Rotating Algal Biofilm Reactors: Mathematical Modeling and Lipid Production

OpenAIRE

Woolsey, Paul A.

2011-01-01

Harvesting of algal biomass presents a large barrier to the success of biofuels made from algae feedstock. Small cell sizes coupled with dilute concentrations of biomass in lagoon systems make separation an expensive and energy intense-process. The rotating algal biofilm reactor (RABR) has been developed at USU to provide a sustainable technology solution to this issue. Algae cells grown as a biofilm are concentrated in one location for ease of harvesting of high density biomass. A mathematic...

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 modelling of fluidized bed reactors

Energy Technology Data Exchange (ETDEWEB)

Werther, J [BASF A.G., Ludwigshafen am Rhein (Germany, F.R.)

1978-11-01

Among the many fluidized bed models to be found in the literature, the two-phase model originally proposed by May has proved most suitable for accomodation of recent advances in flow mechanics: this model resolves the gas/solids fluidized bed into a bubble phase and a suspension phase surrounding the bubbles. Its limitation to slow reactions is a disadvantage. On the basis of the analogy between fluidized beds and gas/liquid systems, a general two-phase model that is valid for fast reactions has therefore been developed and its validity is confirmed by comparison with the experimental results obtained by others. The model describes mass transfer across the phase interface with the aid of the film theory known from gas/liquid reactor technology, and the reaction occurring in the suspension phase as a pseudo-homogeneous reaction. Since the dependence of the performance of fluidized bed reactors upon geometry is accounted for, the model can also be used for scale-up calculations. Its use is illustrated with the aid of design diagrams.

Adapting Dynamic Mathematical Models to a Pilot Anaerobic Digestion Reactor

Directory of Open Access Journals (Sweden)

F. Haugen, R. Bakke, and B. Lie

2013-04-01

Full Text Available A dynamic model has been adapted to a pilot anaerobic reactor fed diarymanure. Both steady-state data from online sensors and laboratory analysis anddynamic operational data from online sensors are used in the model adaptation.The model is based on material balances, and comprises four state variables,namely biodegradable volatile solids, volatile fatty acids, acid generatingmicrobes (acidogens, and methane generating microbes (methanogens. The modelcan predict the methane gas flow produced in the reactor. The model may beused for optimal reactor design and operation, state-estimation and control.Also, a dynamic model for the reactor temperature based on energy balance ofthe liquid in the reactor is adapted. This model may be used for optimizationand control when energy and economy are taken into account.

Dynamic bioconversion mathematical modelling and simulation of urban organic waste co-digestion in continuously stirred tank reactor

DEFF Research Database (Denmark)

Fitamo, Temesgen Mathewos; Boldrin, Alessio; Dorini, G.

of this study was to apply a dynamic mathematical model to simulate the co-digestion of different urban organic wastes (UOW). The modelling was based on experimental activities, during which two reactors (R1, R2) were operated at hydraulic retention times (HRT) of 30, 20, 15, 10 days, in thermophilic conditions......The application of anaerobic digestion (AD) as process technology is increasing worldwide: the production of biogas, a versatile form of renewable energy, from biomass and organic waste materials allows mitigating greenhouse gas emission from the energy and transportation sectors while treating...... waste. However, the successful operation of AD processes is challenged by economic and technological issues. To overcome these barriers, mathematical modelling of the bioconversion process can provide support to develop strategies for controlling and optimizing the AD process. The objective...

Mathematical modeling of quartz particle melting process in plasma-chemical reactor

Energy Technology Data Exchange (ETDEWEB)

Volokitin, Oleg, E-mail: volokitin-oleg@mail.ru; Volokitin, Gennady, E-mail: vgg-tomsk@mail.ru; Skripnikova, Nelli, E-mail: nks2003@mai.ru; Shekhovtsov, Valentin, E-mail: shehovcov2010@yandex.ru [Tomsk State University of Architecture and Building, 2, Solyanaya Sq., 634003, Tomsk (Russian Federation); Vlasov, Viktor, E-mail: rector@tsuab.ru [Tomsk State University of Architecture and Building, 2, Solyanaya Sq., 634003, Tomsk (Russian Federation); National Research Tomsk Polytechnic University, 30, Lenin Ave., 634050, Tomsk (Russian Federation)

2016-01-15

Among silica-based materials vitreous silica has a special place. The paper presents the melting process of a quartz particle under conditions of low-temperature plasma. A mathematical model is designed for stages of melting in the experimental plasma-chemical reactor. As calculation data show, quartz particles having the radius of 0.21≤ r{sub p} ≤0.64 mm completely melt at W = 0.65 l/s particle feed rate depending on the Nusselt number, while 0.14≤ r{sub p} ≤0.44 mm particles melt at W = 1.4 l/s. Calculation data showed that 2 mm and 0.4 mm quartz particles completely melted during and 0.1 s respectively. Thus, phase transformations occurred in silicon dioxide play the important part in its heating up to the melting temperature.

Mathematical modelling of plant transients in the PWR for simulator purposes

International Nuclear Information System (INIS)

Hartel, K.

1984-01-01

This chapter presents the results of the testing of anticipated and abnormal plant transients in pressurized water reactors (PWRs) of the type WWER 440 by means of the numerical simulation of 32 different, stationary and nonstationary, operational regimes. Topics considered include the formation of the PWR mathematical model, the physical approximation of the reactor core, the structure of the reactor core model, a mathematical approximation of the reactor model, the selection of numerical methods, and a computerized simulation system. The necessity of a PWR simulator in Czechoslovakia is justified by the present status and the outlook for the further development of the Czechoslovak nuclear power complex

Stochastic model of energetic nuclear reactor

International Nuclear Information System (INIS)

Bojko, R.V.; Ryazanov, V.V.

2002-01-01

Behaviour of nuclear reactor was treated using the theory of branching processes. As mathematical model descriptive the neutron number in time the Markov occasional process is proposed. Application of branching occasional processes with variable regime to the description of neutron behaviour in the reactor makes possible conducting strong description of critical operation regime and demonstrates the severity of the process. Three regimes of the critical behaviour depending on the sign of manipulated variables and feedbacks were discovered. Probability regularities peculiar to the behaviour of the reactor are embodied to the suggested stochastic model [ru

Dynamic Model of an Ammonia Synthesis Reactor Based on Open Information

OpenAIRE

Jinasena, Asanthi; Lie, Bernt; Glemmestad, Bjørn

2016-01-01

Ammonia is a widely used chemical, hence the ammonia manufacturing process has become a standard case study in the scientific community. In the field of mathematical modeling of the dynamics of ammonia synthesis reactors, there is a lack of complete and well documented models. Therefore, the main aim of this work is to develop a complete and well documented mathematical model for observing the dynamic behavior of an industrial ammonia synthesis reactor system. The model is complete enough to ...

Modeling and Control of a Large Nuclear Reactor A Three-Time-Scale Approach

CERN Document Server

Shimjith, S R; Bandyopadhyay, B

2013-01-01

Control analysis and design of large nuclear reactors requires a suitable mathematical model representing the steady state and dynamic behavior of the reactor with reasonable accuracy. This task is, however, quite challenging because of several complex dynamic phenomena existing in a reactor. Quite often, the models developed would be of prohibitively large order, non-linear and of complex structure not readily amenable for control studies. Moreover, the existence of simultaneously occurring dynamic variations at different speeds makes the mathematical model susceptible to numerical ill-conditioning, inhibiting direct application of standard control techniques. This monograph introduces a technique for mathematical modeling of large nuclear reactors in the framework of multi-point kinetics, to obtain a comparatively smaller order model in standard state space form thus overcoming these difficulties. It further brings in innovative methods for controller design for systems exhibiting multi-time-scale property,...

Modeling and control of a large nuclear reactor. A three-time-scale approach

Energy Technology Data Exchange (ETDEWEB)

Shimjith, S.R. [Indian Institute of Technology Bombay, Mumbai (India); Bhabha Atomic Research Centre, Mumbai (India); Tiwari, A.P. [Bhabha Atomic Research Centre, Mumbai (India); Bandyopadhyay, B. [Indian Institute of Technology Bombay, Mumbai (India). IDP in Systems and Control Engineering

2013-07-01

Recent research on Modeling and Control of a Large Nuclear Reactor. Presents a three-time-scale approach. Written by leading experts in the field. Control analysis and design of large nuclear reactors requires a suitable mathematical model representing the steady state and dynamic behavior of the reactor with reasonable accuracy. This task is, however, quite challenging because of several complex dynamic phenomena existing in a reactor. Quite often, the models developed would be of prohibitively large order, non-linear and of complex structure not readily amenable for control studies. Moreover, the existence of simultaneously occurring dynamic variations at different speeds makes the mathematical model susceptible to numerical ill-conditioning, inhibiting direct application of standard control techniques. This monograph introduces a technique for mathematical modeling of large nuclear reactors in the framework of multi-point kinetics, to obtain a comparatively smaller order model in standard state space form thus overcoming these difficulties. It further brings in innovative methods for controller design for systems exhibiting multi-time-scale property, with emphasis on three-time-scale systems.

Model based design of biochemical micro-reactors

Directory of Open Access Journals (Sweden)

Tobias eElbinger

2016-02-01

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

Advances in Reactor Physics, Mathematics and Computation. Volume 2

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, Volume 2, are divided into 7 sessions bearing on: - session 7: Deterministic transport methods 1 (7 conferences), - session 8: Interpretation and analysis of reactor instrumentation (6 conferences), - session 9: High speed computing applied to reactor operations (5 conferences), - session 10: Diffusion theory and kinetics (7 conferences), - session 11: Fast reactor design, validation and operating experience (8 conferences), - session 12: Deterministic transport methods 2 (7 conferences), - session 13: Application of expert systems to physical aspects of reactor design and operation.

Dynamic analysis of reactor containment building using axisymmetric finite element model

International Nuclear Information System (INIS)

Thakkar, S.K.; Dubey, R.N.

1989-01-01

The structural safety of nuclear reactor building during earthquake is of great importance in view of possibility of radiation hazards. The rational evaluation of forces and displacements in various portions of structure and foundation during strong ground motion is most important for safe performance and economic design of the reactor building. The accuracy of results of dynamic analysis is naturally dependent on the type of mathematical model employed. Three types of mathematical models are employed for dynamic analysis of reactor building beam model axisymmetric finite element model and three dimensional model. In this paper emphasis is laid on axisymmetric model. This model of containment building is considered a reinfinement over conventional beam model of the structure. The nuclear reactor building on a rocky foundation is considered herein. The foundation-structure interaction is relatively less in this condition. The objective of the paper is to highlight the significance of modelling of non-axisymmetric portion of building, such as reactor internals by equivalent axisymmetric body, on the structural response of the building

Advances in Reactor Physics, Mathematics and Computation. Volume 1

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume one, are divided into 6 sessions bearing on: - session 1: Advances in computational methods including utilization of parallel processing and vectorization (7 conferences) - session 2: Fast, epithermal, reactor physics, calculation, versus measurements (9 conferences) - session 3: New fast and thermal reactor designs (9 conferences) - session 4: Thermal radiation and charged particles transport (7 conferences) - session 5: Super computers (7 conferences) - session 6: Thermal reactor design, validation and operating experience (8 conferences).

Reactor theory and power reactors. 1. Calculational methods for reactors. 2. Reactor kinetics

International Nuclear Information System (INIS)

Henry, A.F.

1980-01-01

Various methods for calculation of neutron flux in power reactors are discussed. Some mathematical models used to describe transients in nuclear reactors and techniques for the reactor kinetics' relevant equations solution are also presented

Mathematical game type optimization of powerful fast reactors

International Nuclear Information System (INIS)

Pavelesku, M.; Dumitresku, Kh.; Adam, S.

1975-01-01

To obtain maximum speed of putting into operation fast breeders it is recommended on the initial stage of putting into operation these reactors to apply lower power which needs less fission materials. That is why there is an attempt to find a configuration of a high-power reactor providing maximum power for minimum mass of fission material. This problem has a structure of the mathematical game with two partners of non-zero-order total and is solved by means of specific aids of theory of games. Optimal distribution of fission and breeding materials in a multizone reactor first is determined by solution of competitive game and then, on its base, by solution of the cooperation game. The second problem the solution for which is searched is developed from remark on the fact that a reactor with minimum coefficient of flux heterogenity has a configuration different from the reactor with power coefficient heterogenity. Maximum burn-up of fuel needs minimum heterogenity of the flux coefficient and the highest power level needs minimum coefficient of power heterogenity. That is why it is possible to put a problem of finding of the reactor configuration having both coefficients with minimum value. This problem has a structure of a mathematical game with two partners of non-zero-order total and is solved analogously giving optimal distribution of fuel from the new point of view. In the report is shown that both these solutions are independent which is a result of the aim put in the problem of optimization. (author)

Mathematical foundation of the application of modal analysis to the investigation of space-time reactor behaviour

International Nuclear Information System (INIS)

Obradovic, D.M.

1970-01-01

In recent years investigations in the field of kinetics and dynamics of nuclear reactors have been directed towards overcoming an insufficiently accurate point reactor model. For that purpose different mathematical approaches have been used. This thesis is devoted to modal analysis because, from the practical point of view, it is a very promising and, from the mathematical and physical point of view, a very interesting method. Some fundamental mathematical problems connected with the application of modal analysis to the investigations of the reactor space-time behaviour are still unsolved and accordingly our purpose is to solve some of these problems. The spectral properties of the diffusion and P 1 operators are studied in some detail applying the Krein-Rutman theory of the K-positive operators, the Krasnosel'skii theory of u 0 operators, and the Keldis theory of the operator families. The formal solution to the initial value problem (as an abstract Cauchy problem), associated with the diffusion and P 1 operators is also studied. Modal analysis is identified as a set of methods in the mathematical literature known as the Galerkin methods (or projection methods). Following this idea (using the results of the mathematical investigations of the Galerkin methods) and using our results of the investigations of the properties of the diffusion and P 1 operators, the applicability of modal analysis to the approximate solution of the diffusion and P 1 equations and of the eigenvalue problems associated with the diffusion and P 1 operators is established. As an example of the application of modal analysis the Bubnov and Galerkin method is applied to a multiregion thermal nuclear reactor for the determination of: (i) frequency response, (ii) eigenvalues and eigenvectors of the stationary diffusion operator, (iii) eigenvalues and eigenvectors of the non-stationary diffusion operators. On the basis of the expressions obtained the corresponding computer programmes for radial

Analysis of dynamic stability and safety of the reactor system by reactor simulator

International Nuclear Information System (INIS)

Raisic, N.

1963-11-01

This document defines the approximations done for establishing a mathematical model of a reactor. Since the model should be used for safety analysis, it was important to choose a mathematical model less stable than the reactor itself. The analysis was performed on the analog computer RAS. Results obtained and conclusions concerned with three possible reactor accidents are presented [sr

Dimensioning of aerated submerged fixed bed biofilm reactors based on a mathematical biofilm model applied to petrochemical wastewater - the link between theory and practice

OpenAIRE

Trojanowicz, Karol; Wójcik, Wtodzimierz

2014-01-01

The description of a biofilm mathematical model application for dimensioning an aerated fixed bed biofilm reactor (ASFBBR) for petrochemical wastewater polishing is presented. A simple one-dimensional model of biofilm, developed by P Harremöes, was chosen for this purpose. The model was calibrated and verified under conditions of oil-refinery effluent. The results of ASFBBR dimensioning on the basis of the biofilm model were compared with the bioreactor dimensions determined by application of...

ADAPTIVE CONTROL SYSTEM OF INDUSTRIAL REACTORS

Directory of Open Access Journals (Sweden)

Vyacheslav K. Mayevski

2014-01-01

Full Text Available This paper describes a mathematical model of an industrial chemical reactor for production of synthetic rubber. During reactor operation the model parameters vary considerably. To create a control algorithm performed transformation of mathematical model of the reactor in order to obtain a dependency that can be used to determine the model parameters are changing during reactor operation.

A modular approach to lead-cooled reactors modelling

Energy Technology Data Exchange (ETDEWEB)

Casamassima, V. [CESI RICERCA, via Rubattino 54, I-20134 Milano (Italy)], E-mail: casamassima@cesiricerca.it; Guagliardi, A. [CESI RICERCA, via Rubattino 54, I-20134 Milano (Italy)], E-mail: guagliardi@cesiricerca.it

2008-06-15

After an overview of the lego plant simulation tools (LegoPST), the paper gives some details about the ongoing LegoPST extension for modelling lead fast reactor plants. It refers to a simple mathematical model of the liquid lead channel dynamic process and shows the preliminary results of its application in dynamic simulation of the BREST 300 liquid lead steam generator. Steady state results agree with reference data [IAEA-TECDOC 1531, Fast Reactor Database, 2006 Update] both for water and lead.

A modular approach to lead-cooled reactors modelling

International Nuclear Information System (INIS)

Casamassima, V.; Guagliardi, A.

2008-01-01

After an overview of the lego plant simulation tools (LegoPST), the paper gives some details about the ongoing LegoPST extension for modelling lead fast reactor plants. It refers to a simple mathematical model of the liquid lead channel dynamic process and shows the preliminary results of its application in dynamic simulation of the BREST 300 liquid lead steam generator. Steady state results agree with reference data [IAEA-TECDOC 1531, Fast Reactor Database, 2006 Update] both for water and lead

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)

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

Science.gov (United States)

Kumar, B Shiva; Venkateswarlu, Ch

2014-08-01

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

Mathematical modelling

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...

Mathematical models in nuclear safety and radiation protection of nuclear energy

International Nuclear Information System (INIS)

1993-01-01

This collection of papers contains the full texts of 33 reports presented at the Seminar, all of which are indexed and abstracted separately for the INIS database. The topics of the reports cover the mathematical models and computer codes for risk analysis, reactor reliability simulating, safety-related benchmarks, thermohydraulic studies, reactor kinetics, hypothetical accidents and their radiological consequences, etc. The investigations refer mainly to WWER-440 and WWER-1000 type reactors of the Kozloduy NPP

A mathematical model of the accumulation of radionuclides by oysters (C. virginica) aquacultured in the effluent of a nuclear power reactor to include major biological parameters

International Nuclear Information System (INIS)

Hess, C.T.; Smith, C.W.; Price, A.H.

1977-01-01

The uptake, accumulation and loss of radionuclides by the American oyster (C. virginica) aquacultured in the effluent of a nuclear power reactor has been measured monthly for 3 yr at four field stations in the Montsweag Estuary of the Sheepscot River and at a control station in the nearby Damariscotta River Estuary, southern central coastal Maine, U.S.A. A mathematical model for the time variation of the specific activity of the oysters has been developed to include the physical half-lives of the various radionuclides, the biological half-lives of the various radionuclides (biological depuration), the water temperature (oyster hibernation) and shell growth. The resulting first order linear differential equation incorporating these phenomena is driven by the liquid radionuclide effluent release of the Maine Yankee Nuclear Reactor. Comparison of the monthly measurements of the specific activity for 58 Co, 60 Co, 54 Mn, 134 Cs and 137 Cs in oysters with model calculations show close agreement over all ranges of variation observed. A special feature of this mathematical model is its ability to describe the non-chemostatic field situation. (author)

A new mathematical model for nitrogen gas production with special emphasis on the role of attached growth media in anammox hybrid reactor.

Science.gov (United States)

Tomar, Swati; Gupta, Sunil Kumar

2015-11-01

The present study emphasised on the development of new mathematical models based on mass balance and stoichiometry of nitrogen removal in anammox hybrid reactor (AHR). The performance of AHR at varying hydraulic retention times (HRTs) and nitrogen loading rates (NLRs) revealed that nitrogen removal efficiency (NRE) increases with increase in HRT and was found optimal (89 %) at HRT of 2 days. Mass balance of nitrogen revealed that major fraction (74.1 %) of input nitrogen is converted into N2 gas followed by 11.2 % utilised in biomass synthesis. Attached growth media (AGM) in AHR contributed to an additional 15.4 % ammonium removal and reduced the sludge washout rate by 29 %. This also enhanced the sludge retention capacity of AHR and thus minimised the formation of nitrate in the treated effluent, which is one of the bottlenecks of anammox process. Process kinetics was also studied using various mathematical models. The mass balance model derived from total nitrogen was found most precise and predicted N2 gas with least error (1.68 ± 4.44 %). Model validation for substrate removal kinetics dictated comparatively higher correlation for Grau second-order model (0.952) than modified Stover-Kincannon model (0.920). The study concluded that owing to features of high biomass retention, less nitrate formation and consistently higher nitrogen removal efficiency, this reactor configuration is techno-economically most efficient and viable. The study opens the door for researchers and scientists for pilot-scale testing of AHR leading to its wide industrial application.

CFD Model of HDS Catalyst Tests in Trickle-Bed Reactor

OpenAIRE

Tukač, V.

2014-01-01

The goal of this study was to evaluate hydrodynamic influence on experimental HDS catalyst activity measurement carried out in pilot scale trickle-bed reactor. Hydrodynamic data were evaluated by RTD method in laboratory glass model of pilot reactor. Mathematical models of the process were formulated both like 1D pseudohomogeneou and 3D heterogeneous ones. The aim of this work was to forecast interaction between intrinsic reaction kinetic, hydrodynamics and mass transfer.

An integrated mathematical model for chemical oxygen demand (COD) removal in moving bed biofilm reactors (MBBR) including predation and hydrolysis.

Science.gov (United States)

Revilla, Marta; Galán, Berta; Viguri, Javier R

2016-07-01

An integrated mathematical model is proposed for modelling a moving bed biofilm reactor (MBBR) for removal of chemical oxygen demand (COD) under aerobic conditions. The composite model combines the following: (i) a one-dimensional biofilm model, (ii) a bulk liquid model, and (iii) biological processes in the bulk liquid and biofilm considering the interactions among autotrophic, heterotrophic and predator microorganisms. Depending on the values for the soluble biodegradable COD loading rate (SCLR), the model takes into account a) the hydrolysis of slowly biodegradable compounds in the bulk liquid, and b) the growth of predator microorganisms in the bulk liquid and in the biofilm. The integration of the model and the SCLR allows a general description of the behaviour of COD removal by the MBBR under various conditions. The model is applied for two in-series MBBR wastewater plant from an integrated cellulose and viscose production and accurately describes the experimental concentrations of COD, total suspended solids (TSS), nitrogen and phosphorous obtained during 14 months working at different SCLRs and nutrient dosages. The representation of the microorganism group distribution in the biofilm and in the bulk liquid allow for verification of the presence of predator microorganisms in the second reactor under some operational conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

Mathematical modeling of an in-line low-NOx calciner

DEFF Research Database (Denmark)

Iliuta, Ion; Dam-Johansen, Kim; Jensen, Lars Skaarup

2002-01-01

The reduction of the NOx content in in-line-calciner-type kiln systems can be made by optimization of the primary filing in the rotary kiln and of the secondary firing in the calciner. Because the optimization of calciner offers greater opportunities the mathematical modeling of this reactor...

Analysis of dynamic stability and safety of reactor system by reactor simulator

International Nuclear Information System (INIS)

Raisic, N.

1963-11-01

In order to enable qualitative analysis of dynamic properties of reactors RA and RB, mathematical models of these reactors were formulated and adapted for solution on analog computer. This report contains basic assessments for creating the model and complete equations for each reactor. Model was used to analyse three possible accidents at the RA reactor and possible hypothetical accidents at the RB reactor

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

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…

RSMASS: A simple model for estimating reactor and shield masses

International Nuclear Information System (INIS)

Marshall, A.C.; Aragon, J.; Gallup, D.

1987-01-01

A simple mathematical model (RSMASS) has been developed to provide rapid estimates of reactor and shield masses for space-based reactor power systems. Approximations are used rather than correlations or detailed calculations to estimate the reactor fuel mass and the masses of the moderator, structure, reflector, pressure vessel, miscellaneous components, and the reactor shield. The fuel mass is determined either by neutronics limits, thermal/hydraulic limits, or fuel damage limits, whichever yields the largest mass. RSMASS requires the reactor power and energy, 24 reactor parameters, and 20 shield parameters to be specified. This parametric approach should be applicable to a very broad range of reactor types. Reactor and shield masses calculated by RSMASS were found to be in good agreement with the masses obtained from detailed calculations

Application of data mining in three-dimensional space time reactor model

International Nuclear Information System (INIS)

Jiang Botao; Zhao Fuyu

2011-01-01

A high-fidelity three-dimensional space time nodal method has been developed to simulate the dynamics of the reactor core for real time simulation. This three-dimensional reactor core mathematical model can be composed of six sub-models, neutron kinetics model, cay heat model, fuel conduction model, thermal hydraulics model, lower plenum model, and core flow distribution model. During simulation of each sub-model some operation data will be produced and lots of valuable, important information reflecting the reactor core operation status could be hidden in, so how to discovery these information becomes the primary mission people concern. Under this background, data mining (DM) is just created and developed to solve this problem, no matter what engineering aspects or business fields. Generally speaking, data mining is a process of finding some useful and interested information from huge data pool. Support Vector Machine (SVM) is a new technique of data mining appeared in recent years, and SVR is a transformed method of SVM which is applied in regression cases. This paper presents only two significant sub-models of three-dimensional reactor core mathematical model, the nodal space time neutron kinetics model and the thermal hydraulics model, based on which the neutron flux and enthalpy distributions of the core are obtained by solving the three-dimensional nodal space time kinetics equations and energy equations for both single and two-phase flows respectively. Moreover, it describes that the three-dimensional reactor core model can also be used to calculate and determine the reactivity effects of the moderator temperature, boron concentration, fuel temperature, coolant void, xenon worth, samarium worth, control element positions (CEAs) and core burnup status. Besides these, the main mathematic theory of SVR is introduced briefly next, on the basis of which SVR is applied to dealing with the data generated by two sample calculation, rod ejection transient and axial

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

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…

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)

Modeling of Hybrid Growth Wastewater Bio-reactor

International Nuclear Information System (INIS)

EI Nashaei, S.; Garhyan, P.; Prasad, P.; Abdel Halim, H.S.; Ibrahim, G.

2004-01-01

The attached/suspended growth mixed reactors are considered one of the recently tried approaches to improve the performance of the biological treatment by increasing the volume of the accumulated biomass in terms of attached growth as well as suspended growth. Moreover, the domestic WW can be easily mixed with a high strength non-hazardous industrial wastewater and treated together in these bio-reactors if the need arises. Modeling of Hybrid hybrid growth wastewater reactor addresses the need of understanding the rational of such system in order to achieve better design and operation parameters. This paper aims at developing a heterogeneous mathematical model for hybrid growth system considering the effect of diffusion, external mass transfer, and power input to the system in a rational manner. The model will be based on distinguishing between liquid/solid phase (bio-film and bio-floc). This model would be a step ahead to the fine tuning the design of hybrid systems based on the experimental data of a pilot plant to be implemented in near future

Mathematical modelling

CERN Document Server

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.

Advances in Reactor physics, mathematics and computation. Volume 3

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume 3, are divided into sessions bearing on: - poster sessions on benchmark and codes: 35 conferences - review of status of assembly spectrum codes: 9 conferences - Numerical methods in fluid mechanics and thermal hydraulics: 16 conferences - stochastic transport and methods: 7 conferences.

Optimisation of gas-cooled reactors with the aid of mathematical computers

Energy Technology Data Exchange (ETDEWEB)

Margen, P H

1959-04-15

Reactor optimisation is the task of finding the combination of values of the independent variables in a reactor design producing the lowest cost of electricity. In a gas-cooled reactor the number of independent variables is particularly large and the optimisation process is, therefore, laborious. The present note describes a procedure for performing the entire optimisation procedure with the aid of a mathematical computer in a single operation, thus saving time for the design staff. Detailed equations and numerical constants are proposed for the thermal and cost relations involved. The reactor physics equations, on the other hand are merely stated as general functions of the relevant variables. The task of expressing these functions as detailed equations will be covered by separate documents prepared by the reactor physics department.

Optimisation of gas-cooled reactors with the aid of mathematical computers

International Nuclear Information System (INIS)

Margen, P.H.

1959-04-01

Reactor optimisation is the task of finding the combination of values of the independent variables in a reactor design producing the lowest cost of electricity. In a gas-cooled reactor the number of independent variables is particularly large and the optimisation process is, therefore, laborious. The present note describes a procedure for performing the entire optimisation procedure with the aid of a mathematical computer in a single operation, thus saving time for the design staff. Detailed equations and numerical constants are proposed for the thermal and cost relations involved. The reactor physics equations, on the other hand are merely stated as general functions of the relevant variables. The task of expressing these functions as detailed equations will be covered by separate documents prepared by the reactor physics department

Mathematical model for safety analysis of heavy water power reactor

International Nuclear Information System (INIS)

Milovanovic, M.; Humo, E.; Mitrovic, S.

1966-01-01

Fundamental information in formulating the mathematical model for accident analysis is concerned with reactivity changes of the system. These parameters are: changes of fuel and moderator temperature, changes of the upper reflector thickness, reactivity changes due to moderator density variation dependent on the steam quantity and neutron flux distribution in the core

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

Science.gov (United States)

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…

Study on model of onset of nucleate boiling in natural circulation with subcooled boiling using unascertained mathematics

Energy Technology Data Exchange (ETDEWEB)

Zhou Tao [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)]. E-mail: zhoutao@mail.tsinghua.edu.cn; Wang Zenghui [Department of Engineering Mechanics, Tsinghua University, Beijing 100084 (China); Yang Ruichang [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)

2005-10-01

Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well.

Study on model of onset of nucleate boiling in natural circulation with subcooled boiling using unascertained mathematics

International Nuclear Information System (INIS)

Zhou Tao; Wang Zenghui; Yang Ruichang

2005-01-01

Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well

State-space model predictive control method for core power control in pressurized water reactor nuclear power stations

Energy Technology Data Exchange (ETDEWEB)

Wang, Guo Xu; Wu, Jie; Zeng, Bifan; Wu, Wangqiang; Ma, Xiao Qian [School of Electric Power, South China University of Technology, Guangzhou (China); Xu, Zhibin [Electric Power Research Institute of Guangdong Power Grid Corporation, Guangzhou (China)

2017-02-15

A well-performed core power control to track load changes is crucial in pressurized water reactor (PWR) nuclear power stations. It is challenging to keep the core power stable at the desired value within acceptable error bands for the safety demands of the PWR due to the sensitivity of nuclear reactors. In this paper, a state-space model predictive control (MPC) method was applied to the control of the core power. The model for core power control was based on mathematical models of the reactor core, the MPC model, and quadratic programming (QP). The mathematical models of the reactor core were based on neutron dynamic models, thermal hydraulic models, and reactivity models. The MPC model was presented in state-space model form, and QP was introduced for optimization solution under system constraints. Simulations of the proposed state-space MPC control system in PWR were designed for control performance analysis, and the simulation results manifest the effectiveness and the good performance of the proposed control method for core power control.

Metabolic modeling of synthesis gas fermentation in bubble column reactors.

Science.gov (United States)

Chen, Jin; Gomez, Jose A; Höffner, Kai; Barton, Paul I; Henson, Michael A

2015-01-01

A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors. We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining a genome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convective and dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield a large set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using the MATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellular parameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO and H2 conversions. Our computational study demonstrated that mathematical modeling provides a complementary tool to experimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictions could guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical production in syngas bubble column reactors.

Development of Mathematical Model and Analysis Code for Estimating Drop Behavior of the Control Rod Assembly in the Sodium Cooled Fast Reactor

International Nuclear Information System (INIS)

Oh, Se-Hong; Kang, SeungHoon; Choi, Choengryul; Yoon, Kyung Ho; Cheon, Jin Sik

2016-01-01

On receiving the scram signal, the control rod assemblies are released to fall into the reactor core by its weight. Thus drop time and falling velocity of the control rod assembly must be estimated for the safety evaluation. There are three typical ways to estimate the drop behavior of the control rod assembly in scram action: Experimental, numerical and theoretical methods. But experimental and numerical(CFD) method require a lot of cost and time. Thus, these methods are difficult to apply to the initial design process. In this study, mathematical model and theoretical analysis code have been developed in order to estimate drop behavior of the control rod assembly to provide the underlying data for the design optimization. Mathematical model and theoretical analysis code have been developed in order to estimate drop behavior of the control rod assembly to provide the underlying data for the design optimization. A simplified control rod assembly model is considered to minimize the uncertainty in the development process. And the hydraulic circuit analysis technique is adopted to evaluate the internal/external flow distribution of the control rod assembly. Finally, the theoretical analysis code(named as HEXCON) has been developed based on the mathematical model. To verify the reliability of the developed code, CFD analysis has been conducted. And a calculation using the developed analysis code was carried out under the same condition, and both results were compared

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

Science.gov (United States)

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

2015-03-01

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

Contribution to the modelling of gas-solid reactions and reactors

International Nuclear Information System (INIS)

Patisson, F.

2005-09-01

Gas-solid reactions control a great number of major industrial processes involving matter transformation. This dissertation aims at showing that mathematical modelling is a useful tool for both understanding phenomena and optimising processes. First, the physical processes associated with a gas-solid reaction are presented in detail for a single particle, together with the corresponding available kinetic grain models. A second part is devoted to the modelling of multiparticle reactors. Different approaches, notably for coupling grain models and reactor models, are illustrated through various case studies: coal pyrolysis in a rotary kiln, production of uranium tetrafluoride in a moving bed furnace, on-grate incineration of municipal solid wastes, thermogravimetric apparatus, nuclear fuel making, steel-making electric arc furnace. (author)

Mathematical modeling

CERN Document Server

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.

Two-channel model for dynamic analysis of GCR type reactor, Mathematical model; Dvokanalni model za dinamicku analizu reaktora GCR tipa, formulacija matematickog modela

Energy Technology Data Exchange (ETDEWEB)

Bingulac, B; Lazarevic, B; Matausek, M; Radanovic, Lj [Institut za nuklearne nauke Boris Kidric, Vinca, Beograd (Yugoslavia)

1964-07-01

A two-channel model for reactor dynamic analysis was developed. It enables representation of time dependent behaviour of a reactor as a whole and to obtain time and space dependent changes of temperature in any of the reactor channel. Model is suitable for follow-up of phenomena in limited time intervals up to few tens of minutes, since long term variations caused by fuel burnup and fission products are not taken into account in the model. Parameters are defined to cover the reactor power range from minimum to maximum. Model describes two main processes in the reactor: power generation dependent on the neutron flux and cooling.

Mathematical model of the reformer sponge iron cycle

Energy Technology Data Exchange (ETDEWEB)

Fraser, S.; Hacker, V.; Evers, B.; Hierzer, J.; Besenhard, J.O. [Graz University of Technology, Graz (Austria). Inst. for Chemical Technology of Inorganic Materials Christian Doppler Pilot-Lab. for Fuel Cell Systems

2003-07-01

An innovative hydrogen production process called the Reformer Sponge Iron Cycle (RESC), based on redox reactions of iron ore pellets, was mathematically modeled. The hydrogen is produced by blowing steam over hot iron pellets in the oxidation stage, resulting in the oxidation of the iron. Synthesis gas coming from a reformer mixed with a fraction of recycled off-gas was used to reduce the iron oxide pellets (wuestite and-or magnetite) in the reduction stage, leading once more to iron . Once the mathematical model was developed, it was verified utilizing experimental data. Based on calculations of the equilibrium gas concentrations for reformer and sponge iron reactor (SIR), the model computes mass fluxes, molar fluxes, partial pressures, and variations of them throughout the complete cycle. The recycle rate, which determines the fraction of SIR off-gas recycled and added to the input gas stream, was optimized to maximize the amount of iron oxide reduced for a certain input gas flow. 5 refs., 4 figs.

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

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…

A long term radiological risk model for plutonium-fueled and fission reactor space nuclear system

International Nuclear Information System (INIS)

Bartram, B.W.; Dougherty, D.K.

1987-01-01

This report describes the optimization of the RISK III mathematical model, which provides risk assessment for the use of a plutonium-fueled, fission reactor in space systems. The report discusses possible scenarios leading to radiation releases on the ground; distinctions are made for an intact reactor and a dispersed reactor. Also included are projected dose equivalents for various accident situations. 54 refs., 31 figs., 11 tabs

Mathematical model of the reformer sponge iron cycle

International Nuclear Information System (INIS)

Fraser, S.; Hacker, V.; Evers, B.; Hierzer, J.; Besenhard, J.O.

2003-01-01

A mathematical model of the Reformer Sponge Iron Cycle (RESC), an innovative hydrogen production process based on redox reactions of iron ore pellets is presented. In the oxidation stage of the RESC, hydrogen is produced by blowing steam over hot iron pellets, hence oxidizing the iron. In the reduction stage, synthesis gas coming from a reformer mixed with a fraction of recycled off-gas is used to reduce the iron oxide pellets (wuestite and/or magnetite) back into iron again. A mathematical model of the complete RESC was developed and verified with experimental data. The model is based on calculations of the equilibrium gas concentrations for reformer and Sponge Iron Reactor (SIR). The current model computes mass fluxes, molar fluxes, partial pressures and variations of the respective throughout the complete cycle. The recycle rate, determining the fraction of SIR off-gas recycled and added to the input gas stream was subsequently optimized in order to maximize the amount of iron oxide reduced for a certain input gas flow. (author)

Mathematical modelling techniques

CERN Document Server

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

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

Science.gov (United States)

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…

A mathematical model of an automatic assembler to stack fuel pellets

International Nuclear Information System (INIS)

Jarvis, R.G.; Joynes, R.; Bretzlaff, C.I.

1980-11-01

Fuel elements for CANDU reactors are assembled from stacks of cylindrical UO 2 pellets, with close tolerances on lengths and diameters. Present stacking techniques involve extensive manual operations and they can be speeded up and reduced in cost by an automated device. If gamma-active fuel is handled such a device is essential. An automatic fuel pellet assembly process was modelled mathematically. The model indicated a suitable sequence of pellet manipulations to arrive at a stack length that was always within tolerance. This sequence was used as the inital input for the design of mechanical hardware. The mechanical design and the refinement of the mathematical model proceeded simultaneously. Mechanical constraints were allowed for in the model, and its optimized sequence of operations was incorporated in a microcomputer program to control the mechanical hardware. (auth)

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

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…

Critical evaluation of the experiments and mathematical models for the determination of fission product release from the spherical fuel elements in cases of core heating accidents in modular HTR's

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 modeling of the voloxidation process. Final report

International Nuclear Information System (INIS)

Stanford, T.G.

1979-06-01

A mathematical model of the voloxidation process, a head-end reprocessing step for the removal of volatile fission products from spent nuclear fuel, has been developed. Three types of voloxidizer operation have been considered; co-current operation in which the gas and solid streams flow in the same direction, countercurrent operation in which the gas and solid streams flow in opposite directions, and semi-batch operation in which the gas stream passes through the reactor while the solids remain in it and are processed batch wise. Because of the complexity of the physical ahd chemical processes which occur during the voloxidation process and the lack of currently available kinetic data, a global kinetic model has been adapted for this study. Test cases for each mode of operation have been simulated using representative values of the model parameters. To process 714 kgm/day of spent nuclear fuel, using an oxidizing atmosphere containing 20 mole percent oxygen, it was found that a reactor 0.7 m in diameter and 2.49 m in length would be required for both cocurrent and countercurrent modes of operation while for semibatch operation a 0.3 m 3 reactor and an 88200 sec batch processing time would be required

MATHEMATICAL 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.

A new model for anaerobic processes of up-flow anaerobic sludge blanket reactors based on cellular automata

DEFF Research Database (Denmark)

Skiadas, Ioannis V.; Ahring, Birgitte Kiær

2002-01-01

characteristics and lead to different reactor behaviour. A dynamic mathematical model has been developed for the anaerobic digestion of a glucose based synthetic wastewater in UASB reactors. Cellular automata (CA) theory has been applied to simulate the granule development process. The model takes...... into consideration that granule diameter and granule microbial composition are functions of the reactor operational parameters and is capable of predicting the UASB performance and the layer structure of the granules....

Computer modelling of radioactive source terms at a tokamak reactor

International Nuclear Information System (INIS)

Meide, A.

1984-12-01

The Monte Carlo code MCNP has been used to create a simple three-dimensional mathematical model representing 1/12 of a tokamak fusion reactor for studies of the exposure rate level from neutrons as well as gamma rays from the activated materials, and for later estimates of the consequences to the environment, public, and operating personnel. The model is based on the recommendations from the NET/INTOR workshops. (author)

Mathematical modeling of methyl ester concentration distribution in a continuous membrane tubular reactor and comparison with conventional tubular reactor

Science.gov (United States)

Talaghat, M. R.; Jokar, S. M.; Modarres, E.

2017-10-01

The reduction of fossil fuel resources and environmental issues made researchers find alternative fuels include biodiesels. One of the most widely used methods for production of biodiesel on a commercial scale is transesterification method. In this work, the biodiesel production by a transesterification method was modeled. Sodium hydroxide was considered as a catalyst to produce biodiesel from canola oil and methanol in a continuous tubular ceramic membranes reactor. As the Biodiesel production reaction from triglycerides is an equilibrium reaction, the reaction rate constants depend on temperature and related linearly to catalyst concentration. By using the mass balance for a membrane tubular reactor and considering the variation of raw materials and products concentration with time, the set of governing equations were solved by numerical methods. The results clearly show the superiority of membrane reactor than conventional tubular reactors. Afterward, the influences of molar ratio of alcohol to oil, weight percentage of the catalyst, and residence time on the performance of biodiesel production reactor were investigated.

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....

Modeling and performance of the MHTGR [Modular High-Temperature Gas-Cooled Reactor] reactor cavity cooling system

International Nuclear Information System (INIS)

Conklin, J.C.

1990-04-01

The Reactor Cavity Cooling System (RCCS) of the Modular High- Temperature Gas-Cooled Reactor (MHTGR) proposed by the U.S. Department of Energy is designed to remove the nuclear afterheat passively in the event that neither the heat transport system nor the shutdown cooling circulator subsystem is available. A computer dynamic simulation for the physical and mathematical modeling of and RCCS is described here. Two conclusions can be made form computations performed under the assumption of a uniform reactor vessel temperature. First, the heat transferred across the annulus from the reactor vessel and then to ambient conditions is very dependent on the surface emissivities of the reactor vessel and RCCS panels. These emissivities should be periodically checked to ensure the safety function of the RCCS. Second, the heat transfer from the reactor vessel is reduced by a maximum of 10% by the presence of steam at 1 atm in the reactor cavity annulus for an assumed constant in the transmission of radiant energy across the annulus can be expected to result in an increase in the reactor vessel temperature for the MHTGR. Further investigation of participating radiation media, including small particles, in the reactor cavity annulus is warranted. 26 refs., 7 figs., 1 tab

Co-digestion and model simulations of source separated municipal organic waste with cattle manure under batch and continuously stirred tank reactors

DEFF Research Database (Denmark)

Tsapekos, Panagiotis; Kougias, Panagiotis; Kuthiala, Sidhant

2018-01-01

reactor was comparable with the results obtained from the batch assay (i.e. expected value). Finally, the outputs from an applied mathematical model were in good agreement with the experimental data obtained from the continuous reactor operation, demonstrating that the BioModel can...

Trickle bed reactor model to simulate the performance of commercial diesel hydrotreating unit

Energy Technology Data Exchange (ETDEWEB)

C. Murali; R.K. Voolapalli; N. Ravichander; D.T. Gokak; N.V. Choudary [Bharat Petroleum Corporation Ltd., Udyog Kendra (India). Corporate R& amp; D Centre

2007-05-15

A two phase mathematical model was developed to simulate the performance of bench scale and commercial hydrotreating reactors. Major hydrotreating reactions, namely, hydrodesulphurization, hydrodearomatization and olefins saturation were modeled. Experiments were carried out in a fixed bed reactor to study the effect of different process variables and these results were used for estimating kinetic parameters. Significant amount of feed vaporization (20-50%) was estimated under normal operating conditions of DHDS suggesting the importance of considering feed vaporization in DHDS modeling. The model was validated with plant operating data, under close to ultra low sulphur levels by correctly accounting for feed vaporization in heat balance relations and appropriate use of hydrodynamic correlations. The model could predict the product quality, reactor bed temperature profiles and chemical hydrogen consumption in commercial plant adequately. 14 refs., 7 figs., 6 tabs.

Analysis of dynamic stability and safety of reactor system by reactor simulator; Analiza dinamicke stabilnosti i sigurnosti reaktorskog sistema pomocu reaktorskog simulatora

Energy Technology Data Exchange (ETDEWEB)

Raisic, N [Boris Kidric Institute of Nuclear Sciences Vinca, Belgrade (Yugoslavia)

1963-11-15

In order to enable qualitative analysis of dynamic properties of reactors RA and RB, mathematical models of these reactors were formulated and adapted for solution on analog computer. This report contains basic assessments for creating the model and complete equations for each reactor. Model was used to analyse three possible accidents at the RA reactor and possible hypothetical accidents at the RB reactor.

Method of experimental and theoretical modeling for multiple pressure tube rupture for RBMK reactor

International Nuclear Information System (INIS)

Medvedeva, N.Y.; Goldstein, R.V.; Burrows, J.A.

2001-01-01

The rupture of single RBMK reactor channels has occurred at a number of stations with a variety of initiating events. It is assumed in RBMK Safety Cases that the force of the escaping fluid will not cause neighbouring channels to break. This assumption has not been justified. A chain reaction of tube breaks could over-pressurise the reactor cavity leading to catastrophic failure of the containment. To validate the claims of the RBMK Safety Cases the Electrogorsk Research and Engineering Centre, in participation with experts from the Institute of Mechanics of RAS, has developed the method of interacting multiscale physical and mathematical modelling for coupled thermophysical, hydrogasodynamic processes and deformation and break processes causing and (or) accompanying potential failures, design and beyond the design RBMK reactor accidents. To realise the method the set of rigs, physical and mathematical models and specialized computer codes are under creation. This article sets out an experimental philosophy and programme for achieving this objective to solve the problem of credibility or non-credibility for multiple fuel channel rupture in RBMK.(author)

A comparative study of time series modeling methods for reactor noise analysis

International Nuclear Information System (INIS)

Kitamura, Masaharu; Shigeno, Kei; Sugiyama, Kazusuke

1978-01-01

Two modeling algorithms were developed to study at-power reactor noise as a multi-input, multi-output process. A class of linear, discrete time description named autoregressive-moving average model was used as a compact mathematical expression of the objective process. One of the model estimation (modeling) algorithms is based on the theory of Kalman filtering, and the other on a conjugate gradient method. By introducing some modifications in the formulation of the problem, realization of the practically usable algorithms was made feasible. Through the testing with several simulation models, reliability and effectiveness of these algorithms were confirmed. By applying these algorithms to experimental data obtained from a nuclear power plant, interesting knowledge about the at-power reactor noise was found out. (author)

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...

Dynamics analysis of a boiling water reactor based on multivariable autoregressive modeling

International Nuclear Information System (INIS)

Oguma, Ritsuo; Matsubara, Kunihiko

1980-01-01

The establishment of the highly reliable mathematical model for the dynamic characteristics of a reactor is indispensable for the achievement of safe operation in reactor plants. The authors have tried to model the dynamic characteristics of a reactor based on the identification technique, taking the JPDR (Japan Power Demonstration Reactor) as the object, as one of the technical studies for diagnosing BWR anomaly, and employed the multivariable autoregressive modeling (MAR method) as one of the useful methods for forwarding the analysis. In this paper, the outline of the system analysis by MAR modeling is explained, and the identification experiments and their analysis results performed in the phase 4 of the power increase test of the JPDR are described. The authors evaluated the results of identification based on only reactor noises, making reference to the results of identification in the case of exciting the system by applying artificial irregular disturbance, in order to clarify the extent in which the modeling is possible by reactor noises only. However, some difficulties were encountered. The largest problem is the one concerning the separation and identification of the noise sources exciting the variables from the dynamic characteristics among the variables. If the effective technique can be obtained to this problem, the approach by the identification technique based on the probability model might be a powerful tool in the field of reactor noise analysis and the development of diagnosis technics. (Wakatsuki, Y.)

Modelling of sludge blanket height and flow pattern in UASB reactors treating municipal wastewater

International Nuclear Information System (INIS)

Singh, K.S.; Viraraghavan, T.

2002-01-01

Two upflow anaerobic sludge blanket (UASB) reactors were started-up and operated for approximately 900 days to examine the feasibility of treating municipal wastewater under low temperature conditions. A modified solid distribution model was formulated by incorporating the variation of biogas production rate with a change in temperature. This model was used to optimize the sludge blanket height of UASB reactors for an effective operation of gas-liquid-solid (GLS) separation device. This model was found to simulate well the solid distribution as confirmed experimental observation of solid profile along the height of the reactor. Mathematical analysis of tracer curves indicated the presence of a mixed type of flow pattern in the sludge-bed zone of the reactor. It was found that the dead-zone and by-pass flow fraction were impacted by the change in operating temperatures. (author)

Modeling and simulation of an isothermal reactor for methanol steam reforming

Directory of Open Access Journals (Sweden)

Raphael Menechini Neto

2014-04-01

Full Text Available Due to growing electricity demand, cheap renewable energy sources are needed. Fuel cells are an interesting alternative for generating electricity since they use hydrogen as their main fuel and release only water and heat to the environment. Although fuel cells show great flexibility in size and operating temperature (some models even operate at low temperatures, the technology has the drawback for hydrogen transportation and storage. However, hydrogen may be produced from methanol steam reforming obtained from renewable sources such as biomass. The use of methanol as raw material in hydrogen production process by steam reforming is highly interesting owing to the fact that alcohol has the best hydrogen carbon-1 ratio (4:1 and may be processed at low temperatures and atmospheric pressures. They are features which are desirable for its use in autonomous fuel cells. Current research develops a mathematical model of an isothermal methanol steam reforming reactor and validates it against experimental data from the literature. The mathematical model was solved numerically by MATLAB® and the comparison of its predictions for different experimental conditions indicated that the developed model and the methodology for its numerical solution were adequate. Further, a preliminary analysis was undertaken on methanol steam reforming reactor project for autonomous fuel cell.

Conceptual design of a nucleo electric simulator with PBMR reactor based in Reduced order models

International Nuclear Information System (INIS)

Valle H, J.; Morales S, J.B.

2005-01-01

This project has as purpose to know to depth the operation of a PBMR nucleo electric type (Pebble Bed Modular Reactor), which has a reactor of moderate graphite spheres and fuel of uranium dioxide cooled with Helium and Brayton thermodynamic cycle. The simulator seeks to describe the dynamics of the one process of energy generation in the nuclear fuel, the process of transport toward the coolant one and the conversion to mechanical energy in the turbo-generators as well as in the heat exchangers indispensable for the process. The dynamics of reload of the fuel elements it is not modeled in detail but their effects are represented in the parameters of the pattern. They are modeled also the turbo-compressors of the primary circuit of the work fluid. The control of the power of the nuclear reactor is modeled by means of reactivity functions specified in the simulation platform. The proposed mathematical models will be settled in the platform of simulation of Simulink-Mat Lab. The proposed control panels for this simulator can be designed and to implement using the box of tools of Simulink that facilitates this process. The work presents the mathematical models more important used for their future implementation in Simulink. (Author)

Description of mathematical models and computer programs

International Nuclear Information System (INIS)

1977-01-01

The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives

Mathematical Modeling: A Structured Process

Science.gov (United States)

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…

M and c'99 : Mathematics and computation, reactor physics and environmental analysis in nuclear applications, Madrid, September 27-30, 1999

International Nuclear Information System (INIS)

Aragones, J. M.; Ahnert, C.; Cabellos, O.

1999-01-01

The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)

Modelling an industrial anaerobic granular reactor using a multi-scale approach

DEFF Research Database (Denmark)

Feldman, Hannah; Flores Alsina, Xavier; Ramin, Pedram

2017-01-01

The objective of this paper is to show the results of an industrial project dealing with modelling of anaerobic digesters. A multi-scale mathematical approach is developed to describe reactor hydrodynamics, granule growth/distribution and microbial competition/inhibition for substrate/space within...... the biofilm. The main biochemical and physico-chemical processes in the model are based on the Anaerobic Digestion Model No 1 (ADM1) extended with the fate of phosphorus (P), sulfur (S) and ethanol (Et-OH). Wastewater dynamic conditions are reproduced and data frequency increased using the Benchmark...... simulations show the effects on the overall process performance when operational (pH) and loading (S:COD) conditions are modified. Lastly, the effect of intra-granular precipitation on the overall organic/inorganic distribution is assessed at: 1) different times; and, 2) reactor heights. Finally...

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

Science.gov (United States)

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…

Model for spatial synthesis of automated control system of the GCR type reactor; Model za prostornu sintezu sistema automatskog upravljanja reaktora GCR tipa

Energy Technology Data Exchange (ETDEWEB)

Lazarevic, B; Matausek, M [Institut za nuklearne nauke ' Boris Kidric' , Vinca, Belgrade (Yugoslavia)

1966-07-01

This paper describes the model which was developed for synthesis of spatial distribution of automated control elements in the reactor. It represents a general reliable mathematical model for analyzing transition states and synthesis of the automated control and regulation systems of GCR type reactors. One-dimensional system was defined under assumption that the time dependence of parameters of the neutron diffusion equation are identical in the total volume of the reactor and that spatial distribution of neutrons is time independent. It is shown that this assumption is satisfactory in case of short term variations which are relevant for safety analysis.

Dynamic analysis of the PEC fast reactor vessel: On-site tests and mathematical models

International Nuclear Information System (INIS)

Zola, M.; Martelli, A.; Masoni, P.; Scandola, G.

1988-01-01

This paper presents the main features and results of the on-site dynamic tests and the related numerical analyses carried out for the PEC reactor vessel. The purpose is to provide an example of on-site testing of large components, stressing the problems encountered during the experiments, as well as in the processing phase of the test results and for the comparisons between calculations and measurements. Tests, performed by ISMES on behalf of ENEA, allowed the dynamic response of the empty vessel to be measured, thus providing data for the verification of the numerical models of the vessel supporting structure adopted in the PEC reactor-block seismic analysis. An axisymmetric model of the vessel, implemented in the NOVAX code, had been developed in the framework of the detailed numerical studies performed by NOVATOME (again on behalf of ENEA), to check the beam schematization with fluid added mass model adopted by ANSALDO in SAP-IV and ANSYS for the reactor-block design calculations. Furthermore, a numerical model, describing vessel supporting structure in detail, was also developed by ANSALDO and implemented in the SAP-IV code. The test conditions were analysed by use of these and the design models. Comparisons between calculations and measurements showed particularly good agreement with regard to first natural frequency of the vessel and rocking stiffness of the vessel supporting structure, i.e. those parameters on which vessel seismic amplification mainly depends: this demonstrated the adequacy of the design analysis to correctly calculate the seismic motion at the PEC core diagrid. (author). 5 refs, 23 figs, 4 tabs

Dynamic analysis of the PEC fast reactor vessel: on-site tests and mathematical models

International Nuclear Information System (INIS)

Zola, Maurizio; Martelli, Alessandro; Maresca, Giuseppe; Masoni, Paolo; Scandola, Giani; Descleves, Pierre

1988-01-01

This paper presents the main features and results of the on-site dynamic tests and the related numerical analysis carried out for the PEC reactor vessel. The purpose is to provide an example of on-site testing of large components, stressing the problems encountered during the experiments, as well as in the processing phase of the test results and for the comparisons between calculations and measurements. Tests, performed by ISMES on behalf of ENEA, allowed the dynamic response of the empty vessel to be measured, thus providing data for the verification of the numerical models of the vessel supporting structure adopted in the PEC reactor-block seismic analysis. An axisymmetric model of the vessel, implemented in the vessel, implemented in the NOVAK code, had been developed in the framework of the detailed numerical studies performed by NOVATOME (again on behalf of ENEA), to check the beam schematization with fluid added mass model adopted by ANSALDO in SAP-IV and ANSYS for the reactor-block design calculations. Furthermore, a numerical model, describing vessel supporting structure in detail, was also developed by ANSALDO and implemented in the SAP-IV code. The test conditions were analysed by use of these and the design models. Comparisons between calculations and measurements showed particularly good agreement with regard to first natural frequency of the vessel and rocking stiffness of the vessel supporting structure, i.e. those parameters on which vessel seismic amplification mainly depends: this demonstrated the adequacy of the design analysis to correctly calculate the seismic motion at the PEC core diagrid. (author)

Modeling of requirement specification for safety critical real time computer system using formal mathematical specifications

International Nuclear Information System (INIS)

Sankar, Bindu; Sasidhar Rao, B.; Ilango Sambasivam, S.; Swaminathan, P.

2002-01-01

Full text: Real time computer systems are increasingly used for safety critical supervision and control of nuclear reactors. Typical application areas are supervision of reactor core against coolant flow blockage, supervision of clad hot spot, supervision of undesirable power excursion, power control and control logic for fuel handling systems. The most frequent cause of fault in safety critical real time computer system is traced to fuzziness in requirement specification. To ensure the specified safety, it is necessary to model the requirement specification of safety critical real time computer systems using formal mathematical methods. Modeling eliminates the fuzziness in the requirement specification and also helps to prepare the verification and validation schemes. Test data can be easily designed from the model of the requirement specification. Z and B are the popular languages used for modeling the requirement specification. A typical safety critical real time computer system for supervising the reactor core of prototype fast breeder reactor (PFBR) against flow blockage is taken as case study. Modeling techniques and the actual model are explained in detail. The advantages of modeling for ensuring the safety are summarized

Finite mathematics models and applications

CERN Document Server

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

Science.gov (United States)

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

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

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

Science.gov (United States)

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 problems in meteorological modelling

CERN Document Server

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...

Simplified model for the thermo-hydraulic simulation of the hot channel of a PWR type nuclear reactor

International Nuclear Information System (INIS)

Belem, J.A.T.

1993-09-01

The present work deals with the thermal-hydraulic analysis of the hot channel of a standard PWR type reactor utilizing a simplified mathematical model that considers constant the water mass flux during single-phase flow and reduction of the flow when the steam quality is increasing in the channel (two-phase flow). The model has been applied to the Angra-1 reactor and it has proved satisfactory when compared to other ones. (author). 25 refs, 15 figs, 3 tabs

Dynamic behaviour of CANDU reactor

International Nuclear Information System (INIS)

Subramanian, M.G.; Srikantiah, G.; Pai, M.A.

1976-01-01

Understanding of the dynamic behaviour of a reactor system in a power station is essential for evolving control stragies as well as design modifications. The dynamic behaviour of Rajasthan Atomic Power Station is studied. Mathematical models for the reactor, the steam generator and the steam drum with the natural circulation loop are developed from physical principles like conservation of mass, momentum and energy. Each of these models is then simulated on a digital computer to obtain the characteristics during transients. The models are then combined to yield a dynamic mathematical model of the system comprising the reactor, the steam generator and the steam drum and this results in a nonlinear model. Using this model, responses of the system for various disturbances like step change in the area of the steam valve, step change in the temperature of feed water are obtained and are discussed. These models could be used to devise new control laws using optimal control theory or to evaluate the performance of existing control schemes. (author)

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

Science.gov (United States)

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…

Three-dimensional reactor dynamics code for VVER type nuclear reactors

Energy Technology Data Exchange (ETDEWEB)

Kyrki-Rajamaeki, R. [VTT Energy, Espoo (Finland)

1995-10-01

A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. (79 refs.).

Three-dimensional reactor dynamics code for VVER type nuclear reactors

International Nuclear Information System (INIS)

Kyrki-Rajamaeki, R.

1995-10-01

A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. (79 refs.)

M and c'99 : Mathematics and computation, reactor physics and environmental analysis in nuclear applications, Madrid, September 27-30, 1999

Energy Technology Data Exchange (ETDEWEB)

Aragones, J. M.; Ahnert, C.; Cabellos, O.

1999-07-01

The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)

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

Science.gov (United States)

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

CERN Document Server

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

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

Science.gov (United States)

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

CERN Document Server

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

Science.gov (United States)

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…

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

Science.gov (United States)

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 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...

Studies on modelling of bubble driven flows in chemical reactors

Energy Technology Data Exchange (ETDEWEB)

Grevskott, Sverre

1997-12-31

Multiphase reactors are widely used in the process industry, especially in the petrochemical industry. They very often are characterized by very good thermal control and high heat transfer coefficients against heating and cooling surfaces. This thesis first reviews recent advances in bubble column modelling, focusing on the fundamental flow equations, drag forces, transversal forces and added mass forces. The mathematical equations for the bubble column reactor are developed, using an Eulerian description for the continuous and dispersed phase in tensor notation. Conservation equations for mass, momentum, energy and chemical species are given, and the k-{epsilon} and Rice-Geary models for turbulence are described. The different algebraic solvers used in the model are described, as are relaxation procedures. Simulation results are presented and compared with experimental values. Attention is focused on the modelling of void fractions and gas velocities in the column. The energy conservation equation has been included in the bubble column model in order to model temperature distributions in a heated reactor. The conservation equation of chemical species has been included to simulate absorption of CO{sub 2}. Simulated axial and radial mass fraction profiles for CO{sub 2} in the gas phase are compared with measured values. Simulations of the dynamic behaviour of the column are also presented. 189 refs., 124 figs., 1 tab.

Development of modeling tools for pin-by-pin precise reactor simulation

International Nuclear Information System (INIS)

Ma Yan; Li Shu; Li Gang; Zhang Baoyin; Deng Li; Fu Yuanguang

2013-01-01

In order to develop large-scale transport simulation and calculation method (such as simulation of whole reactor core pin-by-pin problem), the Institute of Applied Physics and Computational Mathematics developed the neutron-photon coupled transport code JMCT and the toolkit JCOGIN. Creating physical calculation model easily and efficiently can essentially reduce problem solving time. Currently, lots of visual modeling programs have been developed based on different CAD systems. In this article, the developing idea of a visual modeling tool based on field oriented development was introduced. Considering the feature of physical modeling, fast and convenient operation modules were developed. In order to solve the storage and conversion problems of large scale models, the data structure and conversional algorithm based on the hierarchical geometry tree were designed. The automatic conversion and generation of physical model input file for JMCT were realized. By using this modeling tool, the Dayawan reactor whole core physical model was created, and the transformed file was delivered to JMCT for transport calculation. The results validate the correctness of the visual modeling tool. (authors)

Accident transient processes at NPPs with the WWER type reactors

International Nuclear Information System (INIS)

Bukrinskij, A.M.

1982-01-01

Thermal-physical and nuclear-physical transient processes at NPPs with the WWER type reactors during accidents with the main technological equipment failures and the accidents with loss of coolant in the primary and secondary coolant circuits are considered. Mathematical methods used for these processes modelling is described. Examples of concrete calculations for accidents with different failures are given. Comparative analysis of the results of dynamic tests at the Novo-Voronezh-3 reactor is presented. It is concluded that the modern NPP design is impossible without application of mathematical modelling methods. The mathematical modelling of transients is also necessary for proper and safe NPP operation. Mathematical modelling of accidents at NPPs is a comparatively new method of investigation. Its success and development are completely based on the progress in modern computer development. With their improvement the mathematical models will become more complicate and adequacy of real physical process representation by their means will increase

Optimising the anaerobic co-digestion of urban organic waste using dynamic bioconversion mathematical modelling

DEFF Research Database (Denmark)

Fitamo, Temesgen Mathewos; Boldrin, Alessio; Dorini, G.

2016-01-01

Mathematical anaerobic bioconversion models are often used as a convenient way to simulate the conversion of organic materials to biogas. The aim of the study was to apply a mathematical model for simulating the anaerobic co-digestion of various types of urban organic waste, in order to develop...... in a continuously stirred tank reactor. The model's outputs were validated with experimental results obtained in thermophilic conditions, with mixed sludge as a single substrate and urban organic waste as a co-substrate at hydraulic retention times of 30, 20, 15 and 10 days. The predicted performance parameter...... (methane productivity and yield) and operational parameter (concentration of ammonia and volatile fatty acid) values were reasonable and displayed good correlation and accuracy. The model was later applied to identify optimal scenarios for an urban organic waste co-digestion process. The simulation...

Two-phase coolant pump model of pressurized light water nuclear reactors

International Nuclear Information System (INIS)

Santos, G.A. dos; Freitas, R.L.

1990-01-01

The two-phase coolant pump model of pressurized light water nuclear reactors is an important point for the loss of primary coolant accident analysis. The homologous curves set up the complete performance of the pump and are input for accidents analysis thermal-hydraulic codes. This work propose a mathematical model able to predict the two-phase homologous curves where it was incorporated geometric and operational pump condition. The results were compared with the experimental tests data from literature and it has showed a good agreement. (author)

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

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

Science.gov (United States)

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

CERN Document Server

Bender, Edward A

2000-01-01

Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

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

Science.gov (United States)

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…

Model study of an automatic controller of the IBR-2 pulsed reactor

International Nuclear Information System (INIS)

Pepelyshev, Yu.N.; Popov, A.K.

2007-01-01

For calculation of power transients in the IBR-2 reactor a special mathematical model of dynamics taking into account the discontinuous jump of reactivity by an automatic controller with the step motor is created. In the model the nonlinear dependence of the energy of power pulse on the reactivity and the influence of warming up of the reactor on the reactivity by means of introduction of a nonlinear feedback 'power-pulse energy - reactivity' are taken into account. With the help of the model the transients of relative deviation of power-pulse energy are calculated at various (random, mixed and regular) reactivity disturbances at the reactor mean power 1.475 MW. It is shown that to improve the quality of processes the choice of such regular values of parameters of the automatic controller is expedient, at which the least effect of smoothing of a signal acting on an automatic controller and the least speed of an automatic controller are provided, and the reduction of efficiency of one step of the automatic controller and introduction of a five-percent dead space are also expedient

Mathematical modeling of a fast-breeder-reactor generating unit

International Nuclear Information System (INIS)

Kim, V.E.; Golovach, E.A.; Senkin, V.I.

1984-01-01

Dynamics equations are given for a reactor, intermediate heat exchanger, steam generator, and turbogenerator. The dynamic characteristics of the generating unit are described when perturbations occur in grid frequency, turbine valves, and feedwater consumption

Reactor training simulator for the Replacement Research Reactor (RRR)

International Nuclear Information System (INIS)

Etchepareborda, A; Flury, C.A; Lema, F; Maciel, F; Alegrechi, D; Damico, M; Ibarra, G; Muguiro, M; Gimenez, M; Schlamp, M; Vertullo, A

2004-01-01

The main features of the ANSTO Replacement Research Reactor (RRR) Reactor Training Simulator (RTS) are presented.The RTS is a full-scope and partial replica simulator.Its scope includes a complete set of plant normal evolutions and malfunctions obtained from the plant design basis accidents list.All the systems necessary to implement the operating procedures associated to these transients are included.Within these systems both the variables connected to the plant SCADA and the local variables are modelled, leading to several thousands input-output variables in the plant mathematical model (PMM).The trainee interacts with the same plant SCADA, a Foxboro I/A Series system.Control room hardware is emulated through graphical displays with touch-screen.The main system models were tested against RELAP outputs.The RTS includes several modules: a model manager (MM) that encapsulates the plant mathematical model; a simulator human machine interface, where the trainee interacts with the plant SCADA; and an instructor console (IC), where the instructor commands the simulation.The PMM is built using Matlab-Simulink with specific libraries of components designed to facilitate the development of the nuclear, hydraulic, ventilation and electrical plant systems models [es

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

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

Comparison of rate theory based modeling calculations with the surveillance test results of Korean light water reactors

International Nuclear Information System (INIS)

Lee, Gyeong Geun; Lee, Yong Bok; Kim, Min Chul; Kwon, Junh Yun

2012-01-01

Neutron irradiation to reactor pressure vessel (RPV) steels causes a decrease in fracture toughness and an increase in yield strength while in service. It is generally accepted that the growth of point defect cluster (PDC) and copper rich precipitate (CRP) affects radiation hardening of RPV steels. A number of models have been proposed to account for the embrittlement of RPV steels. The rate theory based modeling mathematically described the evolution of radiation induced microstructures of ferritic steels under neutron irradiation. In this work, we compared the rate theory based modeling calculation with the surveillance test results of Korean Light Water Reactors (LWRs)

Simulation of styrene polymerization reactors: kinetic and thermodynamic modeling

Directory of Open Access Journals (Sweden)

A. S. Almeida

2008-06-01

Full Text Available A mathematical model for the free radical polymerization of styrene is developed to predict the steady-state and dynamic behavior of a continuous process. Special emphasis is given for the kinetic and thermodynamic models, where the most sensitive parameters were estimated using data from an industrial plant. The thermodynamic model is based on a cubic equation of state and a mixing rule applied to the low-pressure vapor-liquid equilibrium of polymeric solutions, suitable for modeling the auto-refrigerated polymerization reactors, which use the vaporization rate to remove the reaction heat from the exothermic reactions. The simulation results show the high predictive capability of the proposed model when compared with plant data for conversion, average molecular weights, polydispersity, melt flow index, and thermal properties for different polymer grades.

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

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

Mathematical models for plant-herbivore interactions

Science.gov (United States)

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.

Horizontal bioreactor for ethanol production by immobilized cells. Pt. 3. Reactor modeling and experimental verification

Energy Technology Data Exchange (ETDEWEB)

Woehrer, W

1989-04-05

A mathematical model which describes ethanol formation in a horizontal tank reactor containing Saccharomyces cerevisiae immobilized in small beads of calcium alignate has been developed. The design equations combine flow dynamics of the reactor as well as product formation kinetics. The model was verified for 11 continuous experiments, where dilution rate, feed glucose concentration and bead volume fraction were varied. The model predicts effluent ethanol concentration and CO/sub 2/ production rate within the experimental error. A simplification of the model is possible, when the feed glucose concentration does not exceed 150 kg/m/sup 3/. The simplification results in an analytical solution of the design equation and hence can easily be applied for design purposes as well as for optimization studies.

Reactor physics and reactor computations

International Nuclear Information System (INIS)

Ronen, Y.; Elias, E.

1994-01-01

Mathematical methods and computer calculations for nuclear and thermonuclear reactor kinetics, reactor physics, neutron transport theory, core lattice parameters, waste treatment by transmutation, breeding, nuclear and thermonuclear fuels are the main interests of the conference

Characteristics of a reactor with power reactivity feedback

International Nuclear Information System (INIS)

Li Fengyu; Zhang Yusheng; Zhang Guangfu; Liu Ying

2008-01-01

The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equation qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, and the other is hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stabilities in the mathematical sense and in the physical sense is indicated. (authors)

Conceptual design of a nucleo electric simulator with PBMR reactor based in Reduced order models; Diseno conceptual de un simulador de nucleo electrica con reactor PBMR basado en modelos de orden reducido

Energy Technology Data Exchange (ETDEWEB)

Valle H, J.; Morales S, J.B. [UNAM, DEPFI, Campus Morelos, en IMTA Jiutepec, Morelos (Mexico)]. e-mail: jms0620@yahoo.com

2005-07-01

This project has as purpose to know to depth the operation of a PBMR nucleo electric type (Pebble Bed Modular Reactor), which has a reactor of moderate graphite spheres and fuel of uranium dioxide cooled with Helium and Brayton thermodynamic cycle. The simulator seeks to describe the dynamics of the one process of energy generation in the nuclear fuel, the process of transport toward the coolant one and the conversion to mechanical energy in the turbo-generators as well as in the heat exchangers indispensable for the process. The dynamics of reload of the fuel elements it is not modeled in detail but their effects are represented in the parameters of the pattern. They are modeled also the turbo-compressors of the primary circuit of the work fluid. The control of the power of the nuclear reactor is modeled by means of reactivity functions specified in the simulation platform. The proposed mathematical models will be settled in the platform of simulation of Simulink-Mat Lab. The proposed control panels for this simulator can be designed and to implement using the box of tools of Simulink that facilitates this process. The work presents the mathematical models more important used for their future implementation in Simulink. (Author)

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.

Multigroup perturbation model for kinetic analysis of nuclear reactors

International Nuclear Information System (INIS)

Souza, G.M.

1989-01-01

The scope of this work is the development of a multigroup perturbation theory for the purpose of Kinetic and dynamic analysis of nuclear reactors. The equations that describe the reactor behavior were presented in all generality and written in the shorthand notation of matrices and vectors. In the derivation of those equations indetermined operators and discretizing factors were introduced and then determined by comparision with conventional equations. Fick's Law was developed in higher orders for neutron and importance current density. The solution of the direct and adjoint fields were represented by combination of the eigenfunctions of the B and B* operators and the eigenvalue modulus equality was established mathematically. In the derivation of the reactivity expression the B operator perturbation was split in two non coupled to the flux form and level. The prompt neutrons effective mean life was derived from reactor equations and importance conservation. The establishment of the Nordheim's equation, although modified, was based on Gandini. Finally, a mathematical interpretation of the flux-trap region was avented. (author)

A fast linear predictive adaptive model of packed bed coupled with UASB reactor treating onion waste to produce biofuel.

Science.gov (United States)

Milquez-Sanabria, Harvey; Blanco-Cocom, Luis; Alzate-Gaviria, Liliana

2016-10-03

Agro-industrial wastes are an energy source for different industries. However, its application has not reached small industries. Previous and current research activities performed on the acidogenic phase of two-phase anaerobic digestion processes deal particularly with process optimization of the acid-phase reactors operating with a wide variety of substrates, both soluble and complex in nature. Mathematical models for anaerobic digestion have been developed to understand and improve the efficient operation of the process. At present, lineal models with the advantages of requiring less data, predicting future behavior and updating when a new set of data becomes available have been developed. The aim of this research was to contribute to the reduction of organic solid waste, generate biogas and develop a simple but accurate mathematical model to predict the behavior of the UASB reactor. The system was maintained separate for 14 days during which hydrolytic and acetogenic bacteria broke down onion waste, produced and accumulated volatile fatty acids. On this day, two reactors were coupled and the system continued for 16 days more. The biogas and methane yields and volatile solid reduction were 0.6 ± 0.05 m 3 (kg VS removed ) -1 , 0.43 ± 0.06 m 3 (kg VS removed ) -1 and 83.5 ± 9.8 %, respectively. The model application showed a good prediction of all process parameters defined; maximum error between experimental and predicted value was 1.84 % for alkalinity profile. A linear predictive adaptive model for anaerobic digestion of onion waste in a two-stage process was determined under batch-fed condition. Organic load rate (OLR) was maintained constant for the entire operation, modifying effluent hydrolysis reactor feed to UASB reactor. This condition avoids intoxication of UASB reactor and also limits external buffer addition.

Fuel element cladding state change mathematical model for a WWER-1000 plant operated in the mode of varying loading

Directory of Open Access Journals (Sweden)

S. N. Pelykh

2010-09-01

Full Text Available Main features of a fuel element cladding state change mathematical model for a WWER-1000 reactor plant operated in the mode of varying loading are listed. The integrated model is based on the energy creep theory, uses the finite element method for imultaneous solution of the fuel element heat conduction and mechanical deformation equa-tions. Proposed mathematical model allows us to determine the influence of the WWER-1000 regime parameters and fuel assembly design characteristics on the change of cladding properties under different loading conditions of normal operation, as well as the cladding limiting state at variable loading depending on the length, depth and number of cycles.

Assessment of some interfacial shear correlations in a model of ECC bypass flow in PWR reactor downcomer

International Nuclear Information System (INIS)

Popov, N.K.; Rohatgi, U.S.

1987-01-01

The bypass/refill process in the PWR reactor downcomer, following a large rupture of a cold leg coolant supply pipe, is a complicated thermo-hydraulic two-phase flow phenomenon. Mathematical modeling of such phenomena is always accompanied with a difficult task of selection of suitable constitutive correlations. In a typically hydrodynamic phenomenon, like ECC refill process of the reactor lower plenum is considered, the phasic interfacial friction is the most influential constitutive correlation. Therefore, assessment of the well-known widely-used interfacial friction constitutive correlations in the model of ECC bypass/refill process, is the subject of this paper

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

Mathematical Modeling and Computational Thinking

Science.gov (United States)

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…

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

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…

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

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

Science.gov (United States)

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…

Modelling for Temperature Non-Isothermal Continuous Stirred Tank Reactor Using Fuzzy Logic

OpenAIRE

Nasser Mohamed Ramli; Mohamad Syafiq Mohamad

2017-01-01

Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of...

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

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

CERN Document Server

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.

Calculation models for a nuclear reactor

International Nuclear Information System (INIS)

Tashanii, Ahmed Ali

2010-01-01

Determination of different parameters of nuclear reactors requires neutron transport calculations. Due to complicity of geometry and material composition of the reactor core, neutron calculations were performed for simplified models of the real arrangement. In frame of the present work two models were used for calculations. First, an elementary cell model was used to prepare cross section data set for a homogenized-core reactor model. The homogenized-core reactor model was then used to perform neutron transport calculation. The nuclear reactor is a tank-shaped thermal reactor. The semi-cylindrical core arrangement consists of aluminum made fuel bundles immersed in water which acts as a moderator as well as a coolant. Each fuel bundle consists of aluminum cladded fuel rods arranged in square lattices. (author)

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

Concepts of mathematical modeling

CERN Document Server

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

Breeding description for fast reactors and symbiotic reactor systems

International Nuclear Information System (INIS)

Hanan, N.A.

1979-01-01

A mathematical model was developed to provide a breeding description for fast reactors and symbiotic reactor systems by means of figures of merit type quantities. The model was used to investigate the effect of several parameters and different fuel usage strategies on the figures of merit which provide the breeding description. The integrated fuel cycle model for a single-reactor is reviewed. The excess discharge is automatically used to fuel identical reactors. The resulting model describes the accumulation of fuel in a system of identical reactors. Finite burnup and out-of-pile delays and losses are treated in the model. The model is then extended from fast breeder park to symbiotic reactor systems. The asymptotic behavior of the fuel accumulation is analyzed. The asymptotic growth rate appears as the largest eigenvalue in the solution of the characteristic equations of the time dependent differential balance equations for the system. The eigenvector corresponding to the growth rate is the core equilibrium composition. The analogy of the long-term fuel cycle equations, in the framework of this model, and the neutron balance equations is explored. An eigenvalue problem adjoint to the one generated by the characteristic equations of the system is defined. The eigenvector corresponding to the largest eigenvalue, i.e. to the growth rate, represents the ''isotopic breeding worths.'' Analogously to the neutron adjoint flux it is shown that the isotopic breeding worths represent the importance of an isotope for breeding, i.e. for the growth rate of a system

Dynamic Behavior of Reverse Flow Reactor for Lean Methane Combustion

OpenAIRE

Yogi W. Budhi; M. Effendy; Yazid Bindar; Subagjo

2014-01-01

The stability of reactor operation for catalytic oxidation of lean CH4 has been investigated through modeling and simulation, particularly the influence of switching time and heat extraction on reverse flow reactor (RFR) performance. A mathematical model of the RFR was developed, based on one-dimensional pseudo-homogeneous model for mass and heat balances, incorporating heat loss through the reactor wall. The configuration of the RFR consisted of inert-catalyst-inert, with or without heat ext...

Proceedings of 2. Yugoslav symposium on reactor physics, Part 3, Herceg Novi (Yugoslavia), 27-29 Sep 1966

International Nuclear Information System (INIS)

1966-01-01

This Volume 3 of the Proceedings of 2. Yugoslav symposium on reactor physics includes three papers describing the following: model for spatial synthesis of automated control system of the GCR type reactor; model for analysis of hydrodynamic processes at the BHWR type reactors; mathematical model for safety analysis of heavy water power reactor

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

CERN Document Server

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

Pressurized water reactor system model for control system design and analysis

International Nuclear Information System (INIS)

Cooper, K.F.; Cain, J.T.

1975-01-01

Satisfactory operation of present generation Pressurized Water Reactor (PWR) Nuclear Power systems requires that several independent and interactive control systems be designed. Since it is not practical to use an actual PWR system as a design tool, a mathematical model of the system must be developed as a design and analysis tool. The model presented has been developed to be used as an aid in applying optimal control theory to design and implement new control systems for PWR plants. To be applicable, the model developed must represent the PWR system in its normal operating range. For safety analysis the operating conditions of the system are usually abnormal and, therefore, the system modeling requirements are different from those for control system design and analysis

Fuel management of mixed reactor type power plant systems

International Nuclear Information System (INIS)

Csom, Gyula

1988-01-01

In equilibrium symbiotic power plant system containing both thermal reactors and fast breeders, excess plutonium produced by the fast breeders is used to enrich the fuel of the thermal reactors. In plutonium deficient symbiotic power plant system plutonium is supplied both by thermal plants and fast breeders. Mathematical models were constructed and different equations solved to characterize the fuel utilization of both systems if they contain only a single thermal type and a single fast type reactor. The more plutonium is produced in the system, the higher output ratio of thermal to fast reactors is achieved in equilibrium symbiotic power plant system. Mathematical equations were derived to calculate the doubling time and the breeding gain of the equilibrium symbiotic system. (V.N.) 2 figs.; 2 tabs

Implementation into a CFD code of neutron kinetics and fuel pin models for nuclear reactor transient analyses

International Nuclear Information System (INIS)

Chen Zhao; Chen, Xue-Nong; Rineiski, Andrei; Zhao Pengcheng; Chen Hongli

2014-01-01

Safety analysis is an important tool for justifying the safety of nuclear reactors. The traditional method for nuclear reactor safety analysis is performed by means of system codes, which use one-dimensional lumped-parameter method to model real reactor systems. However, there are many multi-dimensional thermal-hydraulic phenomena cannot be predicated using traditional one-dimensional system codes. This problem is extremely important for pool-type nuclear systems. Computational fluid dynamics (CFD) codes are powerful numerical simulation tools to solve multi-dimensional thermal-hydraulics problems, which are widely used in industrial applications for single phase flows. In order to use general CFD codes to solve nuclear reactor transient problems, some additional models beyond general ones are required. Neutron kinetics model for power calculation and fuel pin model for fuel pin temperature calculation are two important models of these additional models. The motivation of this work is to develop an advance numerical simulation method for nuclear reactor safety analysis by implementing neutron kinetics model and fuel pin model into general CFD codes. In this paper, the Point Kinetics Model (PKM) and Fuel Pin Model (FPM) are implemented into a general CFD code FLUENT. The improved FLUENT was called as FLUENT/PK. The mathematical models and implementary method of FLUENT/PK are descripted and two demonstration application cases, e.g. the unprotected transient overpower (UTOP) accident of a Liquid Metal cooled Fast Reactor (LMFR) and the unprotected beam overpower (UBOP) accident of an Accelerator Driven System (ADS), are presented. (author)

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

Science.gov (United States)

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…

Gas-liquid reactor / separator: dynamics and operability characteristics

NARCIS (Netherlands)

Ranade, V.; Kuipers, J.A.M.; Versteeg, Geert

1999-01-01

A comprehensive mathematical model is developed to simulate gas¿liquid reactor in which both, reactants as well as products enter or leave the reactor in gas phase while the reactions take place in liquid phase. A case of first-order reaction (isothermal) was investigated in detail using the dynamic

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

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.

Mathematical foundations of transport theory

International Nuclear Information System (INIS)

Ershov, Yu.I.; Shikhov, S.B.

1985-01-01

Main items of application of the operator equations analyzing method in transport theory problems are considered. The mathematical theory of a reactor critical state is presented. Theorems of existence of positive solutions of non-linear non-stationary equations taking into account the temperature and xenon feedbacks are proved. Conditions for stability and asymptotic stability of steady-state regimes for different distributed models of a nuclear reactor are obtained on the basis of the modern operator perturbation theory, certain problems on control using an absorber are considered

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

Science.gov (United States)

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…

Theoretical-experimental modelling of the momentum equation for PWR reactor steam generators

International Nuclear Information System (INIS)

Rodrigues, L.A.H.

1994-01-01

A mathematical model in steady-state conditions of the momentum equation at the secondary side of a vertical U-tube steam generator with recirculation is presented. The U-tube test section was the 150 bar - Circuito Termoidraulico Experimental - CTE-150. This facility is a Experimental Thermal-hydraulic Circuit and operates at the same conditions (pressure and temperature) of a typical PWR reactor. A comparison between the Homogeneous and Separate Flow models was done. those models were verified and compared with experimental data for several operational conditions. The results show that the model fits very well the experimental data and seems to be appropriate to study water recirculation of a steam generator secondary side. (author)

Biofilm reactors for ethanol production

Energy Technology Data Exchange (ETDEWEB)

Vega, J L; Clausen, E C; Gaddy, J L

1988-07-01

Whole cell immobilization has been studied in the laboratory during the last few years as a method to improve the performance and economics of most fermentation processes. Among the various techniques available for cell immobilization, methods that provide generation of a biofilm offer reduced diffusional resistance, high productivities, and simple operation. This paper reviews some of the important aspects of biofilm reactors for ethanol production, including reactor start-up, steady state behavior, process stability, and mathematical modeling. Special emphasis is placed on covalently bonded Saccharomyces cerevisiae in packed bed reactors.

Mechanical core coupling and reactors stability

International Nuclear Information System (INIS)

Suarez Antola, R.

2006-01-01

Structural parts of nuclear reactors are complex mechanical systems, able to vibrate with a set of proper frequencies when suitably excited. Cyclical variations in the strain state of the materials, including density perturbations, are produced. This periodic changes may affect reactor reactivity. But a variation in reactivity affects reactor thermal power, thus modifying the temperature field of the abovementiones materials. If the variation in temperature fields is fast enough, thermal-mechanical coupling may produce fast variations in strain states, and this, at its turn, modifies the reactivity, and so on. This coupling between mechanical vibrations of the structure and the materials of the core, with power oscillations of the reactor, not only may not be excluded a priori, but it seems that it has been present in some stage of the incidents or accidents that happened during the development of nuclear reactor technology. The purpose of the present communication is: (a) To review and generalize some mathematical models that were proposed in order to describe thermal-mechanical coupling in nuclear reactors. (b) To discuss some conditions in which significant instabilities could arise, including large amplitude power oscillations coupled with mechanical vibrations whose amplitudes are too small to be excluded by conventional criteria of mechanical design. Enough Certain aspects of thr physical safety of nuclear power reactors, that are objected by people that opposes to the renaissance of nucleoelectric generation, are discussed in the framework of the mathematical model proposed in this paper [es

A WIMS-NESTLE reactor physics model for an RBMK reactor

International Nuclear Information System (INIS)

Perry, R.T.; Meriwether, G.H.

1996-01-01

This work describes the static neutronic calculations made for a three-dimensional model of an RBMK (Russian) reactor. Future work will involve the use of this neutronic model and a thermal-hydraulic model in coupled calculations. The lattice code, WIMS-D, was used to obtain the cross sections for the static neutronic calculations. The static reactor neutronic calculations were made with NESTLE, a three-dimensional nodal diffusion code. The methods used to establish an RBMK reactor model for use in these codes are discussed, and the cross sections calculated are given

A WIMS-NESTLE reactor physics model for an RBMK reactor

International Nuclear Information System (INIS)

Perry, R.T.; Meriwether, G.H.

1996-01-01

This work describes the static neutronic calculations made for a three-dimensional model of an RBMK (Russian) reactor. Future work will involve the use of this neutronic model and a thermal-hydraulic model in coupled calculations. The lattice code, WIMS-D, was used to obtain the cross sections for the static neutronic calculations. The static reactor neutronic calculations were made with NESTLE, a three-dimensional nodal diffusion code. The methods used to establish an RBMK reactor model for use in these codes are discussed, and the cross sections calculated are given. (author)

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

Science.gov (United States)

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

Mathematical model and computer code for coated particles performance at normal operating conditions

International Nuclear Information System (INIS)

Golubev, I.; Kadarmetov, I.; Makarov, V.

2002-01-01

Computer modeling of thermo-mechanical behavior of coated particles during operating both at normal and off-normal conditions has a very significant role particularly on a stage of new reactors development. In Russia a big experience has been accumulated on fabrication and reactor tests of CP and fuel elements with UO 2 kernels. However, this experience cannot be using in full volume for development of a new reactor installation GT-MHR. This is due to very deep burn-up of the fuel based on plutonium oxide (up to 70% fima). Therefore the mathematical modeling of CP thermal-mechanical behavior and failure prediction becomes particularly important. The authors have a clean understanding that serviceability of fuel with high burn-ups are defined not only by thermo-mechanics, but also by structured changes in coating materials, thermodynamics of chemical processes, 'amoeba-effect', formation CO etc. In the report the first steps of development of integrate code for numerical modeling of coated particles behavior and some calculating results concerning the influence of various design parameters on fuel coated particles endurance for GT-MHR normal operating conditions are submitted. A failure model is developed to predict the fraction of TRISO-coated particles. In this model it is assumed that the failure of CP depends not only on probability of SiC-layer fracture but also on the PyC-layers damage. The coated particle is considered as a uniform design. (author)

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

Science.gov (United States)

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

Science.gov (United States)

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.

Proceedings of the 6. National Meeting of Reactor Physics and Thermohydraulic

International Nuclear Information System (INIS)

1986-01-01

The proceedings of the 6. National Meeting of Reactor Physics and Thermohydraulic - 6. ENFIR - allow to evaluate the present status of development in reactor physics and thermohydraulic fields. The mathematical models and methods for calculating neutronic of nuclear reactors, safety reactor analysis, measuring methods of neutronic parameters, computerized simulation of accidents, transients and thermohydraulic analysis are presented. (M.C.K.) [pt

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

Science.gov (United States)

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

NARCIS (Netherlands)

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

An analysis of the falling film gas-liquid reactor

NARCIS (Netherlands)

Davis, E.J.; Ouwerkerk-Dijkers, van M.P.; Venkatesh, S.

1979-01-01

A mathematical model of the falling film reactor is developed to predict the conversion and temperature distribution in the reactor as a function of the gas and liquid flow rates, physical properties, the feed composition of the reactive gas and carrier gas and other parameters of the system.

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

CERN Document Server

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...

Mathematical model of organic substrate degradation in solid waste windrow composting.

Science.gov (United States)

Seng, Bunrith; Kristanti, Risky Ayu; Hadibarata, Tony; Hirayama, Kimiaki; Katayama-Hirayama, Keiko; Kaneko, Hidehiro

2016-01-01

Organic solid waste composting is a complex process that involves many coupled physical, chemical and biological mechanisms. To understand this complexity and to ease in planning, design and management of the composting plant, mathematical model for simulation is usually applied. The aim of this paper is to develop a mathematical model of organic substrate degradation and its performance evaluation in solid waste windrow composting system. The present model is a biomass-dependent model, considering biological growth processes under the limitation of moisture, oxygen and substrate contents, and temperature. The main output of this model is substrate content which was divided into two categories: slowly and rapidly degradable substrates. To validate the model, it was applied to a laboratory scale windrow composting of a mixture of wood chips and dog food. The wastes were filled into a cylindrical reactor of 6 cm diameter and 1 m height. The simulation program was run for 3 weeks with 1 s stepwise. The simulated results were in reasonably good agreement with the experimental results. The MC and temperature of model simulation were found to be matched with those of experiment, but limited for rapidly degradable substrates. Under anaerobic zone, the degradation of rapidly degradable substrate needs to be incorporated into the model to achieve full simulation of a long period static pile composting. This model is a useful tool to estimate the changes of substrate content during composting period, and acts as a basic model for further development of a sophisticated model.

Multi-objective optimization of the reactor coolant system

International Nuclear Information System (INIS)

Chen Lei; Yan Changqi; Wang Jianjun

2014-01-01

Background: Weight and size are important criteria in evaluating the performance of a nuclear power plant. It is of great theoretical value and engineering significance to reduce the weight and volume of the components for a nuclear power plant by the optimization methodology. Purpose: In order to provide a new method for the optimization of nuclear power plant multi-objective, the concept of the non-dominated solution was introduced. Methods: Based on the parameters of Qinshan I nuclear power plant, the mathematical models of the reactor core, the reactor vessel, the main pipe, the pressurizer and the steam generator were built and verified. The sensitivity analyses were carried out to study the influences of the design variables on the objectives. A modified non-dominated sorting genetic algorithm was proposed and employed to optimize the weight and the volume of the reactor coolant system. Results: The results show that the component mathematical models are reliable, the modified non-dominated sorting generic algorithm is effective, and the reactor inlet temperature is the most important variable which influences the distribution of the non-dominated solutions. Conclusion: The optimization results could provide a reference to the design of such reactor coolant system. (authors)

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

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.

Proceedings of the international conference on mathematics and computations, reactor physics, and environmental analyses. Volume 1 and 2

International Nuclear Information System (INIS)

Anon.

1995-01-01

The International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses marks the sixteenth biennial topical meeting of the Mathematics and Computation (M ampersand C) Division of the American Nuclear Society (ANS). This conference combines many traditional features of M ampersand C conferences with several new aspects. The meeting is, for the first time, being held in Portland, Oregon and sponsored by the ANS Eastern Washington Section. Three of the cosponsors - the ANS Reactor Physics Division, the European Nuclear Society, and the Atomic Energy Society of Japan - have participated in a series of such meetings, with very successful results. The fourth cosponsor, the ANS Environmental Science Division, is participating for the first time as a cosponsor of a M ampersand C topical meeting, as a result of the M ampersand C Division's decision to formally include the area of environmental analyses as a major focus of the conference, another 'first.' Separate abstracts have been submitted to the energy database for contributions to this conference

Modeling the competitive effect of ammonium oxidizers and heterotrophs on the degradation of MTBE in a packed bed reactor

DEFF Research Database (Denmark)

Waul, Christopher Kevin; Arvin, Erik; Schmidt, Jens Ejbye

2008-01-01

A mathematical model was used to study effects on the degradation of methyl tert-butyl ether (MTBE) in a packed bed reactor due to the presence of contaminants such as ammonium, and the mix of benzene, toluene, ethylbenzene and xylenes (BTEX). It was shown that competition between the slower...

Particle bed reactor modeling

Science.gov (United States)

Sapyta, Joe; Reid, Hank; Walton, Lew

The topics are presented in viewgraph form and include the following: particle bed reactor (PBR) core cross section; PBR bleed cycle; fuel and moderator flow paths; PBR modeling requirements; characteristics of PBR and nuclear thermal propulsion (NTP) modeling; challenges for PBR and NTP modeling; thermal hydraulic computer codes; capabilities for PBR/reactor application; thermal/hydralic codes; limitations; physical correlations; comparison of predicted friction factor and experimental data; frit pressure drop testing; cold frit mask factor; decay heat flow rate; startup transient simulation; and philosophy of systems modeling.

Advanced Reactors-Intermediate Heat Exchanger (IHX) Coupling: Theoretical Modeling and Experimental Validation

Energy Technology Data Exchange (ETDEWEB)

Utgikar, Vivek [Univ. of Idaho, Moscow, ID (United States); Sun, Xiaodong [The Ohio State Univ., Columbus, OH (United States); Christensen, Richard [The Ohio State Univ., Columbus, OH (United States); Sabharwall, Piyush [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2016-12-29

The overall goal of the research project was to model the behavior of the advanced reactorintermediate heat exchange system and to develop advanced control techniques for off-normal conditions. The specific objectives defined for the project were: 1. To develop the steady-state thermal hydraulic design of the intermediate heat exchanger (IHX); 2. To develop mathematical models to describe the advanced nuclear reactor-IHX-chemical process/power generation coupling during normal and off-normal operations, and to simulate models using multiphysics software; 3. To develop control strategies using genetic algorithm or neural network techniques and couple these techniques with the multiphysics software; 4. To validate the models experimentally The project objectives were accomplished by defining and executing four different tasks corresponding to these specific objectives. The first task involved selection of IHX candidates and developing steady state designs for those. The second task involved modeling of the transient and offnormal operation of the reactor-IHX system. The subsequent task dealt with the development of control strategies and involved algorithm development and simulation. The last task involved experimental validation of the thermal hydraulic performances of the two prototype heat exchangers designed and fabricated for the project at steady state and transient conditions to simulate the coupling of the reactor- IHX-process plant system. The experimental work utilized the two test facilities at The Ohio State University (OSU) including one existing High-Temperature Helium Test Facility (HTHF) and the newly developed high-temperature molten salt facility.

Modelling and experimental investigation of waste tyre pyrolysis process in a laboratory reactor

Directory of Open Access Journals (Sweden)

Rudniak Leszek

2017-09-01

Full Text Available A mathematical model of waste tyre pyrolysis process is developed in this work. Tyre material decomposition based on a simplified reaction mechanism leads to main product lumps: noncondensable (gas, condensable (pyrolytic oil and solid (char. The model takes into account kinetics of heat and mass transfer in the grain of the shredded rubber material as well as surrounding gas phase. The main reaction routes were modelled as the pseudo-first order reactions with a rate constant calculated from the Arrhenius type equation using literature values of activation energy determined for main tyre constituents based on TG/DTG measurements and tuned pre-exponential parameter values obtained by fitting theoretical predictions to the experimental results obtained in our laboratory reactor. The model was implemented within the CFD software (ANSYS Fluent. The results of numerical simulation of the pyrolysis process revealed non-uniformity of sample’s porosity and temperature. The simulation predictions were in satisfactory agreement with the experimentally measured mass loss of the tyre sample during pyrolysis process investigated in a laboratory reactor.

Modelling of a falling sludge bed reactor using AQUASIM

African Journals Online (AJOL)

drinie

2001-10-04

Oct 4, 2001 ... products are then used for the biological treatment of acid mine drainage. A mathematical ... solid matter into three valleys inside the reactor, as opposed to an ... conversion of PSS in the presence of sulphate-reducing bacteria ... indicate substrate flow (stoichiometrically) in the form of COD ..... fermentation.

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

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…

Transactions of 2. international seminars on the mathematical/mechanical modelling of reactor fuel elements

International Nuclear Information System (INIS)

Lassmann, K.

1991-01-01

Fuel element modelling is a wide field of activity that spans decades of research and code development for different reactor systems and very different situations such as normal operation, off-normal situations and severe accidents. Modern computer technology helps to take the full advantage of detailed model development performed over the past for daily design analyses, safety analyses, conception of new experiments and investigation of an improved nuclear fuel utilization and fuel element performance. The basic development of the concepts of fuel element modelling can be considered as finished. The future trends are the development of refined models based on a deeper understanding of the physical and mechanical basis. Areas of interest are transient phenomena especially the fission product behaviour, burnup-enhanced phenomena, PCI and fuel reliability, severe core damage and chemical aspects. The seminar presentations reflect this variety

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

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....

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

Science.gov (United States)

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…

Variational methods in the kinetic modeling of nuclear reactors: Recent advances

International Nuclear Information System (INIS)

Dulla, S.; Picca, P.; Ravetto, P.

2009-01-01

The variational approach can be very useful in the study of approximate methods, giving a sound mathematical background to numerical algorithms and computational techniques. The variational approach has been applied to nuclear reactor kinetic equations, to obtain a formulation of standard methods such as point kinetics and quasi-statics. more recently, the multipoint method has also been proposed for the efficient simulation of space-energy transients in nuclear reactors and in source-driven subcritical systems. The method is now founded on a variational basis that allows a consistent definition of integral parameters. The mathematical structure of multipoint and modal methods is also investigated, evidencing merits and shortcomings of both techniques. Some numerical results for simple systems are presented and the errors with respect to reference calculations are reported and discussed. (authors)

Rotating bed reactor for CLC: Bed characteristics dependencies on internal gas mixing

International Nuclear Information System (INIS)

Håkonsen, Silje Fosse; Grande, Carlos A.; Blom, Richard

2014-01-01

Highlights: • A mathematical model for the rotating CLC reactor has been developed. • The model reflects the gas distribution in the reactor during CLC operation. • Radial dispersion in the rotating bed is the main cause for internal gas mixing. • The model can be used to optimize the reactor design and particle characteristics. - Abstract: A newly designed continuous lab-scale rotating bed reactor for chemical looping combustion using CuO/Al 2 O 3 oxygen carrier spheres and methane as fuel gives around 90% CH 4 conversion and >90% CO 2 capture efficiency based on converted methane at 800 °C. However, from a series of experiments using a broad range of operating conditions potential CO 2 purities only in the range 20–65% were yielded, mostly due to nitrogen slip from the air side of the reactor into the effluent CO 2 stream. A mathematical model was developed intending to understand the air-mixing phenomena. The model clearly reflects the gas slippage tendencies observed when varying the process conditions such as rotation frequency, gas flow and the flow if inert gas in the two sectors dividing the air and fuel side of the reactor. Based on the results, it is believed that significant improvements can be made to reduce gas mixing in future modified and scaled-up reactor versions

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

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

Removal of antibiotics in a parallel-plate thin-film-photocatalytic reactor: Process modeling and evolution of transformation by-products and toxicity.

Science.gov (United States)

Özkal, Can Burak; Frontistis, Zacharias; Antonopoulou, Maria; Konstantinou, Ioannis; Mantzavinos, Dionissios; Meriç, Süreyya

2017-10-01

Photocatalytic degradation of sulfamethoxazole (SMX) antibiotic has been studied under recycling batch and homogeneous flow conditions in a thin-film coated immobilized system namely parallel-plate (PPL) reactor. Experimentally designed, statistically evaluated with a factorial design (FD) approach with intent to provide a mathematical model takes into account the parameters influencing process performance. Initial antibiotic concentration, UV energy level, irradiated surface area, water matrix (ultrapure and secondary treated wastewater) and time, were defined as model parameters. A full of 2 5 experimental design was consisted of 32 random experiments. PPL reactor test experiments were carried out in order to set boundary levels for hydraulic, volumetric and defined defined process parameters. TTIP based thin-film with polyethylene glycol+TiO 2 additives were fabricated according to pre-described methodology. Antibiotic degradation was monitored by High Performance Liquid Chromatography analysis while the degradation products were specified by LC-TOF-MS analysis. Acute toxicity of untreated and treated SMX solutions was tested by standard Daphnia magna method. Based on the obtained mathematical model, the response of the immobilized PC system is described with a polynomial equation. The statistically significant positive effects are initial SMX concentration, process time and the combined effect of both, while combined effect of water matrix and irradiated surface area displays an adverse effect on the rate of antibiotic degradation by photocatalytic oxidation. Process efficiency and the validity of the acquired mathematical model was also verified for levofloxacin and cefaclor antibiotics. Immobilized PC degradation in PPL reactor configuration was found capable of providing reduced effluent toxicity by simultaneous degradation of SMX parent compound and TBPs. Copyright © 2017. Published by Elsevier B.V.

Study of PWR reactor efficiency as a function of turbine steam extractions

International Nuclear Information System (INIS)

Rocha, Janine Gandolpho da; Alvim, Antonio Carlos Marques; Martinez, Aquilino Senra

2002-01-01

The objective of this work is to optimize the extractions of the low-pressure turbine of a PWR nuclear reactor, in order to obtain the best thermodynamic cycle efficiency. We have analyzed typical data of a 1300 MW PWR reactor, operating at 25%, 50%, 75% and 100% capacities, respectively. The first stage of this study consists of generating a mathematical model capable of describing the reactor behavior and efficiency at any power level. The second stage of this study consists of to combine the generated mathematical model in an optimization computer program that optimize the extractions flow of the low-pressure turbine until it finds the optimal system efficiency. This work does not alter the nuclear facility project in any way. (author)

Reactor kinetics methods development. Final report

International Nuclear Information System (INIS)

Hansen, K.F.; Henry, A.F.

1978-01-01

This report is a qualitative summary of research conducted at MIT from 1967 to 1977 in the area of reactor kinetics methods. The objectives of the research were to find methods of integration of various mathematical models of nuclear reactor transients. From the beginning the work was aimed at numerical integration methods. Specific areas of research, discussed in more detail following, included: integration of multigroup diffusion theory models by finite difference and finite element methods; response matrix and nodal methods; coarse-mesh homogenization; and special treatment of boundary conditions

Contribution to the modelling of gas-solid reactions and reactors; Contribution a la modelisation des reactions et des reacteurs gaz-solide

Energy Technology Data Exchange (ETDEWEB)

Patisson, F

2005-09-15

Gas-solid reactions control a great number of major industrial processes involving matter transformation. This dissertation aims at showing that mathematical modelling is a useful tool for both understanding phenomena and optimising processes. First, the physical processes associated with a gas-solid reaction are presented in detail for a single particle, together with the corresponding available kinetic grain models. A second part is devoted to the modelling of multiparticle reactors. Different approaches, notably for coupling grain models and reactor models, are illustrated through various case studies: coal pyrolysis in a rotary kiln, production of uranium tetrafluoride in a moving bed furnace, on-grate incineration of municipal solid wastes, thermogravimetric apparatus, nuclear fuel making, steel-making electric arc furnace. (author)

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

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…

Model calibration and validation for OFMSW and sewage sludge co-digestion reactors

International Nuclear Information System (INIS)

Esposito, G.; Frunzo, L.; Panico, A.; Pirozzi, F.

2011-01-01

Highlights: → Disintegration is the limiting step of the anaerobic co-digestion process. → Disintegration kinetic constant does not depend on the waste particle size. → Disintegration kinetic constant depends only on the waste nature and composition. → The model calibration can be performed on organic waste of any particle size. - Abstract: A mathematical model has recently been proposed by the authors to simulate the biochemical processes that prevail in a co-digestion reactor fed with sewage sludge and the organic fraction of municipal solid waste. This model is based on the Anaerobic Digestion Model no. 1 of the International Water Association, which has been extended to include the co-digestion processes, using surface-based kinetics to model the organic waste disintegration and conversion to carbohydrates, proteins and lipids. When organic waste solids are present in the reactor influent, the disintegration process is the rate-limiting step of the overall co-digestion process. The main advantage of the proposed modeling approach is that the kinetic constant of such a process does not depend on the waste particle size distribution (PSD) and rather depends only on the nature and composition of the waste particles. The model calibration aimed to assess the kinetic constant of the disintegration process can therefore be conducted using organic waste samples of any PSD, and the resulting value will be suitable for all the organic wastes of the same nature as the investigated samples, independently of their PSD. This assumption was proven in this study by biomethane potential experiments that were conducted on organic waste samples with different particle sizes. The results of these experiments were used to calibrate and validate the mathematical model, resulting in a good agreement between the simulated and observed data for any investigated particle size of the solid waste. This study confirms the strength of the proposed model and calibration procedure

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

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

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

Science.gov (United States)

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…

Development of the “Approach to Critical” Experiment Simulation Model for the Consort Reactor Using LABVIEW

International Nuclear Information System (INIS)

Abbo, D. N. O.

2015-01-01

Following the shutdown of the CONSORT reactor, the “Approach to Critical” experiment which allowed students to observe and understand the procedure for taking the reactor to critical, balancing the system at low power and increasing the power over a range of powers levels and eventual reactor shutdown, would no longer be possible. It was therefore important to develop a simulation model of the experiment that would enable future students to have comparable training. An “Approach to Critical” Experiment Simulation model for the CONSORT Reactor was developed using Lab-VIEW software to simulate the “Students” experiment version. Lab– VIEW software was chosen due to its good user graphical user interface, offers ready to start functions and also the possibility of improving on the system with new algorithms. The modulation process was used to develop mathematical codes from equations using Lab–VIEW 2012 based on the CONSORT historical experimental data and known literature. The Simulation models the kinetics of a sub-critical reactor with a start-up neutron source, such that control rods are used to increase the power, then achieve power balance and finally shutting down the reactor. Reactivity changes due to temperature effects were neglected. The model was validated by testing the code through performing the three parts of the experiment; Approach to Critical, Doubling time method and Rod drop method, and results compared to the historical experimental data. The results were in agreement with historical data. However the negligible variations were obtained in the Rod drop method due to the reactivity values used to generate the code. (author)

Experiment and modeling of low-concentration methane catalytic combustion in a fluidized bed reactor

International Nuclear Information System (INIS)

Yang, Zhongqing; Yang, Peng; Zhang, Li; Guo, Mingnv; Ran, Jingyu

2016-01-01

Highlights: • The catalytic combustion of 0.15~3 vol. % low concentration methane in a fluidized bed was studied. • A mathematical model was proposed on the basis of gas–solid flow theory. • A comparative analysis of the established model with plug flow, mixed flow and K-L models was carried out. • The axial methane profile along fluidized bed was predicted by using the mathematical model. • The bed temperature has greater impact on methane conversion than fluidized velocity. - Abstract: This study undertakes a theoretical analysis and an experimental investigation into the characteristics of low-concentration methane catalytic combustion in a bubbling fluidized bed reactor using 0.5 wt.% Pd/Al_2O_3 as catalytic particles. A mathematical model is established based on gas–solid flow theory and is used to study the effects of bed temperature and fluidized velocity on methane catalytic combustion, and predict the dimensionless methane concentration axial profile in reactor. It is shown that methane conversion increases with bed temperature, but decreases with increasing fluidized velocity. These theoretical results are found to correlate well with the experimental measurement, with a deviation within 5%. A comparative analysis of the developed model with plug flow, mixed flow and K-L models is also carried out, and this further verifies that the established model better reflects the characteristics of low-concentration methane catalytic combustion in a bubbling fluidized bed. Using this reaction model, it was found that the difference in methane conversion between dense and freeboard zones gradually increases with bed temperature; the dense zone reaction levels off at 650 °C, thereby minimizing the difference between the dense and freeboard regions to around 15%. With an increase in bed temperature, the dimensionless methane concentration in the dense zone decreases exponentially, while in the splash zone, it varies from an exponential decay to a slow

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...

Passive cooling of a fixed bed nuclear reactor

International Nuclear Information System (INIS)

Petry, V.J.; Bortoli, A.L. de; Sefidwash, F.

2005-01-01

Small nuclear reactors without the need for on-site refuelling have greater simplicity, better compliance with passive safety systems, and are more adequate for countries with small electric grids and limited investment capabilities. Here the passive cooling characteristic of the fixed bed nuclear reactor (FBNR), that is being developed under the International Atomic Energy Agency (IAEA) Coordinated Research Project, is studied. A mathematical model is developed to calculate the temperature distribution in the fuel chamber of the reactor. The results demonstrate the passive cooling of this nuclear reactor concept. (authors)

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

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).

Proposed development of a radionuclide washoff model for the German Reactor Safety Study

International Nuclear Information System (INIS)

Helton, J.C.

1982-11-01

This report presents a brief overview of the possible development of a model for the attenuation of radionuclide concentrations in urban environments due to rainfall/runoff relationships. The following sequence of actions is suggested: (1) preliminary review, (2) exploratory modeling, (3) detailed literature review, (4) development of mathematical model, (5) development of computer model, and (6) model review including verification and sensitivity analysis. To facilitate the initiation of the indicated efforts, an introduction to the relevant literature is provided. Further, the following topics are also briefly discussed: (1) radionuclide transport and removal in the terrestrial environment, (2) need for a description of the chemical and physical forms of the radionuclides released in a reactor accident, and (3) potential importance of surface-water contamination. (orig./HP) [de

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

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.

TU Electric reactor physics model verification: Power reactor benchmark

International Nuclear Information System (INIS)

Willingham, C.E.; Killgore, M.R.

1988-01-01

Power reactor benchmark calculations using the advanced code package CASMO-3/SIMULATE-3 have been performed for six cycles of Prairie Island Unit 1. The reload fuel designs for the selected cycles included gadolinia as a burnable absorber, natural uranium axial blankets and increased water-to-fuel ratio. The calculated results for both startup reactor physics tests (boron endpoints, control rod worths, and isothermal temperature coefficients) and full power depletion results were compared to measured plant data. These comparisons show that the TU Electric reactor physics models accurately predict important measured parameters for power reactors

Dimensioning of aerated submerged fixed bed biofilm reactors ...

African Journals Online (AJOL)

The description of a biofilm mathematical model application for dimensioning an aerated fixed bed biofilm reactor (ASFBBR) for petrochemical wastewater polishing is presented. A simple one-dimensional model of biofilm, developed by P Harremöes, was chosen for this purpose. The model was calibrated and verified ...

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

Science.gov (United States)

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.

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

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…

Nuclear reactor physics course for reactor operators

International Nuclear Information System (INIS)

Baeten, P.

2006-01-01

The education and training of nuclear reactor operators is important to guarantee the safe operation of present and future nuclear reactors. Therefore, a course on basic 'Nuclear reactor physics' in the initial and continuous training of reactor operators has proven to be indispensable. In most countries, such training also results from the direct request from the safety authorities to assure the high level of competence of the staff in nuclear reactors. The aim of the basic course on 'Nuclear Reactor Physics for reactor operators' is to provide the reactor operators with a basic understanding of the main concepts relevant to nuclear reactors. Seen the education level of the participants, mathematical derivations are simplified and reduced to a minimum, but not completely eliminated

Radiolysis of the VVER-1000 reactor coolant: An experimental study and mathematical modeling

International Nuclear Information System (INIS)

Arkhipov, O.P.; Bugaenko, V.L.; Kabakchi, S.A.

1995-01-01

Variations in the composition of the coolant for the primary circuit of a VVER-1000 reactor of the Kalinin nuclear power plant upon transition from power-level operation to shutdown was studied experimentally. The data obtained were used for verification of the MORAVA-H2 program developed earlier for simulation of the coolant state in pressurized-water power reactors

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

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.

Biodegradation of phenol with chromium(VI) reduction in an anaerobic fixed-biofilm process-Kinetic model and reactor performance

International Nuclear Information System (INIS)

Lin, Yen-Hui; Wu, Chih-Lung; Hsu, Chih-Hao; Li, Hsin-Lung

2009-01-01

A mathematical model system was derived to describe the simultaneous removal of phenol biodegradation with chromium(VI) reduction in an anaerobic fixed-biofilm reactor. The model system incorporates diffusive mass transport and double Monod kinetics. The model was solved using a combination of the orthogonal collocation method and Gear's method. A laboratory-scale column reactor was employed to validate the kinetic model system. Batch kinetic tests were conducted independently to evaluate the biokinetic parameters used in the model simulation. The removal efficiencies of phenol and chromium(VI) in an anaerobic fixed-biofilm process were approximately 980 mg/g and 910 mg/g, respectively, under a steady-state condition. In the steady state, model-predicted biofilm thickness reached up to 350 μm and suspended cells in the effluent were 85 mg cell/l. The experimental results agree closely with the results of the model simulations.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

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.

Chemical reactor modeling multiphase reactive flows

CERN Document Server

Jakobsen, Hugo A

2014-01-01

Chemical Reactor Modeling closes the gap between Chemical Reaction Engineering and Fluid Mechanics.  The second edition consists of two volumes: Volume 1: Fundamentals. Volume 2: Chemical Engineering Applications In volume 1 most of the fundamental theory is presented. A few numerical model simulation application examples are given to elucidate the link between theory and applications. In volume 2 the chemical reactor equipment to be modeled are described. Several engineering models are introduced and discussed. A survey of the frequently used numerical methods, algorithms and schemes is provided. A few practical engineering applications of the modeling tools are presented and discussed. The working principles of several experimental techniques employed in order to get data for model validation are outlined. The monograph is based on lectures regularly taught in the fourth and fifth years graduate courses in transport phenomena and chemical reactor modeling, and in a post graduate course in modern reactor m...

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Mathematical models in marketing a collection of abstracts

CERN Document Server

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...

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

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

Science.gov (United States)

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 modeling plasma transport in tokamaks

Energy Technology Data Exchange (ETDEWEB)

Quiang, Ji [Univ. of Illinois, Urbana-Champaign, IL (United States)

1997-01-01

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

Mathematical modeling plasma transport in tokamaks

International Nuclear Information System (INIS)

Quiang, Ji

1995-01-01

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

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

Science.gov (United States)

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.

Mathematical modeling of nitrous oxide (N2O) emissions from full-scale wastewater treatment plants.

Science.gov (United States)

Ni, Bing-Jie; Ye, Liu; Law, Yingyu; Byers, Craig; Yuan, Zhiguo

2013-07-16

Mathematical modeling of N2O emissions is of great importance toward understanding the whole environmental impact of wastewater treatment systems. However, information on modeling of N2O emissions from full-scale wastewater treatment plants (WWTP) is still sparse. In this work, a mathematical model based on currently known or hypothesized metabolic pathways for N2O productions by heterotrophic denitrifiers and ammonia-oxidizing bacteria (AOB) is developed and calibrated to describe the N2O emissions from full-scale WWTPs. The model described well the dynamic ammonium, nitrite, nitrate, dissolved oxygen (DO) and N2O data collected from both an open oxidation ditch (OD) system with surface aerators and a sequencing batch reactor (SBR) system with bubbling aeration. The obtained kinetic parameters for N2O production are found to be reasonable as the 95% confidence regions of the estimates are all small with mean values approximately at the center. The model is further validated with independent data sets collected from the same two WWTPs. This is the first time that mathematical modeling of N2O emissions is conducted successfully for full-scale WWTPs. While clearly showing that the NH2OH related pathways could well explain N2O production and emission in the two full-scale plants studied, the modeling results do not prove the dominance of the NH2OH pathways in these plants, nor rule out the possibility of AOB denitrification being a potentially dominating pathway in other WWTPs that are designed or operated differently.

Development of Reactor Console Simulator for PUSPATI TRIGA Reactor

International Nuclear Information System (INIS)

Mohd Idris Taib; Izhar Abu Hussin; Mohd Khairulezwan Abdul Manan; Nufarhana Ayuni Joha; Mohd Sabri Minhat

2012-01-01

The Reactor Console Simulator will be an interactive tool for operator training and teaching of PUSPATI TRIGA Reactor. Behaviour and characteristic for reactor console and reactor itself can be evaluated and understand. This Simulator will be used as complement for actual present reactor console. Implementation of man-machine interface is using computer screens, keyboard and mouse. Multiple screens are used to match the physical of present reactor console. LabVIEW software are using for user interface and mathematical calculation. Polynomial equation based on control rods calibration data as well as operation parameters record was used to calculate the estimated reactor console parameters. (author)

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

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

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.

MATLAB/SIMULINK platform for simulation of CANDU reactor control system

International Nuclear Information System (INIS)

Javidnia, H.; Jiang, J.

2007-01-01

In this paper a simulation platform for CANDU reactors' control system is presented. The platform is built on MATLAB/SIMULINK interactive graphical interface. Since MATLAB/SIMULINK are powerful tools to describe systems mathematically, all the subsystems in a CANDU reactor are represented in MATLAB's language and are implemented in SIMULINK graphical representation. The focus of the paper is on the flux control loop of CANDU reactors. However, the ideas can be extended to include other parts in CANDU power plants and the same technique can be applied to other types of nuclear reactors and their control systems. The CANDU reactor model and xenon feedback model are also discussed in this paper. (author)

An introduction to mathematical modeling a course in mechanics

CERN Document Server

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...

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

Science.gov (United States)

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

Science.gov (United States)

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…

Nitritation performance and biofilm development of co- and counter-diffusion biofilm reactors: Modeling and experimental comparison

DEFF Research Database (Denmark)

Wang, Rongchang; Terada, Akihiko; Lackner, Susanne

2009-01-01

A comparative study was conducted on the start-up performance and biofilm development in two different biofilm reactors with aim of obtaining partial nitritation. The reactors were both operated under oxygen limited conditions, but differed in geometry. While substrates (O-2, NH3) co......-diffused in one geometry, they counter-diffused in the other. Mathematical simulations of these two geometries were implemented in two 1-D multispecies biofilm models using the AQUASIM software. Sensitivity analysis results showed that the oxygen mass transfer coefficient (K-i) and maximum specific growth rate...... results showed that the counter-diffusion biofilms developed faster and attained a larger maximum biofilm thickness than the co-diffusion biofilms. Under oxygen limited condition (DO

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...

Effect of the Impeller Design on Degasification Kinetics Using the Impeller Injector Technique Assisted by Mathematical Modeling

Directory of Open Access Journals (Sweden)

Diego Abreu-López

2017-04-01

Full Text Available A mathematical model was developed to describe the hydrodynamics of a batch reactor for aluminum degassing utilizing the rotor-injector technique. The mathematical model uses the Eulerian algorithm to represent the two-phase system including the simulation of vortex formation at the free surface, and the use of the RNG k-ε model to account for the turbulence in the system. The model was employed to test the performances of three different impeller designs, two of which are available commercially, while the third one is a new design proposed in previous work. The model simulates the hydrodynamics and consequently helps to explain and connect the performances in terms of degassing kinetics and gas consumption found in physical modeling previously reported. Therefore, the model simulates a water physical model. The model reveals that the new impeller design distributes the bubbles more uniformly throughout the ladle, and exhibits a better-agitated bath, since the transfer of momentum to the fluids is better. Gas is evenly distributed with this design because both phases, gas and liquid, are dragged to the bottom of the ladle as a result of the higher pumping effect in comparison to the commercial designs.

Protection of semiconductor converters for controlled bypass reactors

International Nuclear Information System (INIS)

Dolgopolov, A. G.; Akhmetzhanov, N. G.; Karmanov, V. F.

2010-01-01

Possible ways of protecting thyristor converters in systems for magnetizing 110 - 500 kV controlled bypass reactors during switching and automatic reclosing are examined based on experience with the development of equipment, line tests, and mathematical modelling.

The Spectrum of Mathematical Models.

Science.gov (United States)

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.

Gap and impact of LMR [Liquid Metal Reactor] piping systems and reactor components

International Nuclear Information System (INIS)

Ma, D.C.; Gvildys, J.; Chang, Y.W.

1987-01-01

Because of high operation temperature, the LMR (Liquid Metal Reactor) plant is characterized by the thin-walled piping and components. Gaps are often present to allow free thermal expansion during normal plant operation. Under dynamic loadings, such as seismic excitation, if the relative displacement between the components exceeds the gap distance, impacts will occur. Since the components and piping become brittle over their design lifetime, impact is of important concern for it may lead to fractures of components and other serious effects. This paper deals with gap and impact problems in the LMR reactor components and piping systems. Emphasis is on the impacts due to seismic motion. Eight sections are contained in this paper. The gap and impact problems in LMR piping systems are described and a parametric study is performed on the effects of gap-induced support nonlinearity on the dynamics characteristics of the LMR piping systems. Gap and impact problems in the LMR reactor components are identified and their mathematical models are illustrated, and the gap and impact problems in the seismic reactor scram are discussed. The mathematical treatments of various impact models are also described. The uncertainties in the current seismic impact analyses of LMR components and structures are presented. An impact test on a 1/10-scale LMR thermal liner is described. The test results indicated that several clusters of natural modes can be excited by the impact force. The frequency content of the excited modes depends on the duration of the impact force; the shorter the duration, the higher the frequency content

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

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

CERN Document Server

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.

Science.gov (United States)

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

Science.gov (United States)

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.

Model simulation for high-temperature gas desulphurization processes

Energy Technology Data Exchange (ETDEWEB)

Tonini; Zaccagnini; Berg; Vitolo; Tartarelli; Zeppi (Struttura Informatica, Florence (Italy))

1993-01-01

Metal oxides such as zinc ferrite, zinc titanate and tin oxide have been identified as promising adsorbent materials in the removal of sulphur compounds from hot coal gas in power generation operations. A mathematical model for the sulfidation phase in fixed, moving and fluidised bed reactors has been developed. This paper presents kinetic models of spherical sorbent particles applicable to all reactor configurations and a mathematical model limited to the moving bed reactor. 10 refs., 5 figs.

A nodal Grean's function method of reactor core fuel management code, NGCFM2D

International Nuclear Information System (INIS)

Li Dongsheng; Yao Dong.

1987-01-01

This paper presents the mathematical model and program structure of the nodal Green's function method of reactor core fuel management code, NGCFM2D. Computing results of some reactor cores by NGCFM2D are analysed and compared with other codes

Mathematical methods in neutronics

International Nuclear Information System (INIS)

Planchard, J.

1995-01-01

This book presents the mathematical theory of nuclear reactors. It applies to engineers in neutronics and applied mathematicians. After a recall of the elementary notions of neutronics and of diffusion-type partial derivative equations, the theory of reactors criticality calculation is described. (J.S.)

Empirical characterisation and mathematical modelling of settlement in composting batch reactors

OpenAIRE

Illa Alibés, Josep; Prenafeta Boldú, Francesc Xavier; Bonmatí Blasi, August; Flotats Ripoll, Xavier

2012-01-01

The settlement of organic matter during composting was measured at different levels during the active biodegradation phase in forced-aerated static reactors loaded with different mixtures of organic wastes. The temperature evolution and the concentration of oxygen and carbon dioxide were also recorded in the exhaust gases. T

Adaptive control method for core power control in TRIGA Mark II reactor

Science.gov (United States)

Sabri Minhat, Mohd; Selamat, Hazlina; Subha, Nurul Adilla Mohd

2018-01-01

The 1MWth Reactor TRIGA PUSPATI (RTP) Mark II type has undergone more than 35 years of operation. The existing core power control uses feedback control algorithm (FCA). It is challenging to keep the core power stable at the desired value within acceptable error bands to meet the safety demand of RTP due to the sensitivity of nuclear research reactor operation. Currently, the system is not satisfied with power tracking performance and can be improved. Therefore, a new design core power control is very important to improve the current performance in tracking and regulate reactor power by control the movement of control rods. In this paper, the adaptive controller and focus on Model Reference Adaptive Control (MRAC) and Self-Tuning Control (STC) were applied to the control of the core power. The model for core power control was based on mathematical models of the reactor core, adaptive controller model, and control rods selection programming. The mathematical models of the reactor core were based on point kinetics model, thermal hydraulic models, and reactivity models. The adaptive control model was presented using Lyapunov method to ensure stable close loop system and STC Generalised Minimum Variance (GMV) Controller was not necessary to know the exact plant transfer function in designing the core power control. The performance between proposed adaptive control and FCA will be compared via computer simulation and analysed the simulation results manifest the effectiveness and the good performance of the proposed control method for core power control.

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

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

KAUST Repository

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

Science.gov (United States)

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)

Further optimization studies of experimental dynamic responses measured on the HTGC Dragon reactor

International Nuclear Information System (INIS)

Cummins, J.D.

1968-04-01

This report considers some measurements made of the dynamics of the HTGC Dragon reactor and the optimization of a mathematical model which represents the reactor, by altering the parameters until a least squares fit between the experimental responses and the mathematical model is obtained. The experimental information was processed in various ways. The experimental response to an impulse, step or periodic sine wave change in reactivity was processed as an impulse, step or periodic sine wave response respectively and compared with a similar response from the model. In other studies the result of a binary cross correlation experiment (effectively an impulse response input) was processed as a frequency response and this experimental frequency response was compared with the frequency response from the mathematical model. It was possible therefore to compare the optimum values of parameters, obtained for different forms of perturbing signal and for different methods of processing and to relate the optima obtained to the problem of parameter estimation. (author)

Final Stage Development of Reactor Console Simulator

International Nuclear Information System (INIS)

Mohamad Idris Taib; Ridzuan Abdul Mutalib; Zareen Khan Abdul Jalil Khan; Mohd Khairulezwan Abdul Manan; Mohd Sabri Minhat; Nurfarhana Ayuni Joha

2013-01-01

The Reactor Console Simulator PUSPATI TRIGA Reactor was developed since end of 2011 and now in the final stage of development. It is will be an interactive tool for operator training and teaching of PUSPATI TRIGA Reactor. Behavior and characteristic for reactor console and reactor itself can be evaluated and understand. This Simulator will be used as complement for actual present reactor console. Implementation of human system interface (HSI) is using computer screens, keyboard and mouse. Multiple screens are used to match the physical of present reactor console. LabVIEW software are using for user interface and mathematical calculation. Polynomial equation based on control rods calibration data as well as operation parameters record was used to calculate and estimated reactor console parameters. The capabilities in user interface, reactor physics and thermal-hydraulics can be expanded and explored to simulation as well as modeling for New Reactor Console, Research Reactor and Nuclear Power Plant. (author)

Modeling and simulation of ammonia removal from purge gases of ammonia plants using a catalytic Pd-Ag membrane reactor

International Nuclear Information System (INIS)

Rahimpour, M.R.; Asgari, A.

2008-01-01

In this work, the removal of ammonia from synthesis purge gas of an ammonia plant has been investigated. Since the ammonia decomposition is thermodynamically limited, a membrane reactor is used for complete decomposition. A double pipe catalytic membrane reactor is used to remove ammonia from purge gas. The purge gas is flowing in the reaction side and is converted to hydrogen and nitrogen over nickel-alumina catalyst. The hydrogen is transferred through the Pd-Ag membrane of tube side to the shell side. A mathematical model including conservation of mass in the tube and shell side of reactor is proposed. The proposed model was solved numerically and the effects of different parameters on the rector performance were investigated. The effects of pressure, temperature, flow rate (sweep ratio), membrane thickness and reactor diameter have been investigated in the present study. Increasing ammonia conversion was observed by raising the temperature, sweep ratio and reducing membrane thickness. When the pressure increases, the decomposition is gone toward completion but, at low pressure the ammonia conversion in the outset of reactor is higher than other pressures, but complete destruction of the ammonia cannot be achieved. The proposed model can be used for design of an industrial catalytic membrane reactor for removal of ammonia from ammonia plant and reducing NO x emissions

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)

Kinetics of two phase fuel reflected reactors

International Nuclear Information System (INIS)

Buzano, M.L.; Corno, S.E.; Mattioda, F.

2000-01-01

In the present work a self-consistent mathematical model for the local dynamics of a quite particular class of fission reactors has been developed and solved. These devices consist of an innermost multiplying region, in which a significant fraction of the fissile fuel is diluted into a liquid phase, while the complementary fuel fraction operates as a standing solid matrix. This unconventional active region is surrounded by a standard peripheral reflector. For cooling purposes, the fluid fraction of the fuel needs to be circulated through external heat exchangers. The pump driven circulation causes the delayed neutron precursors, dissolved inside the fluid phase, to be spatially homogenized in the core volume well before decaying, while a continuous removal of precursor nuclei from the core takes place as a consequence of the outside circulation. Furthermore, the fraction of the extracted precursors still surviving after the solenoidal trip through the heat exchangers is continuously reinserted into the core. A new type of dynamical model is required to account for these unusual technological features. The mathematical structure of the evolution model presented in this paper consists of a system of integro-differential-difference equations, whose solution is derived in closed-form, by means of fully analytical techniques. Many dynamics and safety features of reactors of this type can be clarified a priori, upon inspection of the mathematical properties of the solution of the model. The rigorous time-eigenvalue generating equation can be explicitly established in the present theoretical context, together with the evaluation of any kind of transients. A short survey on the possible fields of application of these reactors is also presented

Mathematical Modelling Plant Signalling Networks

KAUST Repository

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

CERN Document Server

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...

Modelling the Load Torques of Electric Drive for Polymerization Process

Directory of Open Access Journals (Sweden)

Andrzej Popenda

2007-01-01

Full Text Available The problems of mathematical modelling the load torques on shaft of driving motor designed for applications in polymerization reactors are presented in the paper. The real load of polymerization drive is determined as a function of angular velocity. Mentioned function results from friction in roll-formed slide bearing as well as from friction of ethylene molecules with mixer arms in polymerization reactor chamber. Application of mathematical formulas concerning the centrifugal ventilator is proposed to describe the mixer in reactor chamber. The analytical formulas describing the real loads of polymerization drive are applied in mathematical modelling the power unit of polymerization reactor with specially designed induction motor. The numerical analysis of transient states was made on the basis of formulated mathematical model. Examples of transient responses and trajectories resulting from analysis are presented in the paper.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Science.gov (United States)

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

NARCIS (Netherlands)

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 model use for evaluation of radioactivity spreading in nuclear power plant

International Nuclear Information System (INIS)

Kubik, I.; Gladki, Eh.; Yanchik, O.

1976-01-01

On the basis of knowledges of radioactive products behaviour and their spreading in nuclear power plant under normal and accident conditions a KOMPLEX program is developed in the FORTRAN 4 language, permitting to calculate the activity in separate parts of the nuclear power plant with WWR type reactor. The COMPLEX program includes the following subprograms: AZ - PRIM - for estimating active products in fuel, coolant, on the surfaces of fuel element cans and the primary circuit. The subprogram permits to estimate the coolant activity at the expense of fission fragments for 4 different leakage mechanisms: due to diffusion, considerable fuel element damage, contamination of fuel element can surface and fuel washout by coolant; KOR - the program for estimating active corrosion products; ACT - the program for estimating the activity of activation products; CONT - the program for estimating the activity in the nuclear power plant premises (protection envelop) and ventilating pipe. The desciption of the above subprograms is given. For testing of the mathematical model applicability and the possibilities of the corresponding programs the checking calculations for operating parameters of nuclear power plant with WWR type reactor were carried out. The calculation results obtained have shown the applicability of the model suggested and the corresponding programes for nuclear power plant under normal operation and accident conditions [ru

Thermal hydrodynamic modeling and simulation of hot-gas duct for next-generation nuclear reactor

Energy Technology Data Exchange (ETDEWEB)

Lee, Injun [School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749 (Korea, Republic of); Hong, Sungdeok; Kim, Chansoo [Korea Atomic Energy Research Institute, Daejeon 305-353 (Korea, Republic of); Bai, Cheolho; Hong, Sungyull [School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749 (Korea, Republic of); Shim, Jaesool, E-mail: jshim@ynu.ac.kr [School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749 (Korea, Republic of)

2016-12-15

Highlights: • Thermal hydrodynamic nonlinear model is presented to examine a hot gas duct (HGD) used in a fourth-generation nuclear power reactor. • Experiments and simulation were compared to validate the nonlinear porous model. • Natural convection and radiation are considered to study the effect on the surface temperature of the HGD. • Local Nusselt number is obtained for the optimum design of a possible next-generation HGD. - Abstract: A very high-temperature gas-cooled reactor (VHTR) is a fourth-generation nuclear power reactor that requires an intermediate loop that consists of a hot-gas duct (HGD), an intermediate heat exchanger (IHX), and a process heat exchanger for massive hydrogen production. In this study, a mathematical model and simulation were developed for the HGD in a small-scale nitrogen gas loop that was designed and manufactured by the Korea Atomic Energy Research Institute. These were used to investigate the effect of various important factors on the surface of the HGD. In the modeling, a porous model was considered for a Kaowool insulator inside the HGD. The natural convection and radiation are included in the model. For validation, the modeled external surface temperatures are compared with experimental results obtained while changing the inlet temperatures of the nitrogen working fluid. The simulation results show very good agreement with the experiments. The external surface temperatures of the HGD are obtained with respect to the porosity of insulator, emissivity of radiation, and pressure of the working fluid. The local Nusselt number is also obtained for the optimum design of a possible next-generation HGD.

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.

Thermal-hydraulic analysis techniques for axisymmetric pebble bed nuclear reactor cores

International Nuclear Information System (INIS)

Stroh, K.R.

1979-03-01

The pebble bed reactor's cylindrical core volume contains a random bed of small, spherical fuel-moderator elements. These graphite spheres, containing a central region of dispersed coated-particle fissile and fertile material, are cooled by high pressure helium flowing through the connected interstitial voids. A mathematical model and numerical solution technique have been developed which allow calculation of macroscopic values of thermal-hydraulic variables in an axisymmetric pebble bed nuclear reactor core. The computer program PEBBLE is based on a mathematical model which treats the bed macroscopically as a generating, conducting porous medium. The steady-state model uses a nonlinear Forchheimer-type relation between the coolant pressure gradient and mass flux, with newly derived coefficients for the linear and quadratic resistance terms. The remaining equations in the model make use of mass continuity, and thermal energy balances for the solid and fluid phases

Mathematic modeling of reactor fuel radiation creep at example of uranium and its alloys

International Nuclear Information System (INIS)

Tarasov, V.A.

2001-01-01

The model of a radiation creep is explained within the framework of the mechanism of gliding and climbing dislocations based on the conception of a dislocation as not ideal sink for point radiation defects (PRD). The offered model is efficient for installed concentration PRD, considerably exceeding thermally steady state concentration. The gliding of dislocation are describing as due to moving dislocation kinks in Peierl's relief. The climbing of dislocation are describing as due to moving dislocation jogs. The mathematical model for the computer program simulating the offered model of radiation creep is developed. The complex of the computer programs simulating the radiation creep is developed. The computer simulation researches are conducted and the outcomes of a research of a kinetics of a flexible sliding and climbing dislocation interacting to obstacles of a various type (spherical centre of extension, dislocation prismatic loop and their spatially random distributions) for various installed concentration PRD, external loadings and temperatures are represented. The curves of installed rate of a radiation creep from temperature for uranium and its alloys with small additions of molybdenum (from 0,9 to 1,3 %) are obtained

A model for nuclear research reactor dynamics

Energy Technology Data Exchange (ETDEWEB)

Barati, Ramin, E-mail: Barati.ramin@aut.ac.ir; Setayeshi, Saeed, E-mail: setayesh@aut.ac.ir

2013-09-15

Highlights: • A thirty-fourth order model is used to simulate the dynamics of a research reactor. • We consider delayed neutrons fraction as a function of time. • Variable fuel and temperature reactivity coefficients are used. • WIMS, BORGES and CITVAP codes are used for initial condition calculations. • Results are in agreement with experimental data rather than common codes. -- Abstract: In this paper, a useful thirty-fourth order model is presented to simulate the kinetics and dynamics of a research reactor core. The model considers relevant physical phenomena that govern the core such as reactor kinetics, reactivity feedbacks due to coolant and fuel temperatures (Doppler effects) with variable reactivity coefficients, xenon, samarium, boron concentration, fuel burn up and thermal hydraulics. WIMS and CITVAP codes are used to extract neutron cross sections and calculate the initial neuron flux respectively. The purpose is to present a model with results similar to reality as much as possible with reducing common simplifications in reactor modeling to be used in different analyses such as reactor control, functional reliability and safety. The model predictions are qualified by comparing with experimental data, detailed simulations of reactivity insertion transients, and steady state for Tehran research reactor reported in the literature and satisfactory results have been obtained.

Mathematical modelling in solid mechanics

CERN Document Server

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...

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

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.

Exploring the Relationship between Mathematical Modelling and Classroom Discourse

Science.gov (United States)

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

Science.gov (United States)

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.

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

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

A stochastic physical-mathematical method for reactor kinetics analysis

International Nuclear Information System (INIS)

Velickovic, Lj.

1966-01-01

The developed theoretical model is concerned with BF 3 counter placed in the core of a low power reactor (a few MW) where statistical neutron effects are most evident. Our experiments were somewhat different. The detector used was and ionization chamber with double sampling, in ADC and in the time analyzer. The objective of this model was not to obtain precise numerical calculations, but to explain the method and the essentials of the correlation. Introducing all the six groups of delayed neutrons and possibly photoneutrons the model could be improved to obtained more realistic results

DIAGRAM SOLVE THE USE OF SIMULINK BLOCK DIAGRAM TO SOLVE MATHEMA THEMATICAL CONTROL EQU MATHEMATICAL MODELS AND CONTROL EQUATIONS

Directory of Open Access Journals (Sweden)

N.M. Ghasem

2003-12-01

Full Text Available In this paper, the simulink block diagram is used to solve a model consists of a set of ordinary differential and algebraic equations to control the temperature inside a simple stirred tank heater. The flexibility of simulink block diagram gives students a better understanding of the control systems. The simulink also allows solution of mathematical models and easy visualization of the system variables. A polyethylene fluidized bed reactor is considered as an industrial example and the effect of the Proportional, Integral and Derivative control policy is presented for comparison.

On the mathematical modeling of memristors

KAUST Repository

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

CERN Document Server

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...

Modeling the PUSPATI TRIGA Reactor using MCNP code

International Nuclear Information System (INIS)

Mohamad Hairie Rabir; Mark Dennis Usang; Naim Syauqi Hamzah; Julia Abdul Karim; Mohd Amin Sharifuldin Salleh

2012-01-01

The 1 MW TRIGA MARK II research reactor at Malaysian Nuclear Agency achieved initial criticality on June 28, 1982. The reactor is designed to effectively implement the various fields of basic nuclear research, manpower training, and production of radioisotopes. This paper describes the reactor parameters calculation for the PUSPATI TRIGA REACTOR (RTP); focusing on the application of the developed reactor 3D model for criticality calculation, analysis of power and neutron flux distribution and depletion study of TRIGA fuel. The 3D continuous energy Monte Carlo code MCNP was used to develop a versatile and accurate full model of the TRIGA reactor. The model represents in detailed all important components of the core and shielding with literally no physical approximation. (author)

The chemical energy unit partial oxidation reactor operation simulation modeling

Science.gov (United States)

Mrakin, A. N.; Selivanov, A. A.; Batrakov, P. A.; Sotnikov, D. G.

2018-01-01

The chemical energy unit scheme for synthesis gas, electric and heat energy production which is possible to be used both for the chemical industry on-site facilities and under field conditions is represented in the paper. The partial oxidation reactor gasification process mathematical model is described and reaction products composition and temperature determining algorithm flow diagram is shown. The developed software product verification showed good convergence of the experimental values and calculations according to the other programmes: the temperature determining relative discrepancy amounted from 4 to 5 %, while the absolute composition discrepancy ranged from 1 to 3%. The synthesis gas composition was found out practically not to depend on the supplied into the partial oxidation reactor (POR) water vapour enthalpy and compressor air pressure increase ratio. Moreover, air consumption coefficient α increase from 0.7 to 0.9 was found out to decrease synthesis gas target components (carbon and hydrogen oxides) specific yield by nearly 2 times and synthesis gas target components required ratio was revealed to be seen in the water vapour specific consumption area (from 5 to 6 kg/kg of fuel).

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

Mathematical Modeling of Loop Heat Pipes

Science.gov (United States)

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

KAUST Repository

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.

Science.gov (United States)

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 ...

Structured Mathematical Modeling of Industrial Boiler

Directory of Open Access Journals (Sweden)

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 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. 

Research of three-dimensional transient reactivity feedback in fast reactor

International Nuclear Information System (INIS)

Xu Li; Shi Gong; Ma Dayuan; Yu Hong

2013-01-01

To solve the three-dimensional time-spatial kinetics feedback problems in fast reactor, a mathematical model of the direct reactivity feedback was proposed. Based on the NAS code for fast reactor and the reactivity feedback mechanism, a feedback model which combined the direct reactivity feedback and feedback reflected by the cross section variation was provided for the transient calculation. Furthermore, the fast reactor group collapsing system was added to the code, thus the real time group collapsing calculation could be realized. The isothermal elevated temperature test of CEFR was simulated by using the code. By comparing the calculation result with the test result of the temperature reactivity coefficient, the validity of the model and the code is verified. (authors)

iSTEM: Promoting Fifth Graders' Mathematical Modeling

Science.gov (United States)

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…

Qualitative mathematics for the social sciences mathematical models for research on cultural dynamics

CERN Document Server

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

Maximum neutron flux in thermal reactors

International Nuclear Information System (INIS)

Strugar, P.V.

1968-12-01

Direct approach to the problem is to calculate spatial distribution of fuel concentration if the reactor core directly using the condition of maximum neutron flux and comply with thermal limitations. This paper proved that the problem can be solved by applying the variational calculus, i.e. by using the maximum principle of Pontryagin. Mathematical model of reactor core is based on the two-group neutron diffusion theory with some simplifications which make it appropriate from maximum principle point of view. Here applied theory of maximum principle are suitable for application. The solution of optimum distribution of fuel concentration in the reactor core is obtained in explicit analytical form. The reactor critical dimensions are roots of a system of nonlinear equations and verification of optimum conditions can be done only for specific examples

Mathematical modeling of biological processes

CERN Document Server

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.

Identification of reactor failure states using noise methods, and spatial power distribution

International Nuclear Information System (INIS)

Vavrin, J.; Blazek, J.

1981-01-01

A survey is given of the results achieved. Methodical means and programs were developed for the control computer which may be used in noise diagnostics and in the control of reactor power distribution. Statistical methods of processing the noise components of the signals of measured variables were used for identifying failures of reactors. The method of the synthesis of the neutron flux was used for modelling and evaluating the reactor power distribution. For monitoring and controlling the power distribution a mathematical model of the reactor was constructed suitable for control computers. The uses of noise analysis methods are recommended and directions of further development shown. (J.P.)

Applied research into direct numerical control of A-1 reactor temperature

International Nuclear Information System (INIS)

Karpeta, C.; Volf, K.

1974-01-01

Partial results of research efforts aimed at applying modern control theory in the control of the reactor of the A-1 nuclear power station are presented. A mathematical model of the process dynamics was developed. Some parameters of the model were determined using the results of an experimentally performed reactor scram. The optimal stochastic discrete regulator was determined and closed-loop transients were studied. The possibilities of implementing control routines were investigated using the RPP-16 computer. (author)

Applied Mathematics, Modelling and Computational Science

CERN Document Server

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 ...

Engineering Physics and Mathematics Division progress report for period ending June 30, 1985

International Nuclear Information System (INIS)

1986-02-01

The report is divided into eight sections: (1) nuclear data measurements and evaluation; (2) systems analysis and shielding; (3) applied physics and fusion reactor analysis; (4) mathematical modeling and intelligent control; (5) reliability and human factors research; (6) applied risk and decision analysis; (7) information analysis and data management; and (8) mathematical sciences. Each section then consists of abstracts of presented or published papers

Engineering Physics and Mathematics Division progress report for period ending June 30, 1985

Energy Technology Data Exchange (ETDEWEB)

1986-02-01

The report is divided into eight sections: (1) nuclear data measurements and evaluation; (2) systems analysis and shielding; (3) applied physics and fusion reactor analysis; (4) mathematical modeling and intelligent control; (5) reliability and human factors research; (6) applied risk and decision analysis; (7) information analysis and data management; and (8) mathematical sciences. Each section then consists of abstracts of presented or published papers. (WRF)

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

Science.gov (United States)

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…

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

Science.gov (United States)

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 ...

Influence of ultrasound power on acoustic streaming and micro-bubbles formations in a low frequency sono-reactor: mathematical and 3D computational simulation.

Science.gov (United States)

Sajjadi, Baharak; Raman, Abdul Aziz Abdul; Ibrahim, Shaliza

2015-05-01

This paper aims at investigating the influence of ultrasound power amplitude on liquid behaviour in a low-frequency (24 kHz) sono-reactor. Three types of analysis were employed: (i) mechanical analysis of micro-bubbles formation and their activities/characteristics using mathematical modelling. (ii) Numerical analysis of acoustic streaming, fluid flow pattern, volume fraction of micro-bubbles and turbulence using 3D CFD simulation. (iii) Practical analysis of fluid flow pattern and acoustic streaming under ultrasound irradiation using Particle Image Velocimetry (PIV). In mathematical modelling, a lone micro bubble generated under power ultrasound irradiation was mechanistically analysed. Its characteristics were illustrated as a function of bubble radius, internal temperature and pressure (hot spot conditions) and oscillation (pulsation) velocity. The results showed that ultrasound power significantly affected the conditions of hotspots and bubbles oscillation velocity. From the CFD results, it was observed that the total volume of the micro-bubbles increased by about 4.95% with each 100 W-increase in power amplitude. Furthermore, velocity of acoustic streaming increased from 29 to 119 cm/s as power increased, which was in good agreement with the PIV analysis. Copyright © 2014 Elsevier B.V. All rights reserved.

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

Science.gov (United States)

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

MATLAB/SIMULINK model of CANDU reactor for control studies

International Nuclear Information System (INIS)

Javidnia, H.; Jiang, J.

2006-01-01

In this paper a MATLAB/SIMULINK model is developed for a CANDU type reactor. The data for the reactor are taken from an Indian PHWR, which is very similar to CANDU in its design. Among the different feedback mechanisms in the core of the reactor, only xenon has been considered which plays an important role in spatial oscillations. The model is verified under closed loop scenarios with simple PI controller. The results of the simulation show that this model can be used for controller design and simulation of the reactor systems. Adding models of the other components of a CANDU reactor would ultimately result in a complete model of CANDU plant in MATLAB/SIMULINK. (author)

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)

Structural analysis of reactor fuel elements

International Nuclear Information System (INIS)

Weeks, R.W.

1977-01-01

An overview of fuel-element modeling is presented that traces the development of codes for the prediction of light-water-reactor and fast-breeder-reactor fuel-element performance. It is concluded that although the mathematical analysis is now far advanced, the development and incorporation of mechanistic constitutive equations has not kept pace. The resultant reliance on empirical correlations severely limits the physical insight that can be gained from code extrapolations. Current efforts include modeling of alternate fuel systems, analysis of local fuel-cladding interactions, and development of a predictive capability for off-normal behavior. Future work should help remedy the current constitutive deficiencies and should include the development of deterministic failure criteria for use in design

Molecular modeling: An open invitation for applied mathematics

Science.gov (United States)

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.

Science.gov (United States)

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

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

Science.gov (United States)

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

Simulation and control of the site-dependent neutron density in a nuclear reactor

International Nuclear Information System (INIS)

Stark, K.

1974-01-01

The present work deals with the simulation and control of a pressurized-water reactor such as is used in nuclear power plants today. In the first part of the work, the mathematical model equations of the reactor are set up. They take into consideration the local distribution of the various reactor parameters as far as seems necessary for further investigations. Taking the given approximations, the mathematical model is locally one-dimensional; it is valid for the period of time in which a power control of the reactor must work. The model equations set up are calculated on an analog/hybride computer according to the modal simulation method in true time. The method is distinguished in the present problem here through good convergence and enables the observation of the simulation results as a stationary picture on an oscillograph screen. For this reason, a simulation of this type seems particularly suitable for the training of operational personnel. The aim of the second part of the work is the development of a simple control concept which enables the control of the total power of the reactor as well as of the distribution of the power density in the reactor core. The fundamentals of the control design are the non-linear system equations of the nuclear reactor. The developed control is based on the controlling of eigenfunctions; it controls the total power of the reactor as well as the distribution of the power density in the reactor core where a uniform burn-up of the nuclear fuel is seen to. Part-absorbing control rods amongst others are used as actuators like they are already used in that type of reactors. (orig./LH) [de

OECD Halden reactor project

International Nuclear Information System (INIS)

1979-01-01

This is the nineteenth annual Report on the OECD Halden Reactor Project, describing activities at the Project during 1978, the last year of the 1976-1978 Halden Agreement. Work continued in two main fields: test fuel irradiation and fuel research, and computer-based process supervision and control. Project research on water reactor fuel focusses on various aspects of fuel behavior under normal, and off-normal transient conditions. In 1978, participating organisations continued to submit test fuel for irradiation in the Halden boiling heavy-water reactor, in instrumented test assemblies designed and manufactured by the Project. Work included analysis of the impact of fuel design and reactor operating conditions on fuel cladding behavior. Fuel performance modelling included characterization of thermal and mechanical behavior at high burn-up, of fuel failure modes, and improvement of data qualification procedures to reduce and quantify error bands on in-reactor measurements. Instrument development yielded new or improved designs for measuring rod temperature, internal pressure, axial neutron flux shape determination, and for detecting cladding defects. Work on computer-based methods of reactor supervision and control included continued development of a system for predictive core surveillance, and of special mathematical methods for core power distribution control

Physical models and primary design of reactor based slow positron source at CMRR

Science.gov (United States)

Wang, Guanbo; Li, Rundong; Qian, Dazhi; Yang, Xin

2018-07-01

Slow positron facilities are widely used in material science. A high intensity slow positron source is now at the design stage based on the China Mianyang Research Reactor (CMRR). This paper describes the physical models and our primary design. We use different computer programs or mathematical formula to simulate different physical process, and validate them by proper experiments. Considering the feasibility, we propose a primary design, containing a cadmium shield, a honeycomb arranged W tubes assembly, electrical lenses, and a solenoid. It is planned to be vertically inserted in the Si-doping channel. And the beam intensity is expected to be 5 ×109

Modelling and applications in mathematics education the 14th ICMI study

CERN Document Server

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.

Nuclear reactor power control system based on flexibility model

International Nuclear Information System (INIS)

Li Gang; Zhao Fuyu; Li Chong; Tai Yun

2011-01-01

Design the nuclear reactor power control system in this paper to cater to a nonlinear nuclear reactor. First, calculate linear power models at five power levels of the reactor as five local models and design controllers of the local models as local controllers. Every local controller consists of an optimal controller contrived by the toolbox of Optimal Controller Designer (OCD) and a proportion-integration-differentiation (PID) controller devised via Genetic Algorithm (GA) to set parameters of the PID controller. According to the local models and controllers, apply the principle of flexibility model developed in the paper to obtain the flexibility model and the flexibility controller at every power level. Second, the flexibility model and the flexibility controller at a level structure the power control system of this level. The set of the whole power control systems corresponding to global power levels is to approximately carry out the power control of the reactor. Finally, the nuclear reactor power control system is simulated. The simulation result shows that the idea of flexibility model is feasible and the nuclear reactor power control system is effective. (author)

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.

Modelling aerosol behavior in reactor cooling systems

International Nuclear Information System (INIS)

McDonald, B.H.

1990-01-01

This paper presents an overview of some of the areas of concern in using computer codes to model fission-product aerosol behavior in the reactor cooling system (RCS) of a water-cooled nuclear reactor during a loss-of-coolant accident. The basic physical processes that require modelling include: fission product release and aerosol formation in the reactor core, aerosol transport and deposition in the reactor core and throughout the rest of the RCS, and the interaction between aerosol transport processes and the thermalhydraulics. In addition to these basic physical processes, chemical reactions can have a large influence on the nature of the aerosol and its behavior in the RCS. The focus is on the physics and the implications of numerical methods used in the computer codes to model aerosol behavior in the RCS

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

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.

Science.gov (United States)

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.

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.

The development of fast simulation program for marine reactor parameters

International Nuclear Information System (INIS)

Chen Zhiyun; Hao Jianli; Chen Wenzhen

2012-01-01

Highlights: ► The simplified physical and mathematical models are proposed for a marine reactor system. ► A program is developed with Simulink module and Matlab file. ► The program developed has the merit of easy input preparation, output processing and fast running. ► The program can be used for the fast simulation of marine reactor parameters on the operating field. - Abstract: The fast simulation program for marine reactor parameters is developed based on the Simulink simulating software according to the characteristics of marine reactor with requirement of maneuverability and acute and fast response. The simplified core physical and thermal model, pressurizer model, steam generator model, control rod model, reactivity model and the corresponding Simulink modules are established. The whole program is developed by coupling all the Simulink modules. Two typical transient processes of marine reactor with fast load increase at low power level and load rejection at high power level are adopted to verify the program. The results are compared with those of Relap5/Mod3.2 with good consistency, and the program runs very fast. It is shown that the program is correct and suitable for the fast and accurate simulation of marine reactor parameters on the operating field, which is significant to the marine reactor safe operation.

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

Science.gov (United States)

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.

Science.gov (United States)

Gilbert, Scott F

2018-01-31

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

Mathematical model 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.

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.

MODELING OF TUBULAR ELECTROCHEMICAL REACTOR FOR DYE REMOVAL

Directory of Open Access Journals (Sweden)

V. VIJAYAKUMAR

2017-06-01

Full Text Available The aim of the present investigation is to model a tubular electrochemical reactor for the treatment of synthetic dye wastewater. The tubular reactor was modeled and solved by finite difference method. For the model solution, the column was divided into 11 nodes in the axial direction and the variation in the radial direction has been neglected. An initial dye concentration of 200 mg L-1was taken in the reservoir. The reactor was operated in a batch with recirculation operation. Based on preliminary experiments all parameters have been optimized. The model simulation is compared with the experimental value and it is observed that the model fairly matches well with the experiment. The modeling of tubular electrochemical reactors for dye waste water treatment could be useful in the design and scale up of electrochemical process.

Simulation of emulsion copolymerization reactions in a continuous pulsed sieve-plate column reactor

OpenAIRE

C. Sayer; R. Giudici

2004-01-01

This work addressed the viability of using a pulsed sieve-plate column reactor to carry out continuous vinyl acetate/butyl acrylate emulsion copolymerization reactions. A rigorous mathematical model of emulsion copolymerization reactions in a tubular reactor with axial dispersion was used for this purpose. Operational conditions were defined to attain high monomer conversions at the reactor outlet in a relatively short residence time and, at the same time, produce a copolymer with a more homo...

Bond graph modeling of nuclear reactor dynamics

International Nuclear Information System (INIS)

Tylee, J.L.

1981-01-01

A tenth-order linear model of a pressurized water reactor (PWR) is developed using bond graph techniques. The model describes the nuclear heat generation process and the transfer of this heat to the reactor coolant. Comparisons between the calculated model response and test data from a small-scale PWR show the model to be an adequate representation of the actual plant dynamics. Possible application of the model in an advanced plant diagnostic system is discussed

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

Science.gov (United States)

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

CERN Document Server

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,...

A stochastic physical-mathematical method for reactor kinetics analysis; Jedan stohasticki fizicko-matematicki model za analizu reaktorske kinetike

Energy Technology Data Exchange (ETDEWEB)

Velickovic, Lj [Institut za nuklearne nauke ' Boris Kidric' , Vinca, Belgrade (Yugoslavia)

1966-07-01

The developed theoretical model is concerned with BF{sub 3} counter placed in the core of a low power reactor (a few MW) where statistical neutron effects are most evident. Our experiments were somewhat different. The detector used was and ionization chamber with double sampling, in ADC and in the time analyzer. The objective of this model was not to obtain precise numerical calculations, but to explain the method and the essentials of the correlation. Introducing all the six groups of delayed neutrons and possibly photoneutrons the model could be improved to obtained more realistic results.

Verification of thermo-fluidic CVD reactor model

International Nuclear Information System (INIS)

Lisik, Z; Turczynski, M; Ruta, L; Raj, E

2014-01-01

Presented paper describes the numerical model of CVD (Chemical Vapour Deposition) reactor created in ANSYS CFX, whose main purpose is the evaluation of numerical approaches used to modelling of heat and mass transfer inside the reactor chamber. Verification of the worked out CVD model has been conducted with measurements under various thermal, pressure and gas flow rate conditions. Good agreement between experimental and numerical results confirms correctness of the elaborated model.

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

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

Science.gov (United States)

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

OpenAIRE

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

Science.gov (United States)

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…

How to Introduce Mathematic Modeling in Industrial Design Education

NARCIS (Netherlands)

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

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

Science.gov (United States)

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…

TU electric reactor model verification

International Nuclear Information System (INIS)

Willingham, C.E.; Killgore, M.R.

1989-01-01

Power reactor benchmark calculations using the code package CASMO-3/SIMULATE-3 have been performed for six cycles of Prairie Island Unit 1. The reload fuel designs for the selected cycles include gadolinia as a burnable absorber, natural uranium axial blankets, and increased water-to-fuel ratio. The calculated results for both low-power physics tests (boron end points, control rod worths, and isothermal temperature coefficients) and full-power operation (power distributions and boron letdown) are compared to measured plant data. These comparisons show that the TU Electric reactor physics models accurately predict important physics parameters for power reactors

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

Science.gov (United States)

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…

A computational modeling approach of the jet-like acoustic streaming and heat generation induced by low frequency high power ultrasonic horn reactors.

Science.gov (United States)

Trujillo, Francisco Javier; Knoerzer, Kai

2011-11-01

High power ultrasound reactors have gained a lot of interest in the food industry given the effects that can arise from ultrasonic-induced cavitation in liquid foods. However, most of the new food processing developments have been based on empirical approaches. Thus, there is a need for mathematical models which help to understand, optimize, and scale up ultrasonic reactors. In this work, a computational fluid dynamics (CFD) model was developed to predict the acoustic streaming and induced heat generated by an ultrasonic horn reactor. In the model it is assumed that the horn tip is a fluid inlet, where a turbulent jet flow is injected into the vessel. The hydrodynamic momentum rate of the incoming jet is assumed to be equal to the total acoustic momentum rate emitted by the acoustic power source. CFD velocity predictions show excellent agreement with the experimental data for power densities higher than W(0)/V ≥ 25kWm(-3). This model successfully describes hydrodynamic fields (streaming) generated by low-frequency-high-power ultrasound. Crown Copyright © 2011. Published by Elsevier B.V. All rights reserved.

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.

Fischer-Tropsch Slurry Reactor modeling

Energy Technology Data Exchange (ETDEWEB)

Soong, Y.; Gamwo, I.K.; Harke, F.W. [Pittsburgh Energy Technology Center, PA (United States)] [and others

1995-12-31

This paper reports experimental and theoretical results on hydrodynamic studies. The experiments were conducted in a hot-pressurized Slurry-Bubble Column Reactor (SBCR). It includes experimental results of Drakeol-10 oil/nitrogen/glass beads hydrodynamic study and the development of an ultrasonic technique for measuring solids concentration. A model to describe the flow behavior in reactors was developed. The hydrodynamic properties in a 10.16 cm diameter bubble column with a perforated-plate gas distributor were studied at pressures ranging from 0.1 to 1.36 MPa, and at temperatures from 20 to 200{degrees}C, using a dual hot-wire probe with nitrogen, glass beads, and Drakeol-10 oil as the gas, solid, and liquid phase, respectively. It was found that the addition of 20 oil wt% glass beads in the system has a slight effect on the average gas holdup and bubble size. A well-posed three-dimensional model for bed dynamics was developed from an ill-posed model. The new model has computed solid holdup distributions consistent with experimental observations with no artificial {open_quotes}fountain{close_quotes} as predicted by the earlier model. The model can be applied to a variety of multiphase flows of practical interest. An ultrasonic technique is being developed to measure solids concentration in a three-phase slurry reactor. Preliminary measurements have been made on slurries consisting of molten paraffin wax, glass beads, and nitrogen bubbles at 180 {degrees}C and 0.1 MPa. The data show that both the sound speed and attenuation are well-defined functions of both the solid and gas concentrations in the slurries. The results suggest possibilities to directly measure solids concentration during the operation of an autoclave reactor containing molten wax.

Mathematical models of ABE fermentation: review and analysis.

Science.gov (United States)

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 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

Co-current and counter-current configurations for ethanol steam reforming in a dense Pd-Ag membrane reactor

NARCIS (Netherlands)

Gallucci, F.; de Falco, M.; Tosti, S.; Marrelli, L; Basile, A.

2008-01-01

The ethanol steam-reforming reaction to produce pure hydrogen has been studied theoretically. A mathematical model has been formulated for a traditional system and a palladium membrane reactor packed with a Co-based catalyst and the simulation results related to the membrane reactor for both

Hydrodynamic models for slurry bubble column reactors

Energy Technology Data Exchange (ETDEWEB)

Gidaspow, D. [IIT Center, Chicago, IL (United States)

1995-12-31

The objective of this investigation is to convert a {open_quotes}learning gas-solid-liquid{close_quotes} fluidization model into a predictive design model. This model is capable of predicting local gas, liquid and solids hold-ups and the basic flow regimes: the uniform bubbling, the industrially practical churn-turbulent (bubble coalescence) and the slugging regimes. Current reactor models incorrectly assume that the gas and the particle hold-ups (volume fractions) are uniform in the reactor. They must be given in terms of empirical correlations determined under conditions that radically differ from reactor operation. In the proposed hydrodynamic approach these hold-ups are computed from separate phase momentum balances. Furthermore, the kinetic theory approach computes the high slurry viscosities from collisions of the catalyst particles. Thus particle rheology is not an input into the model.

The development of model generators for specific reactors

Energy Technology Data Exchange (ETDEWEB)

Chow, J.C. [Atomic Energy of Canada Limited, Chalk River, Ontario (Canada)

2012-07-01

Authoring reactor models is a routine task for practitioners in nuclear engineering for reactor design, safety analysis, and code validation. The conventional approach is to use a text-editor to either manually manipulate an existing model or to assemble a new model by copying and pasting or direct typing. This approach is error-prone and substantial effort is required for verification. Alternatively, models can be generated programmatically for a specific system via a centralized data source and with rigid algorithms to generate models consistently and efficiently. This approach is demonstrated here for model generators for MCNP and KENO for the ZED-2 reactor. (author)

Parametric study of sodium aerosols in the cover-gas space of sodium-cooled reactors