathematical model which is basis of choosing the automation equipment of the aim followed was designed and achieved. The achieved Virtual Instruments get the opportunity to be used either in student instruction field with the virtual processes identification techniques or to put the identification of some real processes to good use of diverse beneficiaries. The results of some experimental attempts which were achieved during different thermal processes, illustrate the utility of the demarches performed in this paper.
Power thresholds for fast oscillatory instabilities in nuclear reactors: a simple mathematical model
International Nuclear Information System (INIS)
Suarez-Antola, Roberto; Uruguay)
2007-01-01
The cores of nuclear reactors, including its structural parts and cooling fluids, are complex mechanical systems able to vibrate in a set of normal modes and frequencies, if suitable perturbed. The cyclic variations in the strain state of the core materials may modify the reactivity, and thus thermal power, producing variations in strain due to thermal-elastic effects. If the variation of the temperature field is fast enough and if the Doppler Effect and other stabilizing prompt effects in the fuel are weak enough, a fast oscillatory instability could be produced, coupled with mechanical vibrations of small enough amplitude that they will not be excluded by the procedures of conventional mechanical design. After a careful discussion of the time scales of neutron kinetics, thermal-elastic and vibration phenomena, a simple lumped parameter mathematical model is constructed in order to study, in a first approximation, the stability of the reactor. An integro-differential equation for power kinetics is derived. Under certain conditions, fast oscillatory instabilities are found when power is greater than a threshold value, and the delay in the global power feedback loop is big enough. Approximate analytical formulae are given for the power threshold, critical delay and power oscillation frequency. It is shown that if prompt stabilizing fuel effects are strong enough, dangerous fast power oscillations due to mechanical thermal-nuclear coupling phenomena can not appear at any power level. (author)
Aspects of Mathematical Modelling of Pressure Retarded Osmosis
Anissimov, Yuri G.
2016-01-01
In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696
Mathematical modeling of a convective textile drying process
Directory of Open Access Journals (Sweden)
G. Johann
2014-12-01
Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.
Proposal of a pedagogical model for mathematics teacher education
Directory of Open Access Journals (Sweden)
Alfonso Jiménez Espinosa
2011-01-01
Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.
Hoskinson, Anne-Marie
2010-01-01
Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity…
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...
THERMUS—A thermal model package for ROOT
Wheaton, S.; Cleymans, J.; Hauer, M.
2009-01-01
statistical-thermal models it is required to fit experimental particle multiplicities or particle ratios. In such analyses, the input is a set of experimental yields and ratios, a set of particles comprising the assumed hadron resonance gas formed in the collision and the constraints to be placed on the system. The thermal model parameters consistent with the specified constraints leading to the best-fit to the experimental data are then output. Solution method: THERMUS is a package designed for incorporation into the ROOT [2] framework, used extensively by the heavy-ion community. As such, it utilizes a great deal of ROOT's functionality in its operation. ROOT features used in THERMUS include its containers, the wrapper TMinuit implementing the MINUIT fitting package, and the TMath class of mathematical functions and routines. Arguably the most useful feature is the utilization of CINT as the control language, which allows interactive access to the THERMUS objects. Three distinct statistical ensembles are included in THERMUS, while additional options to include quantum statistics, resonance width and excluded volume corrections are also available. THERMUS provides a default particle list including all mesons (up to the K4∗ (2045)) and baryons (up to the Ω) listed in the July 2002 Particle Physics Booklet [3]. For each typically unstable particle in this list, THERMUS includes a text-file listing its decays. With thermal parameters specified, THERMUS calculates primordial thermal densities either by performing numerical integrations or else, in the case of the Boltzmann approximation without resonance width in the grand-canonical ensemble, by evaluating Bessel functions. Particle decay chains are then used to evaluate experimental observables (i.e. particle yields following resonance decay). Additional detector efficiency factors allow fine-tuning of the model predictions to a specific detector arrangement. When parameters are required to be constrained, use is made of the
Taking the mystery out of mathematical model applications to karst aquifers—A primer
Kuniansky, Eve L.
2014-01-01
Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.
Energy Technology Data Exchange (ETDEWEB)
Lappa, Marcello, E-mail: marcello.lappa@strath.ac.uk
2016-05-15
The relevance of non-equilibrium phenomena, nonlinear behavior, gravitational effects and fluid compressibility in a wide range of problems related to high-temperature gas-dynamics, especially in thermal, mechanical and nuclear engineering, calls for a concerted approach using the tools of the kinetic theory of gases, statistical physics, quantum mechanics, thermodynamics and mathematical modeling in synergy with advanced numerical strategies for the solution of the Navier–Stokes equations. The reason behind such a need is that in many instances of relevance in this field one witnesses a departure from canonical models and the resulting inadequacy of standard CFD approaches, especially those traditionally used to deal with thermal (buoyancy) convection problems. Starting from microscopic considerations and typical concepts of molecular dynamics, passing through the Boltzmann equation and its known solutions, we show how it is possible to remove past assumptions and elaborate an algorithm capable of targeting the broadest range of applications. Moving beyond the Boussinesq approximation, the Sutherland law and the principle of energy equipartition, the resulting method allows most of the fluid properties (density, viscosity, thermal conductivity, heat capacity and diffusivity, etc.) to be derived in a rational and natural way while keeping empirical contamination to the minimum. Special attention is deserved as well to the well-known pressure issue. With the application of the socalled multiple pressure variables concept and a projection-like numerical approach, difficulties with such a term in the momentum equation are circumvented by allowing the hydrodynamic pressure to decouple from its thermodynamic counterpart. The final result is a flexible and modular framework that on the one hand is able to account for all the molecule (translational, rotational and vibrational) degrees of freedom and their effective excitation, and on the other hand can guarantee
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
Ganusov, Vitaly V
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.
Strong inference in mathematical modeling: a method for robust science in the 21st century
Directory of Open Access Journals (Sweden)
Vitaly V. Ganusov
2016-07-01
Full Text Available While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers [1], the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions and data. Following the principle of strong inference for experimental sciences proposed by Platt [2], I suggest ``strong inference in mathematical modeling'' as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are 1 to develop multiple alternative models for the phenomenon in question; 2 to compare the models with available experimental data and to determine which of the models are not consistent with the data; 3 to determine reasons why rejected models failed to explain the data, and 4 to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the 21st century.
A Mathematical Model of the Single Aluminium Diboride Particle Ignition
Directory of Open Access Journals (Sweden)
D. A. Yagodnikov
2014-01-01
Full Text Available The paper presents a developed mathematical model of ignition of the single aluminum diboride particle as an aluminum-boron alloy in the oxidizing environment of a complicated chemical composition containing oxygen, water vapor, and carbon dioxide. The mathematical model is based on the theory of parallel chemical reactions proceeding on the appropriate parts of the particle surface occupied by each element in proportion to their molar share in the alloy. The paper considers a possibility to establish a thermodynamic balance between components over a particle surface in the gas phase. The composition of components is chosen as a result of thermodynamic calculation, namely В g , B2O3 g , BO, B2O2, BO2, Alg , AlO, Al2O, N2. The mathematical model is formed by a system of the differential equations of enthalpy balance, mass of aluminum diboride particle, and of formed oxides, which become isolated by initial and boundary conditions for temperature and size of particles, concentration of an oxidizer, and temperature of gas. The software package “AlB2“ is developed. It is a complete independent module written in Fortran algorithmic language, which together with a package of the subroutines “SPARKS” is used to calculate parameters of burning aluminum diboride particle by the Runge-Kutt method.For stoichiometry of chemical reactions of interaction between aluminum diboride and oxygen, a dynamics of changing temperature of a particle and thickness of an oxide film on its surface is calculated. It was admitted as initial conditions that the aluminum diboride particle radius was 100μ and the reference temperature of environment was 500 K, 1000 K, 2300 K, and 3000 K. Depending on this temperature the aluminum diboride particle temperature was calculated. Changing thickness of the oxide film on the particle surface at various initial gas temperatures characterizes its increase at the initial heating period of ~ 0,01 s and a gradual slowdown of the
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.
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...
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century
Ganusov, Vitaly V.
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750
Modeling Achievement in Mathematics: The Role of Learner and Learning Environment Characteristics
Nasser-Abu Alhija, Fadia; Amasha, Marcel
2012-01-01
This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and…
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.