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Sample records for reactor mathematical modeling

  1. Mathematical Modeling for Simulation of Nuclear Reactor Analysis

    OpenAIRE

    Salah Ud-Din Khan; Shahab Ud-Din Khan

    2013-01-01

    In this paper, we have developed a mathematical model for the nuclear reactor analysis to be implemented in the nuclear reactor code. THEATRe is nuclear reactor analysis code which can only work for the cylindrical type fuel reactor and cannot applicable for the plate type fuel nuclear reactor. Therefore, the current studies encompasses on the modification of THEATRe code for the plate type fuel element. This mathematical model is applicable to the thermal analysis of the reactor which is ver...

  2. Identification of Chemical Reactor Plant’s Mathematical Model

    Directory of Open Access Journals (Sweden)

    Pyakillya Boris

    2015-01-01

    Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.

  3. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor

    Directory of Open Access Journals (Sweden)

    Ahmmed Saadi Ibrehem

    2011-05-01

    Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local:  http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in 

  4. Mathematical modeling of a three-phase trickle bed reactor

    Directory of Open Access Journals (Sweden)

    J. D. Silva

    2012-09-01

    Full Text Available The transient behavior in a three-phase trickle bed reactor system (N2/H2O-KCl/activated carbon, 298 K, 1.01 bar was evaluated using a dynamic tracer method. The system operated with liquid and gas phases flowing downward with constant gas flow Q G = 2.50 x 10-6 m³ s-1 and the liquid phase flow (Q L varying in the range from 4.25x10-6 m³ s-1 to 0.50x10-6 m³ s-1. The evolution of the KCl concentration in the aqueous liquid phase was measured at the outlet of the reactor in response to the concentration increase at reactor inlet. A mathematical model was formulated and the solutions of the equations fitted to the measured tracer concentrations. The order of magnitude of the axial dispersion, liquid-solid mass transfer and partial wetting efficiency coefficients were estimated based on a numerical optimization procedure where the initial values of these coefficients, obtained by empirical correlations, were modified by comparing experimental and calculated tracer concentrations. The final optimized values of the coefficients were calculated by the minimization of a quadratic objective function. Three correlations were proposed to estimate the parameters values under the conditions employed. By comparing experimental and predicted tracer concentration step evolutions under different operating conditions the model was validated.

  5. Mathematical modelling of methane steam reforming in a membrane reactor: an isothermal model

    Energy Technology Data Exchange (ETDEWEB)

    Assaf, E.M. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Dept. de Fisico-Quimica; Jesus, C.D.F.; Assaf, J.M. [Sao Carlos Univ., SP (Brazil). Dept. de Engenharia Quimica

    1998-06-01

    A mathematical modelling of one-dimensional, stationary and isothermic membrane reactor for methane steam reforming was developed to compare the maximum yield for methane conversion in this reactor with that in a conventional fixed-bed reactor. Fick`s first law was used to describe the mechanism of hydrogen permeation. The variables studied include: reaction temperature, hydrogen feed flow rate and membrane thickness. The results show that the membrane reactor presents a higher methane conversion yield than the conventional fixed-bed reactor. (author) 16 refs., 5 figs., 1 tab.; e-mail: eassaf at iqsc.sc.usp.br; mansur at power.ufscar.br

  6. MATHEMATICAL MODELLING OF METHANE STEAM REFORMING IN A MEMBRANE REACTOR: AN ISOTHERMIC MODEL

    Directory of Open Access Journals (Sweden)

    E.M. ASSAF

    1998-06-01

    Full Text Available A mathematical modelling of one-dimensional, stationary and isothermic membrane reactor for methane steam reforming was developed to compare the maximum yield for methane conversion in this reactor with that in a conventional fixed-bed reactor. Fick's first law was used to describe the mechanism of hydrogen permeation. The variables studied include: reaction temperature, hydrogen feed flow rate and membrane thickness. The results show that the membrane reactor presents a higher methane conversion yield than the conventional fixed-bed reactor.

  7. 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.

  8. Mathematical modeling of upflow anaerobic sludge blanket (UASB) reactor treating domestic wastewater.

    Science.gov (United States)

    Elmitwalli, Tarek

    2013-01-01

    Although the upflow anaerobic sludge blanket (UASB) reactor has been widely applied for domestic wastewater treatment in many developing countries, there is no sufficient mathematical model for proper design and operation of the reactor. An empirical model based on non-linear regression was developed to represent the physical and chemical removal of suspended solids (SS) in the reactor. Moreover, a simplified dynamic model based on ADM1 and the empirical model for SS removal was developed for anaerobic digestion of the entrapped SS and dissolved matter in the wastewater. The empirical model showed that effluent suspended chemical oxygen demand (COD(ss)) concentration is directly proportional to the influent COD(ss) concentration and inversely proportional to both the hydraulic retention time (HRT) of the reactor and wastewater temperature. For obtaining sufficient COD(ss) removal, the HRT of the UASB reactor must be higher than 4 h, and higher HRT than 12 h slightly improved COD(ss) removal. The dynamic model results showed that the required time for filling the reactor with sludge mainly depends on influent total chemical oxygen demand (COD(t)) concentration and HRT. The influent COD(t) concentration, HRT and temperature play a crucial role on the performance of the reactor. The results indicated that shorter HRT is needed for optimization of COD(t) removal, as compared with optimization of COD(t) conversion to methane. Based on the model results, the design HRT of the UASB reactor should be selected based on the optimization of wastewater conversion and minimization of biodegradable SS accumulation in the sludge bed, not only based on COD removal, to guarantee a stable reactor performance.

  9. Mathematical modeling of a slurry reactor for DME direct synthesis from syngas

    Institute of Scientific and Technical Information of China (English)

    Sadegh Papari; Mohammad Kazemeini; Moslem Fattahi

    2012-01-01

    In this paper,an axial dispersion mathematical model is developed to simulate a three-phase slurry bubble column reactor for direct synthesis of dimethyl ether (DME) from syngas.This large-scale reactor is modeled using mass and energy balances,catalyst sedimentation and single-bubble as well as two-bubbles class flow hydrodynamics.A comparison between the two hydrodynamic models through pilot plant experimental data from the literature shows that heterogeneous two-bubbles flow model is in better agreement with the experimental data than homogeneous single-bubble gas flow model.Also,by investigating the heterogeneous gas flow and axial dispersion model for small bubbles as well as the large bubbles and slurry (i.e.including paraffins and the catalyst) phase,the temperature profile along the reactor is obtained.A comparison between isothermal and non-isothermal reactors reveals no obvious performance difference between them.The optimum values of reactor diameter and height were obtained at 7 m and 50 m,respectively.The effects of operating variables on the axial catalyst distribution,DME productivity and CO conversion are also investigated in this research.

  10. Mathematical model and computer code for the analysis of advanced fast reactor dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Schukin, N.V. (Moscow Engineering Physics Inst. (Russian Federation)); Korsun, A.S. (Moscow Engineering Physics Inst. (Russian Federation)); Vitruk, S.G. (Moscow Engineering Physics Inst. (Russian Federation)); Zimin, V.G. (Moscow Engineering Physics Inst. (Russian Federation)); Romanin, S.D. (Moscow Engineering Physics Inst. (Russian Federation))

    1993-04-01

    Efficient algorithms for mathematical modeling of 3-D neutron kinetics and thermal hydraulics are described. The model and appropriate computer code make it possible to analyze a variety of transient events ranging from normal operational states to catastrophic accident excursions. To verify the code, a number of calculations of different kind of transients was carried out. The results of the calculations show that the model and the computer code could be used for conceptual design of advanced liquid metal reactors. The detailed description of calculations of TOP WS accident is presented. (orig./DG)

  11. Mathematical Modeling and Simulation of the Dehydrogenation of Ethyl Benzene to Form Styrene Using Steady-State Fixed Bed Reactor

    Directory of Open Access Journals (Sweden)

    Zaidon M. Shakoor

    2013-05-01

    Full Text Available In this research, two models are developed to simulate the steady state fixed bed reactor used for styrene production by ethylbenzene dehydrogenation. The first is one-dimensional model, considered axial gradient only while the second is two-dimensional model considered axial and radial gradients for same variables.The developed mathematical models consisted of nonlinear simultaneous equations in multiple dependent variables. A complete description of the reactor bed involves partial, ordinary differential and algebraic equations (PDEs, ODEs and AEs describing the temperatures, concentrations and pressure drop across the reactor was given. The model equations are solved by finite differences method. The reactor models were coded with Mat lab 6.5 program and various numerical techniques were used to obtain the desired solution.The simulation data for both models were validated with industrial reactor results with a very good concordance.

  12. 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.

    2017-04-01

    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.

  13. THE MATHEMATICAL MODEL DEVELOPMENT OF THE ETHYLBENZENE DEHYDROGENATION PROCESS KINETICS IN A TWO-STAGE ADIABATIC CONTINUOUS REACTOR

    Directory of Open Access Journals (Sweden)

    V. K. Bityukov

    2015-01-01

    Full Text Available The article is devoted to the mathematical modeling of the kinetics of ethyl benzene dehydrogenation in a two-stage adiabatic reactor with a catalytic bed functioning on continuous technology. The analysis of chemical reactions taking place parallel to the main reaction of styrene formation has been carried out on the basis of which a number of assumptions were made proceeding from which a kinetic scheme describing the mechanism of the chemical reactions during the dehydrogenation process was developed. A mathematical model of the dehydrogenation process, describing the dynamics of chemical reactions taking place in each of the two stages of the reactor block at a constant temperature is developed. The estimation of the rate constants of direct and reverse reactions of each component, formation and exhaustion of the reacted mixture was made. The dynamics of the starting material concentration variations (ethyl benzene batch was obtained as well as styrene formation dynamics and all byproducts of dehydrogenation (benzene, toluene, ethylene, carbon, hydrogen, ect.. The calculated the variations of the component composition of the reaction mixture during its passage through the first and second stages of the reactor showed that the proposed mathematical description adequately reproduces the kinetics of the process under investigation. This demonstrates the advantage of the developed model, as well as loyalty to the values found for the rate constants of reactions, which enable the use of models for calculating the kinetics of ethyl benzene dehydrogenation under nonisothermal mode in order to determine the optimal temperature trajectory of the reactor operation. In the future, it will reduce energy and resource consumption, increase the volume of produced styrene and improve the economic indexes of the process.

  14. 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...... 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...... 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...

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

    Science.gov (United States)

    Jabłoński, Sławomir J; Łukaszewicz, Marcin

    2014-12-01

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

  16. 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.

  17. 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.

  18. 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.

  19. Mathematical Modelling of Catalytic Fixed-Bed Reactor for Carbon Dioxide Reforming of Methane over Rh/Al2O3 Catalyst

    Directory of Open Access Journals (Sweden)

    Nor Aishah Saidina Amin

    2010-10-01

    Full Text Available A one-dimensional mathematical model was developed to simulate the performance of catalytic fixed bed reactor for carbon dioxide reforming of methane over Rh/Al2O3 catalyst at atmospheric pressure. The reactions involved in the system are carbon dioxide reforming of methane (CORM and reverse water gas shift reaction (RWGS. The profiles of CH4 and CO2 conversions, CO and H2 yields, molar flow rate and mole raction of all species as well as reactor temperature along the axial bed of catalyst were simulated. In addition, the effects of different reactor temperature on the reactor performance were also studied. The models can also be applied to analyze the performances of lab-scale micro reactor as well as pilot-plant scale reactor with certain modifications and model verification with experimental data. © 2008 BCREC UNDIP. All rights reserved.[Received: 20 August 2008; Accepted: 25 September 2008][How to Cite: N.A.S. Amin, I. Istadi, N.P. Yee. (2008. Mathematical Modelling of Catalytic Fixed-Bed Reactor for Carbon Dioxide Reforming of Methane over Rh/Al2O3 Catalyst. Bulletin of Chemical Reaction Engineering and Catalysis, 3 (1-3: 21-29.  doi:10.9767/bcrec.3.1-3.7120.21-29][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.3.1-3.7120.21-29 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/7120

  20. Mathematical modelling and reactor design for multi-cycle bioregeneration of nitrate exhausted ion exchange resin.

    Science.gov (United States)

    Ebrahimi, Shelir; Roberts, Deborah J

    2016-01-01

    Nitrate contamination is one of the largest issues facing communities worldwide. One of the most common methods for nitrate removal from water is ion exchange using nitrate selective resin. Although these resins have a great capacity for nitrate removal, they are considered non regenerable. The sustainability of nitrate-contaminated water treatment processes can be achieved by regenerating the exhausted resin several times rather than replacing and incineration of exhausted resin. The use of multi-cycle exhaustion/bioregeneration of resin enclosed in a membrane has been shown to be an effective and innovative regeneration method. In this research, the mechanisms for bioregeneration of resin were studied and a mathematical model which incorporated physical desorption process with biological removal kinetics was developed. Regardless of the salt concentration of the solution, this specific resin is a pore-diffusion controlled process (XδD ¯CDr0(5+2α)3) shows that the bioregeneration process is controlled by reaction kinetics and is governed by biological removal of nitrate. The model was validated by comparison to experimental data; the average of R-squared values for cycle 1 to 5 of regeneration was 0.94 ± 0.06 which shows that the developed model predicted the experimental results very well. The model sensitivity for different parameters was evaluated and a model bioreactor design for bioregeneration of highly selective resins was also presented.

  1. 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.

  2. Development of the Mathematics of Learning Curve Models for Evaluating Small Modular Reactor Economics

    Energy Technology Data Exchange (ETDEWEB)

    Harrison, T. J. [ORNL

    2014-02-01

    The cost of nuclear power is a straightforward yet complicated topic. It is straightforward in that the cost of nuclear power is a function of the cost to build the nuclear power plant, the cost to operate and maintain it, and the cost to provide fuel for it. It is complicated in that some of those costs are not necessarily known, introducing uncertainty into the analysis. For large light water reactor (LWR)-based nuclear power plants, the uncertainty is mainly contained within the cost of construction. The typical costs of operations and maintenance (O&M), as well as fuel, are well known based on the current fleet of LWRs. However, the last currently operating reactor to come online was Watts Bar 1 in May 1996; thus, the expected construction costs for gigawatt (GW)-class reactors in the United States are based on information nearly two decades old. Extrapolating construction, O&M, and fuel costs from GW-class LWRs to LWR-based small modular reactors (SMRs) introduces even more complication. The per-installed-kilowatt construction costs for SMRs are likely to be higher than those for the GW-class reactors based on the property of the economy of scale. Generally speaking, the economy of scale is the tendency for overall costs to increase slower than the overall production capacity. For power plants, this means that doubling the power production capacity would be expected to cost less than twice as much. Applying this property in the opposite direction, halving the power production capacity would be expected to cost more than half as much. This can potentially make the SMRs less competitive in the electricity market against the GW-class reactors, as well as against other power sources such as natural gas and subsidized renewables. One factor that can potentially aid the SMRs in achieving economic competitiveness is an economy of numbers, as opposed to the economy of scale, associated with learning curves. The basic concept of the learning curve is that the more a

  3. Development of the Mathematics of Learning Curve Models for Evaluating Small Modular Reactor Economics

    Energy Technology Data Exchange (ETDEWEB)

    Harrison, T. J. [ORNL

    2014-02-01

    The cost of nuclear power is a straightforward yet complicated topic. It is straightforward in that the cost of nuclear power is a function of the cost to build the nuclear power plant, the cost to operate and maintain it, and the cost to provide fuel for it. It is complicated in that some of those costs are not necessarily known, introducing uncertainty into the analysis. For large light water reactor (LWR)-based nuclear power plants, the uncertainty is mainly contained within the cost of construction. The typical costs of operations and maintenance (O&M), as well as fuel, are well known based on the current fleet of LWRs. However, the last currently operating reactor to come online was Watts Bar 1 in May 1996; thus, the expected construction costs for gigawatt (GW)-class reactors in the United States are based on information nearly two decades old. Extrapolating construction, O&M, and fuel costs from GW-class LWRs to LWR-based small modular reactors (SMRs) introduces even more complication. The per-installed-kilowatt construction costs for SMRs are likely to be higher than those for the GW-class reactors based on the property of the economy of scale. Generally speaking, the economy of scale is the tendency for overall costs to increase slower than the overall production capacity. For power plants, this means that doubling the power production capacity would be expected to cost less than twice as much. Applying this property in the opposite direction, halving the power production capacity would be expected to cost more than half as much. This can potentially make the SMRs less competitive in the electricity market against the GW-class reactors, as well as against other power sources such as natural gas and subsidized renewables. One factor that can potentially aid the SMRs in achieving economic competitiveness is an economy of numbers, as opposed to the economy of scale, associated with learning curves. The basic concept of the learning curve is that the more a

  4. Mathematical Modelling of Catalytic Fixed-Bed Reactor for Carbon Dioxide Reforming of Methane over Rh/Al2O3 Catalyst

    Directory of Open Access Journals (Sweden)

    New Pei Yee

    2008-04-01

    Full Text Available A one-dimensional mathematical model was developed to simulate the performance of catalytic fixed bedreactor for carbon dioxide reforming of methane over Rh/Al2O3 catalyst at atmospheric pressure. The reactionsinvolved in the system are carbon dioxide reforming of methane (CORM and reverse water gas shiftreaction (RWGS. The profiles of CH4 and CO2 conversions, CO and H2 yields, molar flow rate and molefraction of all species as well as reactor temperature along the axial bed of catalyst were simulated. In addition,the effects of different reactor temperature on the reactor performance were also studied. The modelscan also be applied to analyze the performances of lab-scale micro reactor as well as pilot-plant scale reactorwith certain modifications and model verification with experimental data. © 2008 BCREC UNDIP. All rights reserved.[Received: 20 August 2008; Accepted: 25 September 2008][How to Cite: N.A.S. Amin, I. Istadi, N.P. Yee. (2008. Mathematical Modelling of Catalytic Fixed-Bed Reactor for Carbon Dioxide Reforming of Methane over Rh/Al2O3 Catalyst. Bulletin of Chemical Reaction Engineering and Catalysis, 3 (1-3: 21-29. doi:10.9767/bcrec.3.1-3.19.21-29

  5. 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…

  6. Mathematical Modeling and Simulation of the Dehydrogenation of Ethyl Benzene to Form Styrene Using Steady-State Fixed Bed Reactor

    National Research Council Canada - National Science Library

    Zaidon M. Shakoor

    2013-01-01

    ... 6.5 program and various numerical techniques were used to obtain the desired solution.The simulation data for both models were validated with industrial reactor results with a very good concordance.

  7. Development of the Mathematics of Learning Curve Models for Evaluating Small Modular Reactor Economics

    Energy Technology Data Exchange (ETDEWEB)

    Harrison, Thomas J. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2014-03-01

    This report documents the efforts to perform dynamic model validation on the Eastern Interconnection (EI) by modeling governor deadband. An on-peak EI dynamic model is modified to represent governor deadband characteristics. Simulation results are compared with synchrophasor measurements collected by the Frequency Monitoring Network (FNET/GridEye). The comparison shows that by modeling governor deadband the simulated frequency response can closely align with the actual system response.

  8. Experimental studies and mathematical modeling of an up-flow biofilm reactor treating mustard oil rich wastewater.

    Science.gov (United States)

    Chakraborty, Chandrima; Chowdhury, Ranjana; Bhattacharya, Pinaki

    2011-05-01

    Bioremediation of lipid-rich model wastewater was investigated in a packed bed biofilm reactor (anaerobic filter). A detailed study was conducted about the influence of fatty acid concentration on biomethanation of the high-fat liquid effluent of edible oil refineries. The biochemical methane potential (BMP) of the liquid waste was reported and maximum cumulative methane production at the exit of the reactor is estimated to be 785 ml CH(4) (STP)/(gVSS added). The effects of hydraulic retention time (HRT), organic loading rate (OLR) and bed porosity on the cold gas efficiency or energy efficiency of the bioconversion process were also investigated. Results revealed that the maximum cold gas efficiency of the process is 42% when the total organic load is 2.1 g COD/l at HRT of 3.33 days. Classical substrate uninhibited Monod model is used to generate the differential system equations which can predict the reactor behavior satisfactorily.

  9. 氯苯反应器数学模型的研究%Study on Mathematical Model of Chlorobenzene Reactor

    Institute of Scientific and Technical Information of China (English)

    邬勇奇; 潘科

    2013-01-01

    Through analyzing mass transfer and response characteristics of gas-liquid flow in chlorobenzene reactor, designing chlorobenzene reactor through CSTR and PFR in series was proposed, in which, the CSTR as main reaction zone accounts for about 80% of full reaction volume. Further calculation shows that the reactor' s outlet conversion rate predicted by the model is consistent with the reactor' s actual conversion rate.%通过对氯苯反应器中气、液两相传质及反应特征的分析,提出了按照CSTR串联PFR模型设计氯苯反应器的观点.其中CSTR为主要反应区域,约占全塔反应体积的80%.进一步的计算表明,用模型预测的反应器出口转化率与反应器的实际转化率一致.

  10. Transient recovery voltage analysis for various current breaking mathematical models: shunt reactor and capacitor bank de-energization study

    Directory of Open Access Journals (Sweden)

    Oramus Piotr

    2015-09-01

    Full Text Available Electric arc is a complex phenomenon occurring during the current interruption process in the power system. Therefore performing digital simulations is often necessary to analyse transient conditions in power system during switching operations. This paper deals with the electric arc modelling and its implementation in simulation software for transient analyses during switching conditions in power system. Cassie, Cassie-Mayr as well as Schwarz-Avdonin equations describing the behaviour of the electric arc during the current interruption process have been implemented in EMTP-ATP simulation software and presented in this paper. The models developed have been used for transient simulations to analyse impact of the particular model and its parameters on Transient Recovery Voltage in different switching scenarios: during shunt reactor switching-off as well as during capacitor bank current switching-off. The selected simulation cases represent typical practical scenarios for inductive and capacitive currents breaking, respectively.

  11. 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.

  12. 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.

    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......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...... (55 oC). Sludge, food waste, grass clippings, garden waste were co-digested with VS-based mixing ratios of 10:67.5:15.75:6.75 and 10:45:31.5:13.5 in R1 and R2 respectively. The BioModel (Angelidaki et al., 1999) was then employed with minor modifications of model parameters. The model outputs were...

  13. A mathematical model for multiple hydrogeneration reactions in a continuous stirred three phase slurry reactor with an evaporating solvent

    NARCIS (Netherlands)

    Janssen, H.J.; Westerterp, K.R.; Vos, J.

    1992-01-01

    An experimental study of the catalytic hydorgenation of 2,4-dinitrotoluene (DNT) in a mini-installation with a continuously operated stirred three-phase slurry reactor and an evaporating solvent is discussed. Some characteristic properties of the reactor system and the influence of the operating par

  14. Qualitative Aspects of the Solutions of a Mathematical Model for the Dynamic Analysis of the Reversible Chemical Reaction SO2(g)+1/2O2(g)<=>SO3(g) in a Catalytic Reactor

    CERN Document Server

    Wilfredo, Angulo

    2014-01-01

    We present some qualitative aspects concerning the solution to the mathematical model describing the dynamical behavior of the reversible chemical reaction SO2(g)+1/2O2(g)SO3(g) carried out in a catalytic reactor used in the process of sulfuric acid production.

  15. Qualitative Aspects of the Solutions of a Mathematical Model for the Dynamic Analysis of the Reversible Chemical Reaction SO2(g)+1/2O2(g)<=>SO3(g) in a Catalytic Reactor

    OpenAIRE

    Wilfredo, Angulo; Joyne, Contreras

    2014-01-01

    We present some qualitative aspects concerning the solution to the mathematical model describing the dynamical behavior of the reversible chemical reaction SO2(g)+1/2O2(g)SO3(g) carried out in a catalytic reactor used in the process of sulfuric acid production.

  16. 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…

  17. Dynamic model of Fast Breeder Test Reactor

    Energy Technology Data Exchange (ETDEWEB)

    Vaidyanathan, G., E-mail: vaidya@igcar.gov.i [Fast Reactor Technology Group, Indira Gandhi Center for Atomic Research, Kalpakkam (India); Kasinathan, N.; Velusamy, K. [Fast Reactor Technology Group, Indira Gandhi Center for Atomic Research, Kalpakkam (India)

    2010-04-15

    Fast Breeder Test Reactor (FBTR) is a 40 M Wt/13.2 MWe sodium cooled reactor operating since 1985. It is a loop type reactor. As part of the safety analysis the response of the plant to various transients is needed. In this connection a computer code named DYNAM was developed to model the reactor core, the intermediate heat exchanger, steam generator, piping, etc. This paper deals with the mathematical model of the various components of FBTR, the numerical techniques to solve the model, and comparison of the predictions of the code with plant measurements. Also presented is the benign response of the plant to a station blackout condition, which brings out the role of the various reactivity feedback mechanisms combined with a gradual coast down of reactor sodium flow.

  18. State space modeling of reactor core in a pressurized water reactor

    Science.gov (United States)

    Ashaari, A.; Ahmad, T.; Shamsuddin, Mustaffa; M, Wan Munirah W.; Abdullah, M. Adib

    2014-07-01

    The power control system of a nuclear reactor is the key system that ensures a safe operation for a nuclear power plant. However, a mathematical model of a nuclear power plant is in the form of nonlinear process and time dependent that give very hard to be described. One of the important components of a Pressurized Water Reactor is the Reactor core. The aim of this study is to analyze the performance of power produced from a reactor core using temperature of the moderator as an input. Mathematical representation of the state space model of the reactor core control system is presented and analyzed in this paper. The data and parameters are taken from a real time VVER-type Pressurized Water Reactor and will be verified using Matlab and Simulink. Based on the simulation conducted, the results show that the temperature of the moderator plays an important role in determining the power of reactor core.

  19. State space modeling of reactor core in a pressurized water reactor

    Energy Technology Data Exchange (ETDEWEB)

    Ashaari, A.; Ahmad, T.; M, Wan Munirah W. [Department of Mathematical Science, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Shamsuddin, Mustaffa [Institute of Ibnu Sina, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Abdullah, M. Adib [Swinburne University of Technology, Faculty of Engineering, Computing and Science, Jalan Simpang Tiga, 93350 Kuching, Sarawak (Malaysia)

    2014-07-10

    The power control system of a nuclear reactor is the key system that ensures a safe operation for a nuclear power plant. However, a mathematical model of a nuclear power plant is in the form of nonlinear process and time dependent that give very hard to be described. One of the important components of a Pressurized Water Reactor is the Reactor core. The aim of this study is to analyze the performance of power produced from a reactor core using temperature of the moderator as an input. Mathematical representation of the state space model of the reactor core control system is presented and analyzed in this paper. The data and parameters are taken from a real time VVER-type Pressurized Water Reactor and will be verified using Matlab and Simulink. Based on the simulation conducted, the results show that the temperature of the moderator plays an important role in determining the power of reactor core.

  20. Mathematical model analysis on the enhancement of aeration efficiency using ladder-type flat membrane module forms in the Submerged Membrane Bio-reactor(SMBR)

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The cross-flow shearing action produced from the inferior aeration in the Submerged Membrane Bio-reactor(SMBR) is an effective way to further improve anti-fouling effects of membrane modules.Based on the widely-applied vertical structure of flat membrane modules,improvements are made that ladder-type flat membrane structure is designed with a certain inclined angle θ so that the cross-flow velocity of bubble near the membrane surface can be held,and the intensity and times of elastic colli-sion between bubbles and membrane surface can be increased.This can improve scouring action of membrane surface on aeration and reduce energy consumption of strong aeration in SMBR.By de-ducing and improving the mathematics model of collision between bubble and vertical flat put forward by Vries,the relatively suitable incline angle θ under certain aeration place and in certain size rang of bubble can be obtained with the computer iterative calculation technology.Finally,for many groups of ladder-type flat membrane in parallel placement in the practical application of SMBR,some sugges-tions are offered:the interval distance of membrane modules is 8―15 mm,and aeration should be op-erated at 5―7 mm among membrane modules,and the optimal design angle of trapeziform membrane is 1.7°―2.5°.

  1. Mathematical model analysis on the enhancement of aeration efficiency using ladder-type flat membrane module forms in the Submerged Membrane Bio-reactor (SMBR)

    Institute of Scientific and Technical Information of China (English)

    LI Bo; YE MaoSheng; YANG FengLin; MA Hui

    2009-01-01

    The cross-flow shearing action produced from the inferior aeration in the Submerged Membrane Bio-reactor (SMBR) Is an effective way to further improve anti-fouling effects of membrane modules.Based on the widely-applied vertical structure of flat membrane modules, improvements are made that ladder-type flat membrane structure is designed with a certain inclined angle θ so that the cross-flow velocity of bubble near the membrane surface can be held, and the intensity and times of elastic colli-sion between bubbles and membrane surface can be increased. This can improve scouring action ofmembrane surface on aeration and reduce energy consumption of strong aeration in SMBR. By de-ducing and improving the mathematics model of collision between bubble and vertical flat put forward by Vries, the relatively suitable Incline angle θ under certain aeration place and in certain size rang ofbubble can be obtained with the computer iterative calculation technology. Finally, for many groups of ladder-type flat membrane in parallel placement in the practical application of SMBR, some sugges-tions are offered: the interval distance of membrane modules is 8--15 mm, and aeration should be op-erated at 5--7 mm among membrane modules, and the optimal design angle of trapeziform membrane is 1.7°--2.5°.

  2. 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....

  3. Teaching Mathematical Modelling.

    Science.gov (United States)

    Jones, Mark S.

    1997-01-01

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

  4. 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

  5. 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.

  6. Comparison of two mathematical models for correlating the organic matter removal efficiency with hydraulic retention time in a hybrid anaerobic baffled reactor treating molasses

    OpenAIRE

    Ghaniyari-Benis, Saeid; Martín, Antonio; Borja Padilla, Rafael; M. A. Martín; Hedayat, N.

    2012-01-01

    A modelling of the anaerobic digestion process of molasses was conducted in a 70-L multistage anaerobic biofilm reactor or hybrid anaerobic baffled reactor with six compartments at an operating temperature of 26 °C. Five hydraulic retention times (6, 16, 24, 72 and 120 h) were studied at a constant influent COD concentration of 10,000 mg/L. Two different kinetic models (one was based on a dispersion model with first-order kinetics for substrate consumption and the other based on a modificati...

  7. Mathematical models of morphogenesis

    Directory of Open Access Journals (Sweden)

    Dilão Rui

    2015-01-01

    Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.

  8. Mathematical modelling of metabolism

    DEFF Research Database (Denmark)

    Gombert, Andreas Karoly; Nielsen, Jens

    2000-01-01

    Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....

  9. 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...

  10. 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

  11. Mathematical modeling in psychological researches

    Directory of Open Access Journals (Sweden)

    Aleksandra Zyolko

    2013-04-01

    Full Text Available The author considers the nature of mathematical modeling and its significance in psychological researches. The author distinguishes the types of mathematical models: deterministic, stochastic models and synergetic models. The system approach is proposed as an instrument of implementation of mathematical modelling in psychological research.

  12. 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.

  13. A model of reactor kinetics

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, A.S.; Thompson, B.R.

    1988-09-01

    The analytical model of nuclear reactor transients, incorporating both mechanical and nuclear effects, simulates reactor kinetics. Linear analysis shows the stability borderline for small power perturbations. In a stable system, initial power disturbances die out with time. With an unstable combination of nuclear and mechanical characteristics, initial disturbances persist and may increase with time. With large instability, oscillations of great magnitude occur. Stability requirements set limits on the power density at which particular reactors can operate. The limiting power density depends largely on the product of two terms: the fraction of delayed neutrons and the frictional damping of vibratory motion in reactor core components. As the fraction of delayed neutrons is essentially fixed, mechanical damping largely determines the maximum power density. A computer program, based on the analytical model, calculates and plots reactor power as a nonlinear function of time in response to assigned values of mechanical and nuclear characteristics.

  14. 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.

  15. 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…

  16. Examples of Mathematical Modeling

    Science.gov (United States)

    Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan

    2008-01-01

    Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520

  17. Mathematical Modelling in European Education

    Science.gov (United States)

    Ferri, Rita Borromeo

    2013-01-01

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

  18. 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

  19. Mathematical modeling in chronobiology.

    Science.gov (United States)

    Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H

    2013-01-01

    Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.

  20. Assessment of start-up mechanisms for anaerobic fluidized bed reactor in series based on mathematical simulation

    Science.gov (United States)

    Sudibyo, Hanifrahmawan; Guntama, Dody; Budhijanto, Wiratni

    2017-05-01

    Anaerobic digestion is associated with long hydraulic residence time and hence leads to huge reactor volume, especially for high rate input to the reactor. To overcome this major drawback, one of the possibilities is optimizing the schemes of reactor configuration and start-up mechanisms. This study aimed to determine the most promising start-up mechanism for anaerobic digestion reactors in series, with respect to the shortest hydraulic residence time to reach the highest biogas production rate. The reactor to be studied is anaerobic fluidized bed reactor (AFBR) which is known as the most efficient reactor for high organic loading rate. Case to be studied is landfill leachate digestion. Although reactor optimization can be conducted experimentally, it could be expensive and time consuming. This study proposed the utilization of mathematical modeling to screen the possibilities towards the best options to be verified experimentally. Kinetic study of landfill leachate anaerobic digestion was first conducted to depict the rate of microbial growth and the rate of substrate consumption. Kinetics constants obtained from this batch experiment were then used in the mathematical model representing AFBR. Several mechanisms were simulated in this study. In the first mechanism, all digesters were started simultaneously. In the second mechanism, each digester was started until it achieved steady-state condition before the next digester was started. The third mechanism was start-up scenario for single reactor as opposed to the previous two mechanisms. These all three mechanisms were simulated for either one-through stream and recycling a portion of the reactor effluent. The mathematical simulation result was used to evaluate each mechanism based on hydraulic residence time required for all digesters in series to reach the steady-state condition, the extent of pollutant removal, and the rate of biogas production. In the need of high sCOD removal, the second mechanism emerged as

  1. 核反应堆内中子泄漏数学模型研究%Study of mathematical model on neutron leakage in reactor

    Institute of Scientific and Technical Information of China (English)

    蔡章生; 蔡志明

    2001-01-01

    In this paper the precise expression of neutron leakage term inpoint-reactor neutron-kinetics equation is derived.It improves the precision of point-reactor neutron-kinetics equation and makes its application range extended from reactor cool restart to prompt supercritical.%导出了点堆中子动力学方程中的中子泄漏表达式,使点堆中子动力学方程的精度提高,应用领域可从反应堆冷启动一直到瞬发超临界

  2. 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...

  3. RSMASS-D models: An improved method for estimating reactor and shield mass for space reactor applications

    Energy Technology Data Exchange (ETDEWEB)

    Marshall, A.C.

    1997-10-01

    Three relatively simple mathematical models have been developed to estimate minimum reactor and radiation shield masses for liquid-metal-cooled reactors (LMRs), in-core thermionic fuel element (TFE) reactors, and out-of-core thermionic reactors (OTRs). The approach was based on much of the methodology developed for the Reactor/Shield Mass (RSMASS) model. Like the original RSMASS models, the new RSMASS-derivative (RSMASS-D) models use a combination of simple equations derived from reactor physics and other fundamental considerations, along with tabulations of data from more detailed neutron and gamma transport theory computations. All three models vary basic design parameters within a range specified by the user to achieve a parameter choice that yields a minimum mass for the power level and operational time of interest. The impact of critical mass, fuel damage, and thermal limitations are accounted for to determine the required fuel mass. The effect of thermionic limitations are also taken into account for the thermionic reactor models. All major reactor component masses are estimated, as well as instrumentation and control (I&C), boom, and safety system masses. A new shield model was developed and incorporated into all three reactor concept models. The new shield model is more accurate and simpler to use than the approach used in the original RSMASS model. The estimated reactor and shield masses agree with the mass predictions from separate detailed calculations within 15 percent for all three models.

  4. 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…

  5. Modeling Chemical Reactors I: Quiescent Reactors

    CERN Document Server

    Michoski, C E; Schmitz, P G

    2010-01-01

    We introduce a fully generalized quiescent chemical reactor system in arbitrary space $\\vdim =1,2$ or 3, with $n\\in\\mathbb{N}$ chemical constituents $\\alpha_{i}$, where the character of the numerical solution is strongly determined by the relative scaling between the local reactivity of species $\\alpha_{i}$ and the local functional diffusivity $\\mathscr{D}_{ij}(\\alpha)$ of the reaction mixture. We develop an operator time-splitting predictor multi-corrector RK--LDG scheme, and utilize $hp$-adaptivity relying only on the entropy $\\mathscr{S}_{\\mathfrak{R}}$ of the reactive system $\\mathfrak{R}$. This condition preserves these bounded nonlinear entropy functionals as a necessarily enforced stability condition on the coupled system. We apply this scheme to a number of application problems in chemical kinetics; including a difficult classical problem arising in nonequilibrium thermodynamics known as the Belousov-Zhabotinskii reaction where we utilize a concentration-dependent diffusivity tensor $\\mathscr{D}_{ij}(...

  6. Modelling solid-convective flash pyrolysis of straw and wood in the Pyrolysis Centrifuge Reactor

    DEFF Research Database (Denmark)

    Bech, Niels; Larsen, Morten Boberg; Jensen, Peter Arendt

    2009-01-01

    Less than a handful of solid-convective pyrolysis reactors for the production of liquid fuel from biomass have been presented and for only a single reactor a detailed mathematical model has been presented. In this article we present a predictive mathematical model of the pyrolysis process...... in the Pyrolysis Centrifuge Reactor, a novel solid-convective flash pyrolysis reactor. The model relies on the original concept for ablative pyrolysis of particles being pyrolysed through the formation of an intermediate liquid compound which is further degraded to form liquid organics, char, and gas. To describe...... that the reacting particle continuously shed the formed char layer....

  7. Mathematical Model for Hit Phenomena

    CERN Document Server

    Ishii, Akira; Hayashi, Takefumi; Matsuda, Naoya; Nakagawa, Takeshi; Arakaki, Hisashi; Yoshida, Narihiko

    2010-01-01

    The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.

  8. Reactor Physics Analysis Models for a CANDU Reactor

    Energy Technology Data Exchange (ETDEWEB)

    Choi, Hang Bok

    2007-10-15

    Canada deuterium uranium (CANDU) reactor physics analysis is typically performed in three steps. At first, macroscopic cross-sections of the reference lattice is produced by modeling the reference fuel channel. Secondly macroscopic cross-sections of reactivity devices in the reactor are generated. The macroscopic cross-sections of a reactivity device are calculated as incremental cross-sections by subtracting macroscopic cross-sections of a three-dimensional lattice without reactivity device from those of a three-dimensional lattice with a reactivity device. Using the macroscopic cross-sections of the reference lattice and incremental cross-sections of the reactivity devices, reactor physics calculations are performed. This report summarizes input data of typical CANDU reactor physics codes, which can be utilized for the future CANDU reactor physics analysis.

  9. Reactor Physics Analysis Models for a CANDU Reactor

    Energy Technology Data Exchange (ETDEWEB)

    Choi, Hang Bok

    2007-10-15

    Canada deuterium uranium (CANDU) reactor physics analysis is typically performed in three steps. At first, macroscopic cross-sections of the reference lattice is produced by modeling the reference fuel channel. Secondly macroscopic cross-sections of reactivity devices in the reactor are generated. The macroscopic cross-sections of a reactivity device are calculated as incremental cross-sections by subtracting macroscopic cross-sections of a three-dimensional lattice without reactivity device from those of a three-dimensional lattice with a reactivity device. Using the macroscopic cross-sections of the reference lattice and incremental cross-sections of the reactivity devices, reactor physics calculations are performed. This report summarizes input data of typical CANDU reactor physics codes, which can be utilized for the future CANDU reactor physics analysis.

  10. 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

  11. Mathematical Models of Biochemical Oscillations

    OpenAIRE

    Conrad, Emery David

    1999-01-01

    The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...

  12. Research on Mathematical Model of Thermo-Economics Analysis for Pressurized Water Reactor Nuclear Cogeneration Plant%热电联产压水堆核电机组热经济性定量分析模型

    Institute of Scientific and Technical Information of China (English)

    严俊杰; 刘继平; 林万超; 陈国慧; 邢秦安

    2001-01-01

    A thermo-economical diagnostic mathematical model for pressurizedwater reactor (PWR) nuclear cogeneration plant is proposed based on heat assignment method.This model simplifies the calculation of thermal system and can be used to calculate the index variations caused by heating steam parameters as temperature,return percentage and return place of the return water.Some examples are given to show the usefulness of this model.%基于热电联产机组热量法分配的特点,建立了热电联产压水堆机组热力系统发生变化对热经济性指标影响的计算模型,提出了供热系统参数——供热回水率、回水温度、回水地点变化对压水堆机组热经济性影响的定量诊断数学模型,可将复杂的热力系统全面计算简化成3个一次方程.通过实例计算,验证了所提数学模型是正确可行的,同时具有概念清晰、计算简捷的特点.

  13. 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 mode...

  14. Mathematical Models of Waiting Time.

    Science.gov (United States)

    Gordon, Sheldon P.; Gordon, Florence S.

    1990-01-01

    Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)

  15. 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…

  16. 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…

  17. Neutrino Mixing Discriminates Geo-reactor Models

    CERN Document Server

    Dye, S T

    2009-01-01

    Geo-reactor models suggest the existence of natural nuclear reactors at different deep-earth locations with loosely defined output power. Reactor fission products undergo beta decay with the emission of electron antineutrinos, which routinely escape the earth. Neutrino mixing distorts the energy spectrum of the electron antineutrinos. Characteristics of the distorted spectrum observed at the earth's surface could specify the location of a geo-reactor, discriminating the models and facilitating more precise power measurement. The existence of a geo-reactor with known position could enable a precision measurement of the neutrino oscillation parameter delta-mass-squared.

  18. 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…

  19. Representations used by mathematics student teachers in mathematical modeling process

    Directory of Open Access Journals (Sweden)

    Aytuğ Özaltun

    2014-02-01

    Full Text Available The purpose of this study is to determine representations used by mathematics student teachers in steps of mathematical modeling process based on their solutions of problems formed in the context of different classification of modeling. The study was conducted with fifteen secondary mathematics student teachers given a Mathematical Modeling course. The participants were separated into five collaboration groups of three students. Data were collected with the detailed written papers given by the groups for the problems and GeoGebra solution files. The groups benefited from verbal, algebraic, figural, tabular and dynamic representations while they were solving the problems. Considering all steps of the process, groups at most used verbal and algebraic representations. While they used only verbal representation in analyzing the problem, they benefited from at most verbal representation and then figural representation in establishing the systematic structure. The most used is algebraic and then verbal representations in the steps of mathematization, meta-mathematization, and mathematical analysis. In the steps of interpretation/evaluation and the model verification, the groups mainly benefited from verbal and then algebraic representations. Further researches towards why representations are preferred in the specific steps of the mathematical modeling process are suggested.Key Words: Mathematical modeling, modeling problems, mathematics student teachers, representations.

  20. 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.

  1. 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…

  2. 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,...

  3. Modeling interdisciplinary activities involving Mathematics

    DEFF Research Database (Denmark)

    Iversen, Steffen Møllegaard

    2006-01-01

    In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

  4. Reactor modeling in heterogeneous photocatalysis: toxicity and biodegradability assessment.

    Science.gov (United States)

    Satuf, M L; José, S; Paggi, J C; Brandi, R J; Cassano, A E; Alfano, O M

    2010-01-01

    Photocatalysis employing titanium dioxide is a useful method to degrade a wide variety of organic and inorganic pollutants from water and air. However, the application of this advanced oxidation process at industrial scale requires the development of mathematical models to design and scale-up photocatalytic reactors. In the present work, intrinsic kinetic expressions previously obtained in a laboratory reactor are employed to predict the performance of a bench scale reactor of different configuration and operating conditions. 4-Chlorophenol was chosen as the model pollutant. The toxicity and biodegradability of the irradiated mixture in the bench photoreactor was also assessed. Good agreement was found between simulation and experimental data. The root mean square error of the estimations was 9.9%. The photocatalytic process clearly enhances the biodegradability of the reacting mixture, and the initial toxicity of the pollutant was significantly reduced by the treatment.

  5. 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....... It is found that the probability of entering the pore is highest when the largest of the radii in the ellipse is equal to half the radius of the pore, in case of molecules with circular radius less than the pore radius. The results are directly related to the macroscopic distribution coefficient...

  6. 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.

  7. Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

    Science.gov (United States)

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

    Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

  8. 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...

  9. 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...

  10. 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...

  11. 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…

  12. 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…

  13. Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas

    Institute of Scientific and Technical Information of China (English)

    Dianhua Liu; Xing Hua; Dingye Fang

    2007-01-01

    A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether (DME) from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ 38×2 mm),and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04.

  14. Mathematical models of human behavior

    DEFF Research Database (Denmark)

    Møllgaard, Anders Edsberg

    data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived......, thereby implying that interactions between spreading processes are driving forces of attention dynamics. Overall, the thesis contributes to a quantitative understanding of a wide range of different human behaviors by applying mathematical modeling to behavioral data. There can be no doubt......During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...

  15. 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

  16. Mathematical models of granular matter

    CERN Document Server

    Mariano, Paolo; Giovine, Pasquale

    2008-01-01

    Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

  17. 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

  18. Mathematical modeling of kidney transport.

    Science.gov (United States)

    Layton, Anita T

    2013-01-01

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

  19. Mathematical Modeling in Combustion Science

    CERN Document Server

    Takeno, Tadao

    1988-01-01

    An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.

  20. A mathematical model of inheritance

    Institute of Scientific and Technical Information of China (English)

    瞿裕忠; 王志坚; 徐家福

    1996-01-01

    Inheritance is regarded as the hallmark of object-oriented programming languages.A mathematical model of inheritance is presented.In this model,the graph-sorted signature is introduced to represent the algebraic structure of the program,and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance.The program’s algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language’s inheritance.

  1. Modeling of a slurry bubble column reactor for Fischer-Tropsch synthesis

    Institute of Scientific and Technical Information of China (English)

    QIAN Wei-xin; MA Hong-fang; LI Tao; YING Wei-yong; FANG Ding-ye

    2012-01-01

    On the basis of the global CO consumption rate model,the lumped product distribution model and the sedimentation-dispersion model of a catalyst,a steady-state,one-dimensional mathematical model of the slurry bubble column reactor for Fischer-Tropsch synthesis were established.The mathematical simulation of the slurry bubble column reactor for Fischer-Tropsch synthesis was carried out under the following typical industrial operating conditions:temperature 230 ℃,pressure 3.0 MPa,gas flow 5× 105 m3/h,catalyst content in slurry phase 30%,reactor diameter 5.0 m and the composition of feed gas:y(H2)=0.60,y(CO)=0.30,y(N2)=0.10.The influences of operating pressure,temperature and m(H2)/m(CO) in feed gas on the reactor's reaction performance were simulated.

  2. A Mathematical Model of Mechanotransduction

    CERN Document Server

    Roth, Bradley J

    2016-01-01

    This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model...

  3. 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.

  4. 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.

  5. Reactors

    CERN Document Server

    International Electrotechnical Commission. Geneva

    1988-01-01

    This standard applies to the following types of reactors: shunt reactors, current-limiting reactors including neutral-earthing reactors, damping reactors, tuning (filter) reactors, earthing transformers (neutral couplers), arc-suppression reactors, smoothing reactors, with the exception of the following reactors: small reactors with a rating generally less than 2 kvar single-phase and 10 kvar three-phase, reactors for special purposes such as high-frequency line traps or reactors mounted on rolling stock.

  6. 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

  7. Mathematical model of induction heating

    Science.gov (United States)

    Rak, Josef

    2017-07-01

    One of mathematical models of induction heating can be described by a parabolic differential equation with the specific Joule looses in the body. Advantage of this method is that the detailed knowledge of the 3D-magnetic field is not necessary and move of the body or the inductor can be easily implemented. The specific Joule looses can computed by solving the Fredholm integral equation of the second kind for the eddy current of density by the Nyström method with the singularity subtraction.

  8. Modeling of Reactor Kinetics and Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Matthew Johnson; Scott Lucas; Pavel Tsvetkov

    2010-09-01

    In order to model a full fuel cycle in a nuclear reactor, it is necessary to simulate the short time-scale kinetic behavior of the reactor as well as the long time-scale dynamics that occur with fuel burnup. The former is modeled using the point kinetics equations, while the latter is modeled by coupling fuel burnup equations with the kinetics equations. When the equations are solved simultaneously with a nonlinear equation solver, the end result is a code with the unique capability of modeling transients at any time during a fuel cycle.

  9. 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.

  10. 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...

  11. A Generative Model of Mathematics Learning

    Science.gov (United States)

    Wittrock, M. C.

    1974-01-01

    The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

  12. 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.

  13. Mathematical models in biological discovery

    CERN Document Server

    Walter, Charles

    1977-01-01

    When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con­ tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog­ ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...

  14. 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.

  15. 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....

  16. Modeling of a fluidized bed reactor for the ethylene-propylene copolymerization

    Directory of Open Access Journals (Sweden)

    Juan Guillermo Cadavid Estrada

    2010-04-01

    Full Text Available A mathematical model for the ethylene - propylene copolymerization with a Ziegler - Natta catalyst in a gas phase fludized bed reactor is presented. The model includes a two active site kinetic model with spontaneous transfer reactions and site deactivation. Also, it is studied and simulated the growth of a polymeric particle which is exposed to an outside atmosphere (monomers concentrations and temperature that represent the emulsion phase conditions of the reactor. Particle growth model is the basis for the study of the sizes distribution into the reactor. Two phase model of Kunii-Levenspiel is the basis for the modelling and simulation of the fluid bed reactor, the models developed consider two extreme cases for the gas mixed grade in emulsion phase (perfectly mixed and plug flow. The solution of the models includes mass (for the two monomers and energy balances, coupled with the particle growth and residence time distribution models.

  17. An Axial Dispersion Model for Evaporating Bubble Column Reactor

    Institute of Scientific and Technical Information of China (English)

    谢刚; 李希

    2004-01-01

    Evaporating bubble column reactor (EBCR) is a kind of aerated reactor in which the reaction heat is removed by the evaporation of volatile reaction mixture. In this paper, a mathematical model that accounts for the gas-liquid exothermic reaction and axial dispersions of both gas and liquid phase is employed to study the performance of EBCR for the process of p-xylene(PX) oxidation. The computational results show that there are remarkable concentration and temperature gradients in EBCR for high ratio of height to diameter (H/DT). The temperature is lower at the bottom of column and higher at the top, due to rapid evaporation induced by the feed gas near the bottom. The concentration profiles in the gas phase are more nonuniform than those (except PX) in the liquid phase, which causes more solvent burning consumption at high H/DT ratio. For p-xylene oxidation, theo ptimal H/DT is around 5.

  18. Building fire zone model with symbolic mathematics

    Institute of Scientific and Technical Information of China (English)

    武红梅; 郜冶; 周允基

    2009-01-01

    To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.

  19. Mathematical modeling in biomedical imaging

    CERN Document Server

    2012-01-01

    This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools.  It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.

  20. 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.

  1. Mathematical model for bone mineralization

    Directory of Open Access Journals (Sweden)

    Svetlana V Komarova

    2015-08-01

    Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.

  2. Mathematical model for the gasification of coal under pressure

    Energy Technology Data Exchange (ETDEWEB)

    Biba, V.; Macak, J.; Kloss, E.; Malecha, J.

    1978-01-01

    A mathematical model for the the high-pressure gasification of solid fuels in the charged layer is presented which permits the quantitative description of the the static behavior of the generator. Deals with the parameters of reaction kinetics and of the transfer of matter and energy which are necessary for developing the model of a fixed-bed reactor. To obtain a practical model, simplifications are needed which concern the gasification, degasification, and drying processes. They are dealt with individually. For calculating the concentration and temperature profiles for the solid and gas phases along the gasification bed height, a system of differential equations was obtained which was supplemented by some algebraic equations.

  3. Mathematical models of human behavior

    DEFF Research Database (Denmark)

    Møllgaard, Anders Edsberg

    During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...

  4. Computacional-representantional model of mathematics (crmmath)

    OpenAIRE

    Toro Carvajal, Luis Alberto

    2016-01-01

    This paper presents the so-called computational representational model of mathematics (MCRMATH), its theoretical importance for mathematics education and its relation with the use of technology tools in mathematics teaching. To do this, from a cognitive point of view, we conduct a research study of representations and we explain the computational-representational model of mind (CRMM).

  5. Modeling of Fischer-Tropsch Synthesis in a Slurry Reactor with Water Permeable Membrane

    Institute of Scientific and Technical Information of China (English)

    Fabiano A. N. Fernandes

    2007-01-01

    Fischer-Tropsch synthesis is an important chemical process for the production of liquid fuels and olefins. In recent years, the abundant availability of natural gas and the increasing demand of olefins, diesel, and waxes have led to a high interest to further develop this process. A mathematical model of a slurry membrane reactor used for syngas polymerization was developed to simulate and compare the maximum yields and operating conditions in the reactor with that in a conventional slurry reactor.The carbon polymerization was studied from a modeling point of view in a slurry reactor with a water permeable membrane and a conventional slurry reactor. Simulation results show that different parameters affect syngas conversion and carbon product distribution, such as the hydrogen to carbon monoxide ratio,and the membrane parameters such as membrane permeance.

  6. 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.

  7. Mathematical Model for Photovoltaic Cells

    Directory of Open Access Journals (Sweden)

    Wafaa ABD EL-BASIT

    2013-11-01

    Full Text Available The study of photovoltaic systems in an efficient manner requires a precise knowledge of the (I-V and (P-V characteristic curves of photovoltaic modules. So, the aim of the present paper is to estimate such characteristics based on different operating conditions. In this concern, a simple one diode mathematical model was implemented using MATLAB script. The output characteristics of PV cell depend on the environmental conditions. For any solar cell, the model parameters are function of the irradiance and the temperature values of the site where the panel is placed. In this paper, the numerical values of the equivalent circuit parameters are generated by the program. As well, the dependence of the cells electrical parameters are analyzed under the influence of different irradiance and temperature levels. The variation of slopes of the (I–V curves of a cell at short-circuit and open-circuit conditions with intensity of illumination in small span of intensity and different temperature levels have been applied to determine the cell parameters, shunt resistance, series resistance. The results show that the efficiency of solar cells has an inverse relationship with temperature, irradiance levels are affected by the change of the photo-generation current and the series resistance in the single diode model.

  8. 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…

  9. 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…

  10. Mathematical Model of Gravitational and Electrostatic Forces

    OpenAIRE

    Krouglov, Alexei

    2006-01-01

    Author presents mathematical model for acting-on-a-distance attractive and repulsive forces based on propagation of energy waves that produces Newton expression for gravitational and Coulomb expression for electrostatic forces. Model uses mathematical observation that difference between two inverse exponential functions of the distance asymptotically converges to function proportional to reciprocal of distance squared.

  11. 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…

  12. Mineral potential mapping with mathematical geological models

    NARCIS (Netherlands)

    Porwal, A.K.

    2006-01-01

    Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based mi

  13. Mathematical Modeling of the Agriculture Crop Technology

    Directory of Open Access Journals (Sweden)

    D. Drucioc

    1999-02-01

    Full Text Available The organized structure of computer system for economic and ecological estimation of agriculture crop technologies is described. The system is composed of six interconnected blocks. The linear, non-linear and stochastic mathematical models for machinery sizing and selection in farm-level cropping system is presented in the mathematical model block of computer system.

  14. Mineral potential mapping with mathematical geological models

    NARCIS (Netherlands)

    Porwal, A.K.

    2006-01-01

    Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based

  15. Mathematical Modeling of Cellular Metabolism.

    Science.gov (United States)

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    2016-01-01

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

  16. 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 pipeli......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...

  17. Advanced Mathematical Model to Describe the Production of Biodiesel Process

    Directory of Open Access Journals (Sweden)

    Hikmat S. Al-Salim

    2009-12-01

    Full Text Available Advanced mathematical model was used to capture the batch reactor characteristics of reacting compounds. The model was applied to batch reactor for the production of bio-diesel from palm and kapok oils. Results of the model were compared with experimental data in terms of conversion of transesterification reaction for the production of bio-diesel under unsteady state. A good agreement was obtained between our model predictions and the experimental data. Both experimental and modeling results showed that the conversion of triglycerides to methyl ester was affected by the process conditions. The transesterification process with temperature of about 70 oC, and methanol ratio to the triglyceride of about 5 times its stoichiometry, and the NAOH catalyst of wt 0.4%, appear to be acceptable process conditions for bio diesel process production from palm oil and kapok oil. The model can be applied for endothermic batch process. © 2009 BCREC UNDIP. All rights reserved[Received: 12 August 2009, Revised: 15 October 2009; Accepted: 18 October 2009][How to Cite: A.S. Ibrehem, H. S. Al-Salim. (2009. Advanced Mathematical Model to Describe the Production of Biodiesel Process. Bulletin of Chemical Reaction Engineering and Catalysis, 4(2: 37-42. doi:10.9767/bcrec.4.2.28.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.28.37-42

  18. Models of iodine behavior in reactor containments

    Energy Technology Data Exchange (ETDEWEB)

    Weber, C.F.; Beahm, E.C.; Kress, T.S.

    1992-10-01

    Models are developed for many phenomena of interest concerning iodine behavior in reactor containments during severe accidents. Processes include speciation in both gas and liquid phases, reactions with surfaces, airborne aerosols, and other materials, and gas-liquid interface behavior. Although some models are largely empirical formulations, every effort has been made to construct mechanistic and rigorous descriptions of relevant chemical processes. All are based on actual experimental data generated at the Oak Ridge National Laboratory (ORNL) or elsewhere, and, hence, considerable data evaluation and parameter estimation are contained in this study. No application or encoding is attempted, but each model is stated in terms of rate processes, with the intention of allowing mechanistic simulation. Taken together, this collection of models represents a best estimate iodine behavior and transport in reactor accidents.

  19. Mathematical modeling in soil science

    Science.gov (United States)

    Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel

    2015-04-01

    Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.

  20. A Seminar in Mathematical Model-Building.

    Science.gov (United States)

    Smith, David A.

    1979-01-01

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

  1. Pebble Bed Reactor Dust Production Model

    Energy Technology Data Exchange (ETDEWEB)

    Abderrafi M. Ougouag; Joshua J. Cogliati

    2008-09-01

    The operation of pebble bed reactors, including fuel circulation, can generate graphite dust, which in turn could be a concern for internal components; and to the near field in the remote event of a break in the coolant circuits. The design of the reactor system must, therefore, take the dust into account and the operation must include contingencies for dust removal and for mitigation of potential releases. Such planning requires a proper assessment of the dust inventory. This paper presents a predictive model of dust generation in an operating pebble bed with recirculating fuel. In this preliminary work the production model is based on the use of the assumption of proportionality between the dust production and the normal force and distance traveled. The model developed in this work uses the slip distances and the inter-pebble forces computed by the authors’ PEBBLES. The code, based on the discrete element method, simulates the relevant static and kinetic friction interactions between the pebbles as well as the recirculation of the pebbles through the reactor vessel. The interaction between pebbles and walls of the reactor vat is treated using the same approach. The amount of dust produced is proportional to the wear coefficient for adhesive wear (taken from literature) and to the slip volume, the product of the contact area and the slip distance. The paper will compare the predicted volume with the measured production rates. The simulation tallies the dust production based on the location of creation. Two peak production zones from intra pebble forces are predicted within the bed. The first zone is located near the pebble inlet chute due to the speed of the dropping pebbles. The second peak zone occurs lower in the reactor with increased pebble contact force due to the weight of supported pebbles. This paper presents the first use of a Discrete Element Method simulation of pebble bed dust production.

  2. MATHEMATICAL MODEL OF GRAIN MICRONIZATION

    Directory of Open Access Journals (Sweden)

    V. A. Afanas’ev

    2014-01-01

    Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.

  3. Applications of mathematical models of road cycling

    OpenAIRE

    Dahmen, Thorsten; Saupe, Dietmar; Wolf, Stefan

    2012-01-01

    This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization p...

  4. The mathematics of cancer: integrating quantitative models.

    Science.gov (United States)

    Altrock, Philipp M; Liu, Lin L; Michor, Franziska

    2015-12-01

    Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

  5. 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.

  6. Mathematical Programming Models in Educational Planning.

    Science.gov (United States)

    McNamara, James F.

    This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…

  7. 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...

  8. A mathematical model of symmetry based on mathematical definition

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.

  9. A mathematical model of symmetry based on mathematical definition

    Institute of Scientific and Technical Information of China (English)

    刘玉生; 杨将新; 吴昭同; 高曙明

    2002-01-01

    Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disignd/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance beeanse of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: ( 1 ) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements ; after which, the mathematical models of syrmmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.

  10. Study of Photovoltaic Cells Engineering Mathematical Model

    Science.gov (United States)

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

    2016-11-01

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

  11. 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

  12. 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)

  13. Mathematical Model and Advanced Control for Gas-phase Olefin Polymerization in Fluidized-bed Catalytic Reactors%气相石蜡聚合在流化床催化反应器中的数学模型和先进控制

    Institute of Scientific and Technical Information of China (English)

    Ahmmed S. Ibrehem; Mohamed Azlan Hussain; Nayef M. Ghasem

    2008-01-01

    In this study, the developments in modeling gas-phase catalyzed olefin polymerization fluidized-bed reactors (FBR) using Ziegler-Natta catalyst is presented. The modified mathematical model to account for mass and heat transfer between the solid particles and the surrounding gas in the emulsion phase is developed in this work to include site activation reaction. This model developed in the present study is subsequently compared with well-known models, namely, the bubble-growth, well-mixed and the constant bubble size models for porous and non porous catalyst. The results we obtained from the model was very close to the constant bubble size model, well-mixed model and bubble growth model at the beginning of the reaction but its overall behavior changed and is closer to the weft-mixed model compared with the bubble growth model and constant bubble size model after half an hour of operation. Neural-network based predictive controller are implemented to control the system and com-pared with the conventional PID controller, giving acceptable results.

  14. Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms

    Science.gov (United States)

    Eric, Chan Chun Ming

    2009-01-01

    The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

  15. Development of a system model for advanced small modular reactors.

    Energy Technology Data Exchange (ETDEWEB)

    Lewis, Tom Goslee,; Holschuh, Thomas Vernon,

    2014-01-01

    This report describes a system model that can be used to analyze three advance small modular reactor (SMR) designs through their lifetime. Neutronics of these reactor designs were evaluated using Monte Carlo N-Particle eXtended (MCNPX/6). The system models were developed in Matlab and Simulink. A major thrust of this research was the initial scoping analysis of Sandias concept of a long-life fast reactor (LLFR). The inherent characteristic of this conceptual design is to minimize the change in reactivity over the lifetime of the reactor. This allows the reactor to operate substantially longer at full power than traditional light water reactors (LWRs) or other SMR designs (e.g. high temperature gas reactor (HTGR)). The system model has subroutines for lifetime reactor feedback and operation calculations, thermal hydraulic effects, load demand changes and a simplified SCO2 Brayton cycle for power conversion.

  16. Mathematical modelling of cucumber (cucumis sativus) drying

    Science.gov (United States)

    Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.

    2014-07-01

    This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.

  17. Mathematical modelling of the calcination process | Olayiwola ...

    African Journals Online (AJOL)

    Mathematical modelling of the calcination process. ... High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces ... From the numerical simulation, it is observed that the gas temperature increases as the ...

  18. 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...... 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......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...

  19. Applied mathematics: Models, Discretizations, and Solvers

    Institute of Scientific and Technical Information of China (English)

    D.E. Keyes

    2007-01-01

    @@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.

  20. Teaching mathematical modelling through project work

    DEFF Research Database (Denmark)

    Blomhøj, Morten; Kjeldsen, Tinne Hoff

    2006-01-01

    The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...... 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...

  1. Cooking Potatoes: Experimentation and Mathematical Modeling.

    Science.gov (United States)

    Chen, Xiao Dong

    2002-01-01

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

  2. Mathematical Modeling of Chemical Stoichiometry

    Science.gov (United States)

    Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

    2007-01-01

    In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

  3. Mathematical modeling in biomedical imaging

    CERN Document Server

    2009-01-01

    This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.

  4. Mathematical Modeling of Chemical Stoichiometry

    Science.gov (United States)

    Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

    2007-01-01

    In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

  5. 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…

  6. Thermal-hydraulic modeling of reactivity accidents in MTR reactors

    Directory of Open Access Journals (Sweden)

    Khater Hany

    2006-01-01

    Full Text Available This paper describes the development of a dynamic model for the thermal-hydraulic analysis of MTR research reactors during a reactivity insertion accident. The model is formulated for coupling reactor kinetics with feedback reactivity and reactor core thermal-hydraulics. To represent the reactor core, two types of channels are considered, average and hot channels. The developed computer program is compiled and executed on a personal computer, using the FORTRAN language. The model is validated by safety-related benchmark calculations for MTR-TYPE reactors of IAEA 10 MW generic reactor for both slow and fast reactivity insertion transients. A good agreement is shown between the present model and the benchmark calculations. Then, the model is used for simulating the uncontrolled withdrawal of a control rod of an ETRR-2 reactor in transient with over power scram trip. The model results for ETRR-2 are analyzed and discussed.

  7. CO2 Absorption in a Lab-Scale Fixed Solid Bed Reactor: Modelling and Experimental Tests

    Directory of Open Access Journals (Sweden)

    Roberto Gabbrielli

    2004-09-01

    Full Text Available The CO2 absorption in a lab-scale fixed solid bed reactor filled with different solid sorbents has been studied under different operative conditions regarding temperature (20-200°C and input gas composition (N2, O2, CO2, H2O at 1bar pressure. The gas leaving the reactor has been analysed to measure the CO2 and O2 concentrations and, consequently, to evaluate the overall CO2 removal efficiency. In order to study the influence of solid sorbent type (i.e. CaO, coal bottom ash, limestone and blast furnace slag and of mass and heat transfer processes on CO2 removal efficiency, a one-dimensional time dependent mathematical model of the reactor, which may be considered a Plug Flow Reactor, has been developed. The quality of the model has been confirmed using the experimental results.

  8. 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...... involved. We argue that progress in students’ conceptual learning needs to be conceptualised separately from that of progress in their modelling competency. Findings are that modelling activities open a window to the students’ images of the mathematical concepts involved; that modelling activities can...... 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....

  9. Mathematical model of cylindrical form tolerance

    Institute of Scientific and Technical Information of China (English)

    蔡敏; 杨将新; 吴昭同

    2004-01-01

    Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.

  10. Mathematical model of cylindrical form tolerance

    Institute of Scientific and Technical Information of China (English)

    蔡敏; 杨将新; 吴昭同

    2004-01-01

    Tolerance is essential for integration of CAD and CAM.Unfortunately,the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression,processing and data transferring with computers.How to interpret its semantics is becoming a focus of relevant studies.This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994,established the mathematical model of form tolerance for cylindrical feature.First,each tolerance in the national standard was established by vector equation.Then on the foundation of tolerance's mathematical definition theory,each tolerance zone's mathematical model was established by inequality based on degrees of feature.At last the variance area of each tolerance zone is derived.This model can interpret the semantics of form tolerance exactly and completely.

  11. Modeling for Anaerobic Fixed-Bed Biofilm Reactors

    Energy Technology Data Exchange (ETDEWEB)

    Liu, B. Y. M.; Pfeffer, J. T.

    1989-06-01

    The specific objectives of this research were: 1. to develop an equilibrium model for chemical aspects of anaerobic reactors; 2. to modify the equilibrium model for non-equilibrium conditions; 3. to incorporate the existing biofilm models into the models above to study the biological and chemical behavior of the fixed-film anaerobic reactors; 4. to experimentally verify the validity of these models; 5. to investigate the biomass-holding ability of difference packing materials for establishing reactor design criteria.

  12. A fast and flexible reactor physics model for simulating neutron spectra and depletion in fast reactors

    Science.gov (United States)

    Recktenwald, Geoff; Deinert, Mark

    2010-03-01

    Determining the time dependent concentration of isotopes within a nuclear reactor core is central to the analysis of nuclear fuel cycles. We present a fast, flexible tool for determining the time dependent neutron spectrum within fast reactors. The code (VBUDS: visualization, burnup, depletion and spectra) uses a two region, multigroup collision probability model to simulate the energy dependent neutron flux and tracks the buildup and burnout of 24 actinides, as well as fission products. While originally developed for LWR simulations, the model is shown to produce fast reactor spectra that show high degree of fidelity to available fast reactor benchmarks.

  13. 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…

  14. 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…

  15. Controllability, Observability, and Stability of Mathematical Models

    OpenAIRE

    Iggidr, Abderrahman

    2004-01-01

    International audience; This article presents an overview of three fundamental concepts in Mathematical System Theory: controllability, stability and observability. These properties play a prominent role in the study of mathematical models and in the understanding of their behavior. They constitute the main research subject in Control Theory. Historically the tools and techniques of Automatic Control have been developed for artificial engineering systems but nowadays they are more and more ap...

  16. On the mathematical modeling of aeolian saltation

    DEFF Research Database (Denmark)

    Jensen, Jens Ledet; Sørensen, Michael

    1983-01-01

    The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...

  17. Modeling and simulation of tube-shell reactor for dimethyl-ether synthesis from coal-based synthesis gas

    Institute of Scientific and Technical Information of China (English)

    CHEN Da-sheng; ZHANG Hai-tao; YING Wei-yong; FANG Ding-ye

    2011-01-01

    Mathematical simulation was performed on tube-shell reactor for dimethyl ether (DME) synthesis from coal-based syngas. The model was established based on kinetics of dimethyl-ether synthesis from syngas over a bifunctional catalyst,which is mixed by methanol synthesis catalyst and dehydration catalyst as 1:1 mass ratio. Methanol synthesis from CO and CO2 and methanol dehydration were selected as three-independent reactions, CO, CO2, and DME as key components to establish the one-dimensional mathematical model of the reactor. The gas concentration and temperature profiles inside the reactor tubes were obtained. The operating conditions affecting DME synthesis were also discussed based on the model. The simulations indicate that higher pressure and lower temperature at the inlet and rich hydrogen in the reactant are favorable in direct DME synthesis in fixed-bed process, and the temperature of boiling water affect the reactor performance seriously.

  18. Monte Carlo modelling of TRIGA research reactor

    Science.gov (United States)

    El Bakkari, B.; Nacir, B.; El Bardouni, T.; El Younoussi, C.; Merroun, O.; Htet, A.; Boulaich, Y.; Zoubair, M.; Boukhal, H.; Chakir, M.

    2010-10-01

    The Moroccan 2 MW TRIGA MARK II research reactor at Centre des Etudes Nucléaires de la Maâmora (CENM) achieved initial criticality on May 2, 2007. The reactor is designed to effectively implement the various fields of basic nuclear research, manpower training, and production of radioisotopes for their use in agriculture, industry, and medicine. This study deals with the neutronic analysis of the 2-MW TRIGA MARK II research reactor at CENM and validation of the results by comparisons with the experimental, operational, and available final safety analysis report (FSAR) values. The study was prepared in collaboration between the Laboratory of Radiation and Nuclear Systems (ERSN-LMR) from Faculty of Sciences of Tetuan (Morocco) and CENM. The 3-D continuous energy Monte Carlo code MCNP (version 5) was used to develop a versatile and accurate full model of the TRIGA core. The model represents in detailed all components of the core with literally no physical approximation. Continuous energy cross-section data from the more recent nuclear data evaluations (ENDF/B-VI.8, ENDF/B-VII.0, JEFF-3.1, and JENDL-3.3) as well as S( α, β) thermal neutron scattering functions distributed with the MCNP code were used. The cross-section libraries were generated by using the NJOY99 system updated to its more recent patch file "up259". The consistency and accuracy of both the Monte Carlo simulation and neutron transport physics were established by benchmarking the TRIGA experiments. Core excess reactivity, total and integral control rods worth as well as power peaking factors were used in the validation process. Results of calculations are analysed and discussed.

  19. 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...

  20. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

    Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

    2010-01-01

    properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......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...... 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...

  1. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

    Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

    2014-01-01

    properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......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...... 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...

  2. 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.

  3. 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...

  4. 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...

  5. Mathematical models and methods for planet Earth

    CERN Document Server

    Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta

    2014-01-01

    In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

  6. Nuclear reactor core modelling in multifunctional simulators

    Energy Technology Data Exchange (ETDEWEB)

    Puska, E.K. [VTT Energy, Nuclear Energy, Espoo (Finland)

    1999-06-01

    The thesis concentrates on the development of nuclear reactor core models for the APROS multifunctional simulation environment and the use of the core models in various kinds of applications. The work was started in 1986 as a part of the development of the entire APROS simulation system. The aim was to create core models that would serve in a reliable manner in an interactive, modular and multifunctional simulator/plant analyser environment. One-dimensional and three-dimensional core neutronics models have been developed. Both models have two energy groups and six delayed neutron groups. The three-dimensional finite difference type core model is able to describe both BWR- and PWR-type cores with quadratic fuel assemblies and VVER-type cores with hexagonal fuel assemblies. The one- and three-dimensional core neutronics models can be connected with the homogeneous, the five-equation or the six-equation thermal hydraulic models of APROS. The key feature of APROS is that the same physical models can be used in various applications. The nuclear reactor core models of APROS have been built in such a manner that the same models can be used in simulator and plant analyser applications, as well as in safety analysis. In the APROS environment the user can select the number of flow channels in the three-dimensional reactor core and either the homogeneous, the five- or the six-equation thermal hydraulic model for these channels. The thermal hydraulic model and the number of flow channels have a decisive effect on the calculation time of the three-dimensional core model and thus, at present, these particular selections make the major difference between a safety analysis core model and a training simulator core model. The emphasis on this thesis is on the three-dimensional core model and its capability to analyse symmetric and asymmetric events in the core. The factors affecting the calculation times of various three-dimensional BWR, PWR and WWER-type APROS core models have been

  7. 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.

  8. Mathematical modeling of complex noise barriers

    Energy Technology Data Exchange (ETDEWEB)

    Hayek, S.I.

    1982-01-01

    Mathematical modeling of the noise reduction efficiency of highway noise barriers depends on the shape and absorptivity of the barrier, the influence of the impedance of the ground under the receiver, the atmospheric conditions as well as traffic details. The mathematical model for a barrier's noise reduction requires the knowledge of point-to-point acoustic diffraction models. In many instances, the shape of the barrier is simple; such as thin wall (edge), sharp wedge, and cylindrically topped berms. However, new designs of more efficient barriers have been investigated recently.

  9. Mathematical Modeling in Continuum Mechanics

    Science.gov (United States)

    Temam, Roger; Miranville, Alain

    2005-06-01

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

  10. Advanced Mathematical Model to Describe the Production of Biodiesel Process

    Directory of Open Access Journals (Sweden)

    Ahmmed S. Ibrehem

    2009-12-01

    Full Text Available Advanced mathematical model was used to capture the batch reactor characteristics of reacting compounds. The model was applied to batch reactor for the production of bio-diesel from palm and kapok oils. Results of the model were compared with experimental data in terms of conversion of transesterification reaction for the production of bio-diesel under unsteady state. A good agreement was obtained between our model predictions and the experimental data. Both experimental and modeling results showed that the conversion of triglycerides to methyl ester was affected by the process conditions. The transesterification process with temperature of about 70 oC, and methanol ratio to the triglyceride of about 5 times its stoichiometry, and the NAOH catalyst of wt 0.4%, appear to be acceptable process conditions for bio diesel process production from palm oil and kapok oil. The model can be applied for endothermic batch process. © 2009 BCREC UNDIP. All rights reserved[Received: 12 August 2009, Revised: 15 October 2009; Accepted: 18 October 2009][How to Cite: A.S. Ibrehem, H. S. Al-Salim. (2009. Advanced Mathematical Model to Describe the Production of Biodiesel Process. Bulletin of Chemical Reaction Engineering and Catalysis, 4(2: 37-42.  doi:10.9767/bcrec.4.2.7109.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.7109.37-42 || or local:  http://ejournal.undip.ac.id/index.php/bcrec/article/view/7109 ] 

  11. About a mathematical model of market

    Science.gov (United States)

    Kulikov, D. A.

    2017-01-01

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

  12. Mathematical human modelling for impact loading

    NARCIS (Netherlands)

    Happee, R.; Hoof, J.F.A.M. van; Lange, R. de

    2001-01-01

    Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models b

  13. Mathematical Modeling of Viral Zoonoses in Wildlife

    OpenAIRE

    2011-01-01

    Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.

  14. Mathematical modelling of magnetically targeted drug delivery

    Energy Technology Data Exchange (ETDEWEB)

    Grief, Andrew D. [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: andrew.grief@nottingham.ac.uk; Richardson, Giles [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: giles.richardson@nottingham.ac.uk

    2005-05-15

    A mathematical model for targeted drug delivery using magnetic particles is developed. This includes a diffusive flux of particles arising from interactions between erythrocytes in the microcirculation. The model is used to track particles in a vessel network. Magnetic field design is discussed and we show that it is impossible to specifically target internal regions using an externally applied field.

  15. Mathematical models of cell self-organization

    Directory of Open Access Journals (Sweden)

    Benoît Perthame

    2011-04-01

    More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions.

  16. Mathematical human modelling for impact loading

    NARCIS (Netherlands)

    Happee, R.; Hoof, J.F.A.M. van; Lange, R. de

    2001-01-01

    Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models

  17. Mathematical human body modelling for impact loading

    NARCIS (Netherlands)

    Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.

    1999-01-01

    Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models

  18. Mathematical model of electrotaxis in osteoblastic cells

    NARCIS (Netherlands)

    Vanegas-Acosta, J.C.; Garzón-Alvarado, D.A.; Zwamborn, A.P.M.

    2012-01-01

    Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF stren

  19. A mathematical model of forgetting and amnesia

    NARCIS (Netherlands)

    Murre, J.M.J.; Chessa, A.G.; Meeter, M.

    2013-01-01

    We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strengt

  20. Building Mathematical Models Of Solid Objects

    Science.gov (United States)

    Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.

    1989-01-01

    Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.

  1. Mathematical human body modelling for impact loading

    NARCIS (Netherlands)

    Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.

    1999-01-01

    Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models b

  2. Model Development and Simulation of Nitrification in SHARON Reactor in Moderate Temperature by Simulink

    Directory of Open Access Journals (Sweden)

    Dr. Adnan Abbas Al-Samawi

    2015-11-01

    Full Text Available In order to reduce the nitrogen compounds in WWTP effluent according to legislations, nitrogen of reject water is removed in separate unit by applying innovative cost effective process named SHARON (Single reactor High activity Ammonium Removal Over Nitrite process which is feasible to apply in moderate weather and more cost effective process due to elimination the heat exchanger required to keep the reject water of high temperature. In addition to the save in oxygen requirement to oxide ammonium by preventing nitrite oxidation and the saving in external COD addition for denitrification. Also, there is no need for large reactor volume because HRT equal to SRT. Significant mathematical model of nitrification process in SHARON reactor was developed based on substances and organisms mass balance as well as organisms kinetics. A relatively favorable consistency was obtained between the experimental and the predicted results of model. A high correlation of (R2=0.946 between model predictions and experimental data sets.

  3. A mathematical model for Neanderthal extinction

    CERN Document Server

    Flores, J C

    1997-01-01

    A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).

  4. 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.

  5. Dynamics of mathematical models in biology bringing mathematics to life

    CERN Document Server

    Zazzu, Valeria; Guarracino, Mario

    2016-01-01

    This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...

  6. 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

  7. 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 ...

  8. The (mathematical modelling process in biosciences

    Directory of Open Access Journals (Sweden)

    Nestor V. Torres

    2015-12-01

    Full Text Available In this communication we introduce a general framework and discussion on the role of models and the modelling process within the scientific activity in the biosciences realm. The objective is sum up the common procedure during the formalization and analysis of a biological problem under the foundations of Systems Biology, which approach 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 the biology. Then, we present the modelization and analysis process 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 presentation the main features and shortcomings of the process are developed together with a set of rules that could help in the modelling endeavour of any biological system. 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 the modelling are currently posing to the current biology.

  9. Mathematical Modelling of Bridges with SAP2000

    OpenAIRE

    Maraž, Miha

    2006-01-01

    The present work describes a relatively new programme module, which is enhanced in the recently released versions of SAP2000 software. The new module, called Bridge Modeler, is intended for simple, parametric mathematical modelling of bridges. The modelling procedure is explained on a test case through the steps of a user-friendly Bridge Wizard. For each step, we described the basic principles and the application possibilities as well as some limitations. We also explained two types of analys...

  10. Mathematical Modeling of Circadian and Homeostatic Interaction

    Science.gov (United States)

    2011-11-16

    Williams and C. Diniz Behn. A Hodgkin- Huxley -type model orexin neuron. SLEEP 32, A25, 2009. 4) C. Diniz Behn, D. Pal, G. Vanini, R. Lydic, G. A. Mashour...Switzerland, September 2009. 11) K. Williams, “A Hodgkin- Huxley -type model orexin neuron”, Associated Professional Sleep Societies Annual Meeting...Seattle, WA, June 2009. 12) K. Williams, “Dynamics in a Hodgkin- Huxley -type model orexin neuron”, Society for Industrial and Applied Mathematics Annual

  11. Mathematical System Theory and System Modeling

    OpenAIRE

    1980-01-01

    Choosing models related effectively to the questions to be addressed is a central issue in the craft of systems analysis. Since the mathematical description the analyst chooses constrains the types of issues he candeal with, it is important for these models to be selected so as to yield limitations that are acceptable in view of the questions the systems analysis seeks to answer. In this paper, the author gives an overview of the central issues affecting the question of model choice. To ...

  12. Modeling of Bubble Column Slurry Reactor for Dimethyl Ether Synthesis from Syngas

    Institute of Scientific and Technical Information of China (English)

    张海涛; 应卫勇; 房鼎业

    2005-01-01

    A mathematical model for a bubble column slurry reactor is presented for dimethyl ether synthesis from syngas. Methanol synthesis from carbon monoxide and carbon dioxide by hydrogenation and the methanol dehydration are considered as independent reactions, in which methanol, dimethyl ether and carbon dioxide are the key components. In this model, the gas phase is considered to be in plug flow and the liquid phase to be in partly back mixing with axial distribution of solid catalyst. The simulation results show that the axial dispersion of solid catalysts, the operational height of the slurry phase in the bubble column slurry reactor, and the reaction results are influenced by the reaction temperature and pressure, which are the basic data for the scale-up of reactor.

  13. Pedagogical Content Knowledge in Mathematical Modelling Instruction

    Science.gov (United States)

    Tan, Liang Soon; Ang, Keng Cheng

    2012-01-01

    This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

  14. Optimization and mathematical modeling in computer architecture

    CERN Document Server

    Sankaralingam, Karu; Nowatzki, Tony

    2013-01-01

    In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

  15. Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas considering catalyst deactivation

    Institute of Scientific and Technical Information of China (English)

    M.Farsi; A.Jahanmiri

    2012-01-01

    In this paper,the effect of water vapor removal on methanol synthesis capacity from syngas in a fixed-bed membrane reactor is studied considering long-term catalyst deactivation.A dynamic heterogeneous one-dimensional mathematical model that is composed of two sides is developed to predict the performance of this configuration.In this configuration,conventional methanol reactor is supported by an aluminasilica composite membrane layer for water vapor removal from reaction zone.To verify the accuracy of the considered model and assumptions,simulation results of the conventional methanol reactor is compared with the industrial plant data under the same process condition.The membrane reactor improves catalyst life time and enhances CO2 conversion to methanol by overcoming the limitation imposed by thermodynamic equilibrium.This configuration has enhanced the methanol production capacity about 4.06% compared with the industrial methanol reactor during the production time.

  16. Modeling life the mathematics of biological systems

    CERN Document Server

    Garfinkel, Alan; Guo, Yina

    2017-01-01

    From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...

  17. Mathematical modeling of the flash converting process

    Energy Technology Data Exchange (ETDEWEB)

    Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)

    1996-12-31

    An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

  18. An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

    Science.gov (United States)

    Bukova-Guzel, Esra

    2011-01-01

    This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

  19. Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling

    Science.gov (United States)

    Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan

    2012-01-01

    The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…

  20. Advanced Small Modular Reactor Economics Model Development

    Energy Technology Data Exchange (ETDEWEB)

    Harrison, Thomas J [ORNL

    2014-10-01

    The US Department of Energy Office of Nuclear Energy’s Advanced Small Modular Reactor (SMR) research and development activities focus on four key areas: Developing assessment methods for evaluating advanced SMR technologies and characteristics; and Developing and testing of materials, fuels and fabrication techniques; and Resolving key regulatory issues identified by US Nuclear Regulatory Commission and industry; and Developing advanced instrumentation and controls and human-machine interfaces. This report focuses on development of assessment methods to evaluate advanced SMR technologies and characteristics. Specifically, this report describes the expansion and application of the economic modeling effort at Oak Ridge National Laboratory. Analysis of the current modeling methods shows that one of the primary concerns for the modeling effort is the handling of uncertainty in cost estimates. Monte Carlo–based methods are commonly used to handle uncertainty, especially when implemented by a stand-alone script within a program such as Python or MATLAB. However, a script-based model requires each potential user to have access to a compiler and an executable capable of handling the script. Making the model accessible to multiple independent analysts is best accomplished by implementing the model in a common computing tool such as Microsoft Excel. Excel is readily available and accessible to most system analysts, but it is not designed for straightforward implementation of a Monte Carlo–based method. Using a Monte Carlo algorithm requires in-spreadsheet scripting and statistical analyses or the use of add-ons such as Crystal Ball. An alternative method uses propagation of error calculations in the existing Excel-based system to estimate system cost uncertainty. This method has the advantage of using Microsoft Excel as is, but it requires the use of simplifying assumptions. These assumptions do not necessarily bring into question the analytical results. In fact, the

  1. 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.

  2. Mathematical modeling models, analysis and applications

    CERN Document Server

    Banerjee, Sandip

    2014-01-01

    ""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298

  3. Hydrodynamical modelling of upflow anaerobic sludge blanket reactors; Modelagem hidrodinamica de reatores anaerobios de escoamento ascendente e manta de lodo (UASB)

    Energy Technology Data Exchange (ETDEWEB)

    Hanisch, Werner Siegfried

    1995-12-31

    The increasing need to treat wastewater consuming a minimum amount of energy is a clear indication of the appropriateness of anaerobic processes. One of them, the upflow anaerobic sludge blanket reactor (UASB), has shown to be a feasible option to treat industrial wastewater and domestic sewage. To improve this treatment system the knowledge if of its hydrodynamic behaviour is fundamental. In this work a mathematical model is proposed to describe physical simulations that were performed in bench scale UASB reactors. The results allow to conclude that the proposed mathematical model is adequate to describe the hydrodynamical behaviour of the above mentioned reactors 27 refs., 78 figs., 12 tabs.

  4. 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.

  5. Constraint theory multidimensional mathematical model management

    CERN Document Server

    Friedman, George J

    2017-01-01

    Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...

  6. Modeling and Design Optimization of Multifunctional Membrane Reactors for Direct Methane Aromatization.

    Science.gov (United States)

    Fouty, Nicholas J; Carrasco, Juan C; Lima, Fernando V

    2017-08-29

    Due to the recent increase of natural gas production in the U.S., utilizing natural gas for higher-value chemicals has become imperative. Direct methane aromatization (DMA) is a promising process used to convert methane to benzene, but it is limited by low conversion of methane and rapid catalyst deactivation by coking. Past work has shown that membrane separation of the hydrogen produced in the DMA reactions can dramatically increase the methane conversion by shifting the equilibrium toward the products, but it also increases coke production. Oxygen introduction into the system has been shown to inhibit this coke production while not inhibiting the benzene production. This paper introduces a novel mathematical model and design to employ both methods in a multifunctional membrane reactor to push the DMA process into further viability. Multifunctional membrane reactors, in this case, are reactors where two different separations occur using two differently selective membranes, on which no systems studies have been found. The proposed multifunctional membrane design incorporates a hydrogen-selective membrane on the outer wall of the reaction zone, and an inner tube filled with airflow surrounded by an oxygen-selective membrane in the middle of the reactor. The design is shown to increase conversion via hydrogen removal by around 100%, and decrease coke production via oxygen addition by 10% when compared to a tubular reactor without any membranes. Optimization studies are performed to determine the best reactor design based on methane conversion, along with coke and benzene production. The obtained optimal design considers a small reactor (length = 25 cm, diameter of reaction tube = 0.7 cm) to subvert coke production and consumption of the product benzene as well as a high permeance (0.01 mol/s·m²·atm(1/4)) through the hydrogen-permeable membrane. This modeling and design approach sets the stage for guiding further development of multifunctional membrane reactor

  7. Reactor models for a series of continuous stirred tank reactors with a gas-liquid-solid leaching system: Part III. Model application

    Science.gov (United States)

    Papangelakis, V. G.; Demopoulos, G. P.

    1992-12-01

    A mathematical model developed to describe the steady-state performance of a three-phase leaching reactor is applied to the analysis and simulation of an industrial process: the high-temperature (180 °C to 200 °C) aqueous pressure oxidation (O2-H2SO4) of refractory pyrite-arsenopyrite (FeS2-FeAsS) gold concentrates. The simulation work reported here centers on the analysis of the autothermal operation of a continuous multistage horizontal autoclave. The focus is on the performance of the first autoclave compartment, since its autothermal “initialization” determines the rate of the whole process. The analysis of the whole autoclave is subsequently done on a stage-by-stage basis. The model considers both possible reaction control regimes, that is, reactor operation limited by the rate of the particle dissolution reaction (surface reaction control) or limited by the rate of O2 transfer at the g-1 interface (gas-transfer control). The decision whether the reactor operates under surface reaction control or gas transfer control is based on whether the gas-transfer capacity of the reactor can or cannot satisfy the oxygen demands of the leaching reactions. With the aid of the model, the effects of feed rate, feed preheating, cooling with water injection, slurry recycling, and autoclave configuration are critically evaluated from the standpoint of optimum autoclave performance.

  8. Mathematical models for Isoptera (Insecta mound growth

    Directory of Open Access Journals (Sweden)

    MLT. Buschini

    Full Text Available In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

  9. Structured Mathematical Modeling of Industrial Boiler

    OpenAIRE

    Abdullah Nur Aziz; Yul Yunazwin Nazaruddin; Parsaulian Siregar; Yazid Bindar

    2014-01-01

    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. T...

  10. Mathematical modeling of rewarming after cold therapy.

    Science.gov (United States)

    Avet, L M

    1978-07-01

    Statistical methods are presented for fitting mathematical models to skin temperature data. Three types of regression curves, namely, linear regression (Y = A + BX), second-degree regression (Y = A + BX + CX2), and asymptotic regression (Y = alpha + betapx), are discussed as possible models for the rewarming process following cold therapy. The data for fitting the curves consists of back surface temperature (degrees C) corresponding to various times after cold pack treatment (19 degrees C, administered for 20 minutes) was terminated.

  11. Modeling of a Reverse Flow Reactor for Methanol Synthesis

    Institute of Scientific and Technical Information of China (English)

    陈晓春; P.L.Silveston; 等

    2003-01-01

    An accurate one-dimensional,heterogeneous model taking account of axial dispersion and heat transfer to the reactor wall,and heat conduction through the reactor wall for methanol synthesis in a bench scale reactor under periodic reversal of flow direction is presented.Adjustable parameters in this model are the effectiveness factors for each of the three reactions occurring in the synthesis and a factor for the bed to wall heat transfer coefficient correlation.Experimental data were used to evaluate these parameters and reasonable values of these parameters were obtained.The model was found to closely predict the reactor performance under a wide range of parameters were obtained.The model was found to closely predict the reactor preformance under a wide range of operating conditions,such as carbon oxide concentrations,volumetric flow rate,and cyclic period.

  12. Optimization of mathematical models for thematic maps

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The thematic map is a major class of maps designed to demonstrate particular features or concepts,functioning as an indispensable tool in geographical research.The process of thematic mapping is one into which geographical research goes deeply and broadly.The key activity and course of thematic map production is the use of mathematical models to create thematic data layers.Therefore,the selection and optimization of mathematical models is in the forefront of thematic map research.The theoretical foundations,mechanisms and methods of mathematical model optimization are expounded in this paper,including two approaches,the phase by phase mode and the multi-aim scheme balance mode.Case studies in eco-environment mapping and emergency mapping are described and analyzed,with a hierarchical analysis method being used in the model optimization for eco-environment fragility and sensitivity assessment mapping in Beibuwan (Guangxi) District,the dynamic system (DS) method being used in the model optimization for ecological security adjustment mapping in Xishuang Banna,Yunnan province,and the multi-phase mode being used in the models for forest fire and infectious diseases mapping.

  13. Formation, characterization and mathematical modeling of the aerobic granular sludge

    Energy Technology Data Exchange (ETDEWEB)

    Ni, Bing-Jie [Queensland Univ., Brisbane, QLD (Australia). Advanced Water Management Centre

    2013-07-01

    Reports on successful aerobic granulation of sludge in pilot-scale reactor for treatment of low-strength municipal wastewater and identifies the key factors responsible for this process. Develops comprehensive models for sludge granulation, microbial interactions and microbial products formation to provide insights into the dynamics of all the soluble and solid components in aerobic granular sludge system. Demonstrates accelerated start-up and optimization of the anaerobic ammonia oxidation process by seeding the reactor with aerobic granules. Aerobic granular sludge technology will play an important role as an innovative technology alternative to the present activated sludge process in industrial and municipal wastewater treatment in the near future. Intended to fill the gaps in the studies of aerobic granular sludge, this thesis comprehensively investigates the formation, characterization and mathematical modeling of aerobic granular sludge, through integrating the process engineering tools and advanced molecular microbiology. The research results of this thesis contributed significantly to the advance of understanding and optimization of the bacterial granulation processes, the next generation of technology for cost-effective biological wastewater treatment.

  14. A reference worldwide model for antineutrinos from reactors

    CERN Document Server

    Baldoncini, Marica; Fiorentini, Giovanni; Mantovani, Fabio; Ricci, Barbara; Strati, Virginia; Xhixha, Gerti

    2014-01-01

    Antineutrinos produced at nuclear reactors constitute a severe source of background for the detection of geoneutrinos, which bring to the Earth's surface information about natural radioactivity in the whole planet. In this framework we provide a reference worldwide model for antineutrinos from reactors, in view of reactors operational records yearly published by the International Atomic Energy Agency (IAEA). We evaluate the expected signal from commercial reactors for ongoing (KamLAND and Borexino), planned (SNO+) and proposed (Juno, RENO-50, LENA and Hanohano) experimental sites. Uncertainties related to reactor antineutrino production, propagation and detection processes are estimated using a Monte Carlo based approach, which provides an overall site dependent uncertainty on the signal in the geoneutrino energy window on the order of 3%. We also implement the off-equilibrium correction to the reference reactor spectra associated with the long-lived isotopes and we estimate a 2.4% increase of the unoscillate...

  15. Analytical model of plasma-chemical etching in planar reactor

    Science.gov (United States)

    Veselov, D. S.; Bakun, A. D.; Voronov, Yu A.; Kireev, V. Yu; Vasileva, O. V.

    2016-09-01

    The paper discusses an analytical model of plasma-chemical etching in planar diode- type reactor. Analytical expressions of etch rate and etch anisotropy were obtained. It is shown that etch anisotropy increases with increasing the ion current and ion energy. At the same time, etch selectivity of processed material decreases as compared with the mask. Etch rate decreases with the distance from the centre axis of the reactor. To decrease the loading effect, it is necessary to reduce the wafer temperature and pressure in the reactor, as well as increase the gas flow rate through the reactor.

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

    Science.gov (United States)

    Lingefjard, Thomas

    2002-01-01

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

  17. Models and structures: mathematical physics

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2003-07-01

    This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems.

  18. THE USE OF SIMULINK BLOCK DIAGRAM TO SOLVE MATHEMATICAL MODELS AND CONTROL EQUATIONS

    OpenAIRE

    Ghasem, N. M.; Departamento de Biología Facultad de Ciencias Pontificia Universidad Javeriana; Hussain, M. A.; Department of Chemical Engineering University of Malaya, 50603 Kuala Lumpur, Malaysia, School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK; Mujtaba, I. M.; Department of Chemical Engineering University of Malaya, 50603 Kuala Lumpur, Malaysia, School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK

    2003-01-01

    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 alsoallows 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 ...

  19. Electrorheological fluids modeling and mathematical theory

    CERN Document Server

    Růžička, Michael

    2000-01-01

    This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

  20. Models of Non-Life Insurance Mathematics

    Directory of Open Access Journals (Sweden)

    Constanta Nicoleta BODEA

    2008-01-01

    Full Text Available In this communication we will discuss two regression credibility models from Non – Life Insurance Mathematics that can be solved by means of matrix theory. In the first regression credibility model, starting from a well-known representation formula of the inverse for a special class of matrices a risk premium will be calculated for a contract with risk parameter q. In the next regression credibility model, we will obtain a credibility solution in the form of a linear combination of the individual estimate (based on the data of a particular state and the collective estimate (based on aggregate USA data. Mathematics Subject Classification: 62P05.

  1. 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)

  2. Mathematical modeling of microbial growth in milk

    Directory of Open Access Journals (Sweden)

    Jhony Tiago Teleken

    2011-12-01

    Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

  3. Analysis of transients in advanced heavy water reactor using lumped parameter models

    Energy Technology Data Exchange (ETDEWEB)

    Manmohan Pandey; Venkata Ramana Eaga; Sankar Sastry, P. [Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati (India); Gupta, S.K.; Lele, H.G.; Chatterjee, B. [Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai (India)

    2005-07-01

    Full text of publication follows: Analysis of transients occurring in nuclear power plants, arising from the complex interplay between core neutronics and thermal-hydraulics, is important for their operation and safety. Numerical simulations of such transients can be carried out extensively at very low computational cost by using lumped parameter mathematical models. The Advanced Heavy Water Reactor (AHWR), being developed in India, is a vertical pressure tube type reactor cooled by boiling light water under natural circulation, using thorium as fuel and heavy water as moderator. In the present work, nonlinear and linear lumped parameter dynamic models for AHWR have been developed and validated with a distributed parameter model. The nonlinear lumped model is based on point reactor kinetics equations and one-dimensional homogeneous equilibrium model of two-phase flow. The distributed model is built with RELAP5/MOD3.2 code. Various types of transients have been simulated numerically, using the lumped model as well as RELAP5. The results have been compared and parameters tuned to make the lumped model match the distributed model (RELAP5) in terms of steady state as well as dynamic behaviour. The linear model has been derived by linearizing the nonlinear model for small perturbations about the steady state. Numerical simulations of transients using the linear model have been compared with results obtained from the nonlinear model. Thus, the range of validity of the linear model has been determined. Stability characteristics of AHWR have been investigated using the lumped parameter models. (authors)

  4. Mathematical Modeling of an Automobile Damper

    Directory of Open Access Journals (Sweden)

    N. B. Kate, T. A. Jadhav

    2013-10-01

    Full Text Available - In an automotive industry, to reduce product development time and increase quality of product, it is essential to reduce the number of physical prototypes and rely more on precise & reliable design for the final design of vehicles. This paper presents a mathematical model for the damping force of the hydraulic shock absorber which is implemented to analyse the shock absorbers mounting brackets attached to the vehicle structure. Physical testing results indicate that the considered shock absorber’s mathematical model is reliable and can be used to calculate the durability target life of mounting brackets. Thus this presented methodology can be utilized as an effective way to reduce time and cost in design and development of automotive components.

  5. Mathematical modelling of the lower urinary tract.

    Science.gov (United States)

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

    2013-03-01

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

  6. Learning to teach mathematical modelling in secondary and tertiary education

    Science.gov (United States)

    Ferri, Rita Borromeo

    2017-07-01

    Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

  7. Mathematical modelling of leprosy and its control.

    Science.gov (United States)

    Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik

    2015-03-01

    Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.

  8. A Mathematical Model for Suppression Subtractive Hybridization

    OpenAIRE

    2002-01-01

    Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assess...

  9. Mathematical modelling of wood and briquettes torrefaction

    Energy Technology Data Exchange (ETDEWEB)

    Felfli, Felix Fonseca; Luengo, Carlos Alberto [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Fisica Gleb Wataghin. Grupo Combustiveis Alternativos; Soler, Pedro Beaton [Universidad de Oriente, Santiago de Cuba (Cuba). Fac. de Ingenieria Mecanica. Centro de Estudios de Eficiencia Energetica; Rocha, Jose Dilcio [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Nucleo Interdisciplinar de Planejamento Energetico (NIPE)

    2004-07-01

    A mathematical model valid for the torrefaction of wood logs and biomass briquettes is presented. The model described both chemical and physical processes, which take place in a moist piece of wood heated at temperatures between 503 and 573 K. Calibration measurements of the temperature profile and mass loss, were performed on dry cylinders of wood samples during torrefaction in an inert atmosphere at 503, 533, and 553 K. The calculated data shows a good agreement with experiments. The model can be a useful tool to estimate projecting and operating parameters for torrefaction furnaces such as minimum time of torrefaction, energy consumption and the mass yield. (author)

  10. INTERVAL OBSERVER FOR A BIOLOGICAL REACTOR MODEL

    Directory of Open Access Journals (Sweden)

    T. A. Kharkovskaia

    2014-05-01

    Full Text Available The method of an interval observer design for nonlinear systems with parametric uncertainties is considered. The interval observer synthesis problem for systems with varying parameters consists in the following. If there is the uncertainty restraint for the state values of the system, limiting the initial conditions of the system and the set of admissible values for the vector of unknown parameters and inputs, the interval existence condition for the estimations of the system state variables, containing the actual state at a given time, needs to be held valid over the whole considered time segment as well. Conditions of the interval observers design for the considered class of systems are shown. They are: limitation of the input and state, the existence of a majorizing function defining the uncertainty vector for the system, Lipschitz continuity or finiteness of this function, the existence of an observer gain with the suitable Lyapunov matrix. The main condition for design of such a device is cooperativity of the interval estimation error dynamics. An individual observer gain matrix selection problem is considered. In order to ensure the property of cooperativity for interval estimation error dynamics, a static transformation of coordinates is proposed. The proposed algorithm is demonstrated by computer modeling of the biological reactor. Possible applications of these interval estimation systems are the spheres of robust control, where the presence of various types of uncertainties in the system dynamics is assumed, biotechnology and environmental systems and processes, mechatronics and robotics, etc.

  11. Study on mathematical model of steam coal blending

    Institute of Scientific and Technical Information of China (English)

    高洪阁; 李白英; 刘泽常; 尹增德

    2002-01-01

    It is necessary to set up a new mathematical model of steam coal blending instead of the old model. Indexes such as moisture content, ash content, volatile matter, sulfur content and heating value in the new mathematical model have linear relation. The new mathematical model can also predict ash-fusion temperature precisely by considering coal ash ratio in steam coal blending, therefore it is possible to obtain linear relation of ash-fusion temperature between single coal and steam coal blending. The new mathematical model can improve precision of steam coal blending and perfect the old mathematical model of steam coal blending.

  12. Mathematical modeling and visualization of functional neuroimages

    DEFF Research Database (Denmark)

    Rasmussen, Peter Mondrup

    This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical...... influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...

  13. Mathematical modeling and visualization of functional neuroimages

    DEFF Research Database (Denmark)

    Rasmussen, Peter Mondrup

    This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...

  14. Mathematical analysis of a muscle architecture model.

    Science.gov (United States)

    Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio

    2009-01-01

    Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.

  15. Laser filamentation mathematical methods and models

    CERN Document Server

    Lorin, Emmanuel; Moloney, Jerome

    2016-01-01

    This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...

  16. Using thermal balance model to determine optimal reactor volume and insulation material needed in a laboratory-scale composting reactor.

    Science.gov (United States)

    Wang, Yongjiang; Pang, Li; Liu, Xinyu; Wang, Yuansheng; Zhou, Kexun; Luo, Fei

    2016-04-01

    A comprehensive model of thermal balance and degradation kinetics was developed to determine the optimal reactor volume and insulation material. Biological heat production and five channels of heat loss were considered in the thermal balance model for a representative reactor. Degradation kinetics was developed to make the model applicable to different types of substrates. Simulation of the model showed that the internal energy accumulation of compost was the significant heat loss channel, following by heat loss through reactor wall, and latent heat of water evaporation. Lower proportion of heat loss occurred through the reactor wall when the reactor volume was larger. Insulating materials with low densities and low conductive coefficients were more desirable for building small reactor systems. Model developed could be used to determine the optimal reactor volume and insulation material needed before the fabrication of a lab-scale composting system.

  17. Thermoregulation in premature infants: A mathematical model.

    Science.gov (United States)

    Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen

    2016-12-01

    In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

  18. The mathematical modeling revolution in extractive metallurgy

    Science.gov (United States)

    Szekely, Julian

    1988-08-01

    A brief review is presented of the current state of extractive metallurgy, and it is shown that it is still a significant part of the national economy. Then a definition is given of mathematical models, and the general philosophy of modeling is discussed, together with the cost of models, hardware, and software options. Several illustrative examples are given, drawn from aluminum electrolysis, flash smelting, tundish operations, and plasma systems. The paper is concluded with the future modeling tasks facing us; these include the more widespread applications of models to represent both existing and new processing operations. It is stressed that models can play a major role in developing a holistic approach to metals and materials processing, where the primary extraction and refining operations are combined with the final processing steps.

  19. Mathematical models of human african trypanosomiasis epidemiology.

    Science.gov (United States)

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

    2015-03-01

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

  20. Mathematical Modelling of Immune Response in Tissues

    Directory of Open Access Journals (Sweden)

    B. Su

    2009-01-01

    Full Text Available We have developed a spatial–temporal mathematical model (PDE to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition. The PDE model is robust to variation in antigen load and it can account for (1 antigen recognition, (2 an innate immune response, (3 an adaptive immune response, (4 the elimination of antigen and subsequent resolution of the immune response or (5 equilibrium of the immune response to the presence of persistent antigen (chronic infection and the formation of a granuloma.

  1. Mathematical methods and models in composites

    CERN Document Server

    Mantic, Vladislav

    2014-01-01

    This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover

  2. MATHEMATICAL MODEL OF THE MICROBIAL FLOODING

    Institute of Scientific and Technical Information of China (English)

    Lei Guang-lun; Zhang Zhong-zhi; Chen Yue-ming

    2003-01-01

    On the basis of growth kinetics of microorganism and the principle of material balance, equations were derived to describe microbial growth, nutrient consumption, metabolites production and their transport in formation. The changes in porosity, permeability, oil viscosity and capillary force were also described as the main facturs of microbial flooding. For reservoirs with black oil properties, three-dimensional three-phase mathematical models with the cosidaration of multi-microbial components were established to depict microbial flooding oil. With this model, calculated results are in good agreement with experimental data.

  3. Mathematical Model of the Processoof Pearlite Austenitization

    Directory of Open Access Journals (Sweden)

    Olejarczyk-Wożeńska I.

    2014-10-01

    Full Text Available The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.

  4. A mathematical model of 'Pride and Prejudice'.

    Science.gov (United States)

    Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro

    2014-04-01

    A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.

  5. Mathematical Modelling of Tyndall Star Initiation

    CERN Document Server

    Harvey, Peter; Katz, Richard F; Lacey, Andrew A

    2015-01-01

    The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid/liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface, and it leads to an interesting class of codimension-2 free boundary problems.

  6. APPLICATION OF MODEL PREDICTIVE CONTROL TO BATCH POLYMERIZATION REACTOR

    Directory of Open Access Journals (Sweden)

    N.M. Ghasem

    2006-06-01

    Full Text Available The absence of a stable operational state in polymerization reactors that operates in batches is factor that determine the need of a special control system. In this study, advanced control methodology is implemented for controlling the operation of a batch polymerization reactor for polystyrene production utilizingmodel predictive control. By utilizing a model of the polymerization process, the necessary operational conditions were determined for producing the polymer within the desired characteristics. The maincontrol objective is to bring the reactor temperature to its target temperature as rapidly as possible with minimal temperature overshoot. Control performance for the proposed method is encouraging. It has been observed that temperature overshoot can be minimized by the proposed method with the use of both reactor and jacket energy balance for reactor temperature control.

  7. 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.

  8. 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…

  9. Calcium phosphate precipitation modeling in a pellet reactor

    OpenAIRE

    Montastruc, Ludovic; Azzaro-Pantel, Catherine; Cabassud, Michel; Biscans, Béatrice

    2002-01-01

    The calcium phosphate precipitation in a pellet reactor can be evaluated by two main parameters: the phosphate conversion ratio and the phosphate removal efficiency. The conversion ratio depends mainly on the pH. The pellet reactor efficiency depends not only on pH but also on the hydrodynamical conditions. An efficiency model based on a thermochemical precipitation approach and an orthokinetic aggregation model is presented. In this paper, the results show that optimal conditions for pellet ...

  10. A mathematical model on Acquired Immunodeficiency Syndrome

    Directory of Open Access Journals (Sweden)

    Buddhadeo Mahato

    2014-10-01

    Full Text Available A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART, many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results.

  11. 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.

  12. A dynamic model of a passively cooled small modular reactor for controller design purposes

    Energy Technology Data Exchange (ETDEWEB)

    Arda, Samet E., E-mail: s.e.arda@asu.edu; Holbert, Keith E., E-mail: holbert@asu.edu

    2015-08-15

    Highlights: • A mathematical dynamic model is developed for a passively cooled small modular reactor. • Reactor response associated single-phase natural circulation is analyzed. • A moving boundary model for a helical-coil steam generator is analyzed. • Dynamic responses of the overall model to representative perturbations are evaluated. • This compact model can be utilized for control system design. - Abstract: An analytical dynamic model for a passively cooled small modular reactor (SMR) is developed using a state-variable lumped parameter approach. Reactor power is represented by the generation time formulation of the point kinetics equations with a single combined neutron precursor group. The heat transfer process in the core is described via an overall heat transfer coefficient by defining two coolant lumps paired to a single fuel lump. In addition, a thermal–hydraulics model for single-phase natural circulation is incorporated. For the helical-coil steam generator, a moving-boundary model including subcooled, two-phase, and superheated regions is utilized. Finally, the hot leg riser and downcomer regions are expressed by first-order lags. The performance of the overall system described by ordinary differential equations (ODEs) is evaluated by the Simulink dynamic environment and directly using a MATLAB ODE solver recommended for stiff systems. Simulation results based on NuScale SMR design data show that the initial steady-state values for 100% power are within range of the design data and the model can predict the system dynamics due to typical perturbations, e.g., control rod movement and change in feedwater mass flow rate and temperature. The model developed in this work can be utilized as a foundation for designing and testing a suitable control algorithm for reactor thermal power.

  13. Waste tyre pyrolysis: modelling of a moving bed reactor.

    Science.gov (United States)

    Aylón, E; Fernández-Colino, A; Murillo, R; Grasa, G; Navarro, M V; García, T; Mastral, A M

    2010-12-01

    This paper describes the development of a new model for waste tyre pyrolysis in a moving bed reactor. This model comprises three different sub-models: a kinetic sub-model that predicts solid conversion in terms of reaction time and temperature, a heat transfer sub-model that calculates the temperature profile inside the particle and the energy flux from the surroundings to the tyre particles and, finally, a hydrodynamic model that predicts the solid flow pattern inside the reactor. These three sub-models have been integrated in order to develop a comprehensive reactor model. Experimental results were obtained in a continuous moving bed reactor and used to validate model predictions, with good approximation achieved between the experimental and simulated results. In addition, a parametric study of the model was carried out, which showed that tyre particle heating is clearly faster than average particle residence time inside the reactor. Therefore, this fast particle heating together with fast reaction kinetics enables total solid conversion to be achieved in this system in accordance with the predictive model.

  14. Incorporating neurophysiological concepts in mathematical thermoregulation models

    Science.gov (United States)

    Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.

    2014-01-01

    Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.

  15. Mathematical model of the Amazon Stirling engine

    Energy Technology Data Exchange (ETDEWEB)

    Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br

    2010-07-01

    The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)

  16. Solar Panel Mathematical Modeling Using Simulink

    Directory of Open Access Journals (Sweden)

    Chandani Sharma

    2014-05-01

    Full Text Available For decades, electricity is a key driver of socio-economy development. Nowadays, in the context of competition there is a direct relationship between electricity generation and sustainable development of the country. This paper presents distinct use of a Photovoltaic array offering great potential as source of electricity. The simulation uses One-diode equivalent circuit in order to investigate I-V and P-V characteristics. The GUI model is designed with Simulink block libraries. The goals of proposed model are to perform a systematic analysis, modeling and evaluation of the key subsystems for obtaining Maximum Power Point of a solar cell. Effect of increasing number of cells is described at Standard Test Conditions by mathematical modeling of equations. It is desirable to achieve maximum power output at a minimum cost under various operating conditions. Index Terms—

  17. Mathematical modelling of risk reduction in reinsurance

    Science.gov (United States)

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

    2017-01-01

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

  18. Mathematical modeling of diesel fuel hydrotreating

    Science.gov (United States)

    Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.

    2015-11-01

    Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.

  19. Mathematical Modeling of Diaphragm Pneumatic Motors

    Directory of Open Access Journals (Sweden)

    Fojtášek Kamil

    2014-03-01

    Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.

  20. Modelling and control design for SHARON/Anammox reactor sequence

    DEFF Research Database (Denmark)

    Valverde Perez, Borja; Mauricio Iglesias, Miguel; Sin, Gürkan

    2012-01-01

    With the perspective of investigating a suitable control design for autotrophic nitrogen removal, this work presents a complete model of the SHARON/Anammox reactor sequence. The dynamics of the reactor were explored pointing out the different scales of the rates in the system: slow microbial...... metabolism against fast chemical reaction and mass transfer. Likewise, the analysis of the dynamics contributed to establish qualitatively the requirements for control of the reactors, both for regulation and for optimal operation. Work in progress on quantitatively analysing different control structure...

  1. A mathematical model of aortic aneurysm formation

    Science.gov (United States)

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

    2017-01-01

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

  2. Mathematical modeling of tornadoes and squall storms

    Directory of Open Access Journals (Sweden)

    Sergey A. Arsen’yev

    2011-04-01

    Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.

  3. Mathematical Simulating Model of Phased-Array Antenna in Multifunction Array Radar

    Institute of Scientific and Technical Information of China (English)

    1999-01-01

    A mathematical simulating model of phased-array antenna in multifunction array radar has been approached in this paper, including the mathematical simulating model of plane phased-array pattern, the mathematical simulating model of directionality factor, the mathematical simulating model of array factor, the mathematical simulating model of array element factor and the mathematical simulating model of beam steering.

  4. 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…

  5. Comparison of Different Mathematical Models of Cavitation

    Directory of Open Access Journals (Sweden)

    Dorota HOMA

    2014-12-01

    Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.

  6. A MATHEMATICAL MODEL OF RESERVOIR SEDIMENTATION

    Institute of Scientific and Technical Information of China (English)

    HUANG Jinchi

    2001-01-01

    Reliable quantitative estimation of bed aggradation or degradation is important for river-training and water management projects. With the development of water resources, sediment problems associated with a dam are becoming more severe. This paper describes some special problems in mathematical model for calculation of degradation and aggradation in a reservoir. The main efforts of this study are on the treatment of some physical processes of fine sediment transport (<0.05 mm). Problems in a reservoir are obviously different from a natural stream, such as the turbid current flow, orifice sediment flushing;and the initiation and consolidation of cohesive sediment deposition. The case of Liujiaxia Reservoir,which is located in the upper reaches of the Yellow River, is employed to verify the model. The results show that the model is applicable in the evaluation of an engineering planing with plenty of fine sediment movement.

  7. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    Science.gov (United States)

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  8. Building Mathematics Achievement Models in Four Countries Using TIMSS 2003

    Science.gov (United States)

    Wang, Ze; Osterlind, Steven J.; Bergin, David A.

    2012-01-01

    Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…

  9. Mathematical modeling of the Phoenix Rising pathway.

    Directory of Open Access Journals (Sweden)

    Chad Liu

    2014-02-01

    Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.

  10. Building a Two Axes Process Model of Understanding Mathematics

    OpenAIRE

    Koyama, Masataka

    1993-01-01

    The purpose of this study is to make clear what kind of characteristics a model of understanding mathematics should have so as to be useful and effective in mathematics education. The models of understanding presented in preceding papers are classified into two large categories, i. e. "aspect model" and "process model". Focusing on the process of understanding mathematics, reflective thinking plays an important role to develop children's understanding, or to progress children's thinking from ...

  11. Mathematical Modeling of Hybrid Electrical Engineering Systems

    Directory of Open Access Journals (Sweden)

    A. A. Lobaty

    2016-01-01

    Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the

  12. 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...

  13. 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

  14. System Thermal Model for the S-Prime Thermionic Reactor

    Science.gov (United States)

    Arx, Alan V. Von

    1994-07-01

    A model has been developed which numerically simulates heat transfer and flow characteristics of the thermal-hydraulic loop of the S-PRIME thermionic reactor. The components for which detailed models have been included are: the thermionic fuel elements (TFEs), heat pipe panels, flow loop and pumps. The reactor start-up operation was then modeled from zero to full power. It includes modelling of the melting of the heat pipe working fluid as well as correlations for the performance of the thermionic cells. The results show that there is stable operation during this period.

  15. Basic Model of a Control Assembly Drop in Nuclear Reactors

    Directory of Open Access Journals (Sweden)

    Radek BULÍN

    2013-06-01

    Full Text Available This paper is focused on the modelling and dynamic analysis of a nonlinear system representing a control assembly of the VVER 440/V213 nuclear reactor. A simple rigid body model intended for basic dynamic analyses is introduced. It contains the influences of the pressurized water and mainly the eects of possible control assembly contacts with guiding tubes inside the reactor. Another approach based on a complex multibody model is further described and the suitability of both modelling approaches is discussed.

  16. 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).

  17. Modelling of Mass Transfer Phenomena in Chemical and Biochemical Reactor Systems using Computational Fluid Dynamics

    DEFF Research Database (Denmark)

    Larsson, Hilde Kristina

    are subsequently evaluated based on their applicability in the four case studies. The evaluations especially focus on the impact of the choice of turbulence model and other modelling decisions made by the user. The conclusion is that CFD is a highly valuable tool for modelling several important parameters...... are presented as well as the theory behind the SST and the k-ε turbulence models. Modelling of additional variables, porous materials and twophase flows are also introduced. The two-phase flows are modelled using the Euler-Euler method, and both dispersed and free-surface flows are simulated. The importance...... of mass transfer with a focus on mixing, gas-liquid transfer of oxygen, and heterogeneous reactor systems is reviewed and mathematical models for these applications are presented. A review of how these mass transfer phenomena have been modelled in the scientific literature is also included. The models...

  18. Parametric study of the Incompletely Stirred Reactor modeling

    Energy Technology Data Exchange (ETDEWEB)

    Mobini, K. [Department of Mechanical Engineering, Shahid Rajaee University, Lavizan, Tehran (Iran); Bilger, R.W. [School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney (Australia)

    2009-09-15

    The Incompletely Stirred Reactor (ISR) is a generalization of the widely-used Perfectly Stirred Reactor (PSR) model and allows for incomplete mixing within the reactor. Its formulation is based on the Conditional Moment Closure (CMC) method. This model is applicable to nonpremixed combustion with strong recirculation such as in a gas turbine combustor primary zone. The model uses the simplifying assumptions that the conditionally-averaged reactive-scalar concentrations are independent of position in the reactor: this results in ordinary differential equations in mixture fraction space. The simplicity of the model permits the use of very complex chemical mechanisms. The effects of the detailed chemistry can be found while still including the effects of micromixing. A parametric study is performed here on an ISR for combustion of methane at overall stoichiometric conditions to investigate the sensitivity of the model to different parameters. The focus here is on emissions of nitric oxide and carbon monoxide. It is shown that the most important parameters in the ISR model are reactor residence time, the chemical mechanism and the core-averaged Probability Density Function (PDF). Using several different shapes for the core-averaged PDF, it is shown that use of a bimodal PDF with a low minimum at stoichiometric mixture fraction and a large variance leads to lower nitric oxide formation. The 'rich-plus-lean' mixing or staged combustion strategy for combustion is thus supported. (author)

  19. Mathematics Teacher Education: A Model from Crimea.

    Science.gov (United States)

    Ferrucci, Beverly J.; Evans, Richard C.

    1993-01-01

    Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)

  20. Knowledge Map: Mathematical Model and Dynamic Behaviors

    Institute of Scientific and Technical Information of China (English)

    Hai Zhuge; Xiang-Feng Luo

    2005-01-01

    Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent and reason not only simple cause-effect relations, but also time-delay causal relations, conditional probabilistic causal relations and sequential relations. The mathematical model and dynamic behaviors of KM are presented. Experiments show that, under certain conditions, the dynamic behaviors of KM can translate between different states. Knowing this condition, experts can control or modify the constructed KM while its dynamic behaviors do not accord with their expectation. Simulations and applications show that KM is more powerful and natural than FCM in emulating real world.

  1. Mathematical Models and Methods for Living Systems

    CERN Document Server

    Chaplain, Mark; Pugliese, Andrea

    2016-01-01

    The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.

  2. A mathematical model of aerosol holding chambers

    DEFF Research Database (Denmark)

    Zak, M; Madsen, J; Berg, E

    1999-01-01

    A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...

  3. Analysis of mathematical modelling on potentiometric biosensors.

    Science.gov (United States)

    Mehala, N; Rajendran, L

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

  4. Laser interaction with biological material mathematical modeling

    CERN Document Server

    Kulikov, Kirill

    2014-01-01

    This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.

  5. Modeling of the simulated countercurrent moving-bed chromatographic reactor used for the oxidative coupling of methane

    Energy Technology Data Exchange (ETDEWEB)

    Tonkovich, A.L.Y. [Pacific Northwest Lab., Richland, WA (United States); Carr, R.W. [Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Chemical Engineering and Materials Sciences

    1994-09-01

    The oxidative coupling reaction of methane (OCM) is a potential industrial reaction for the efficient production of ethylene. Replacement of current technologies requires significant product yield improvements. An experimental novel reactor design, the modified simulated countercurrent moving-bed chromatographic reactor (SCMCR), has reported improved ethane and ethylene product yields over other reported values. An understanding of the reactor operation is aided by concurrent mathematical modeling. The model mimics the exact experimental reactor configuration. Four sections are used; each section contains a reaction column and two separation columns connected in series. The feed is switched from section to section at discrete intervals. Reaction occurs in the first column and is followed by product and reactant separation in the ensuing section columns. Langmuir adsorption isotherms are used. The model does not incorporate the realistic and complex kinetics rising, from the OCM, rather a simplified reaction term is used to qualitatively gain insight into the operation of the modified SCMCR. A unimolecular reaction network is used in the model. The rate constants are set to permit a small fractional conversion, 5% per pass, at the concentrations during the first cycle. Similarly to the experimental reactor, the model adds a make-up feed (defined as percentage of the original feed, where excess methane is fed during the first cycle of the experimental reactor) to augment lost reactants.

  6. A Mathematical Model for Cisplatin Cellular Pharmacodynamics

    Directory of Open Access Journals (Sweden)

    Ardith W. El-Kareh

    2003-03-01

    Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.

  7. Common Mathematical Model of Fatigue Characteristics

    Directory of Open Access Journals (Sweden)

    Z. Maléř

    2004-01-01

    Full Text Available This paper presents a new common mathematical model which is able to describe fatigue characteristics in the whole necessary range by one equation only:log N = A(R + B(R ∙ log Sawhere A(R = AR2 + BR + C and B(R = DR2 + AR + F.This model was verified by five sets of fatigue data taken from the literature and by our own three additional original fatigue sets. The fatigue data usually described the region of N 104 to 3 x 106 and stress ratio of R = -2 to 0.5. In all these cases the proposed model described fatigue results with small scatter. Studying this model, following knowledge was obtained:– the parameter ”stress ratio R” was a good physical characteristic– the proposed model provided a good description of the eight collections of fatigue test results by one equation only– the scatter of the results through the whole scope is only a little greater than that round the individual S/N curve– using this model while testing may reduce the number of test samples and shorten the test time– as the proposed model represents a common form of the S/N curve, it may be used for processing uniform objective fatigue life results, which may enable mutual comparison of fatigue characteristics.

  8. HEMETβ: improvement of hepatocyte metabolism mathematical model.

    Science.gov (United States)

    Orsi, G; De Maria, C; Guzzardi, M; Vozzi, F; Vozzi, G

    2011-10-01

    This article describes hepatocyte metabolism mathematical model (HEMETβ), which is an improved version of HEMET, an effective and versatile virtual cell model based on hepatic cell metabolism. HEMET is based on a set of non-linear differential equations, implemented in Simulink®, which describes the biochemical reactions and energetic cell state, and completely mimics the principal metabolic pathways in hepatic cells. The cell energy function and modular structure are the core of this model. HEMETβ as HEMET model describes hepatic cellular metabolism in standard conditions (cell culture in a plastic multi-well placed in an incubator at 37° C with 5% of CO2) and with excess substrates concentration. The main improvements in HEMETβ are the introductions of Michaelis-Menten models for reversible reactions and enzymatic inhibition. In addition, we eliminated hard non-linearities and modelled cell proliferation and every single aminoacid degradation pathway. All these innovations, combined with a user-friendly aspect, allow researchers to create new cell types and validate new experimental protocols just varying 'peripheral' pathways or model inputs.

  9. UASB反应器模型的研究进展%Research Advances on UASB Reactor Model

    Institute of Scientific and Technical Information of China (English)

    张倩倩; 沈李东; 郭立新; 金仁村

    2013-01-01

    The upflow anaerobic sludge blanket (UASB) reactor can be a kind of efficient and economical rector. Considerable effort has gone into developing mathematical models for UASB reactor in order to optimize its design and regulate the process control systems to enhance its operational efficiency. This article presents a critical review of the different mathematical models containing hydraulic model (compartment axial dispersion model and increasing-sized CSTR model, i.e. ISC model) and reactor model available for UASB reactor.%升流式厌氧污泥床(UASB)是一种高效、经济的厌氧生物反应器.迄今已有大量的研究旨在构建UASB反应器的数学模型,实现反应器设计和运行优化.本文综述了UASB反应器的各种数学模型,包括:水力学模型(轴向扩散模型、体积渐增式CSTR模型即ISC模型)、反应器模型.

  10. Modelling-based Optimisation of the Direct Synthesis of Dimethyl Ether from Syngas in a Commercial Slurry Reactor

    Institute of Scientific and Technical Information of China (English)

    Sadegh Papari; Mohammad Kazemeini; Moslem Fattahi

    2013-01-01

    In the present study,we developed a multi-component one-dimensional mathematical model for simulation and optimisation of a commercial catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2,operating in a chum-turbulent regime.DME productivity and CO conversion were optimised by tuning operating conditions,such as superficial gas velocity,catalyst concentration,catalyst mass over molar gas flow rate (W/F),syngas composition,pressure and temperature.Reactor modelling was accomplished utilising mass balance,global kinetic models and heterogeneous hydrodynamics.In the heterogeneous flow regime,gas was distributed into two bubble phases:small and large.Simulation results were validated using data obtained from a pilot plant.The developed model is also applicable for the design of large-scale slurry reactors.

  11. Swelling in light water reactor internal components: Insights from computational modeling

    Energy Technology Data Exchange (ETDEWEB)

    Stoller, Roger E. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Barashev, Alexander V. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States); Golubov, Stanislav I. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2015-08-01

    A modern cluster dynamics model has been used to investigate the materials and irradiation parameters that control microstructural evolution under the relatively low-temperature exposure conditions that are representative of the operating environment for in-core light water reactor components. The focus is on components fabricated from austenitic stainless steel. The model accounts for the synergistic interaction between radiation-produced vacancies and the helium that is produced by nuclear transmutation reactions. Cavity nucleation rates are shown to be relatively high in this temperature regime (275 to 325°C), but are sensitive to assumptions about the fine scale microstructure produced under low-temperature irradiation. The cavity nucleation rates observed run counter to the expectation that void swelling would not occur under these conditions. This expectation was based on previous research on void swelling in austenitic steels in fast reactors. This misleading impression arose primarily from an absence of relevant data. The results of the computational modeling are generally consistent with recent data obtained by examining ex-service components. However, it has been shown that the sensitivity of the model s predictions of low-temperature swelling behavior to assumptions about the primary damage source term and specification of the mean-field sink strengths is somewhat greater that that observed at higher temperatures. Further assessment of the mathematical model is underway to meet the long-term objective of this research, which is to provide a predictive model of void swelling at relevant lifetime exposures to support extended reactor operations.

  12. Linear models in the mathematics of uncertainty

    CERN Document Server

    Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A

    2013-01-01

    The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data  is difficult to measure and an assumption of randomness and/or statistical validity is questionable.  We apply our methods to real world issues in international relations such as  nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...

  13. 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....

  14. Time variability of α from realistic models of Oklo reactors

    Science.gov (United States)

    Gould, C. R.; Sharapov, E. I.; Lamoreaux, S. K.

    2006-08-01

    We reanalyze Oklo Sm149 data using realistic models of the natural nuclear reactors. Disagreements among recent Oklo determinations of the time evolution of α, the electromagnetic fine structure constant, are shown to be due to different reactor models, which led to different neutron spectra used in the calculations. We use known Oklo reactor epithermal spectral indices as criteria for selecting realistic reactor models. Two Oklo reactors, RZ2 and RZ10, were modeled with MCNP. The resulting neutron spectra were used to calculate the change in the Sm149 effective neutron capture cross section as a function of a possible shift in the energy of the 97.3-meV resonance. We independently deduce ancient Sm149 effective cross sections and use these values to set limits on the time variation of α. Our study resolves a contradictory situation with previous Oklo α results. Our suggested 2σ bound on a possible time variation of α over 2 billion years is stringent: -0.11≤Δα/α≤0.24, in units of 10-7, but model dependent in that it assumes only α has varied over time.

  15. Mathematical problems in modeling artificial heart

    Directory of Open Access Journals (Sweden)

    Ahmed N. U.

    1995-01-01

    Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.

  16. Towards an efficient multiphysics model for nuclear reactor dynamics

    Directory of Open Access Journals (Sweden)

    Obaidurrahman K.

    2015-01-01

    Full Text Available Availability of fast computer resources nowadays has facilitated more in-depth modeling of complex engineering systems which involve strong multiphysics interactions. This multiphysics modeling is an important necessity in nuclear reactor safety studies where efforts are being made worldwide to combine the knowledge from all associated disciplines at one place to accomplish the most realistic simulation of involved phenomenon. On these lines coupled modeling of nuclear reactor neutron kinetics, fuel heat transfer and coolant transport is a regular practice nowadays for transient analysis of reactor core. However optimization between modeling accuracy and computational economy has always been a challenging task to ensure the adequate degree of reliability in such extensive numerical exercises. Complex reactor core modeling involves estimation of evolving 3-D core thermal state, which in turn demands an expensive multichannel based detailed core thermal hydraulics model. A novel approach of power weighted coupling between core neutronics and thermal hydraulics presented in this work aims to reduce the bulk of core thermal calculations in core dynamics modeling to a significant extent without compromising accuracy of computation. Coupled core model has been validated against a series of international benchmarks. Accuracy and computational efficiency of the proposed multiphysics model has been demonstrated by analyzing a reactivity initiated transient.

  17. 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.

  18. A Mathematical Model of Cigarette Smoldering Process

    Directory of Open Access Journals (Sweden)

    Chen P

    2014-12-01

    Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.

  19. Monte Carlo Modeling Electronuclear Processes in Cascade Subcritical Reactor

    CERN Document Server

    Bznuni, S A; Zhamkochyan, V M; Polyanskii, A A; Sosnin, A N; Khudaverdian, A G

    2000-01-01

    Accelerator driven subcritical cascade reactor composed of the main thermal neutron reactor constructed analogous to the core of the VVER-1000 reactor and a booster-reactor, which is constructed similar to the core of the BN-350 fast breeder reactor, is taken as a model example. It is shown by means of Monte Carlo calculations that such system is a safe energy source (k_{eff}=0.94-0.98) and it is capable of transmuting produced radioactive wastes (neutron flux density in the thermal zone is PHI^{max} (r,z)=10^{14} n/(cm^{-2} s^{-1}), neutron flux in the fast zone is respectively equal PHI^{max} (r,z)=2.25 cdot 10^{15} n/(cm^{-2} s^{-1}) if the beam current of the proton accelerator is k_{eff}=0.98 and I=5.3 mA). Suggested configuration of the "cascade" reactor system essentially reduces the requirements on the proton accelerator current.

  20. The Use of Models in Teaching Proof by Mathematical Induction

    Science.gov (United States)

    Ron, Gila; Dreyfus, Tommy

    2004-01-01

    Proof by mathematical induction is known to be conceptually difficult for high school students. This paper presents results from interviews with six experienced high school teachers, concerning the use of models in teaching mathematical induction. Along with creative and adequate use of models, we found explanations, models and examples that…

  1. Computational fluid dynamic modeling of fluidized-bed polymerization reactors

    Energy Technology Data Exchange (ETDEWEB)

    Rokkam, Ram [Iowa State Univ., Ames, IA (United States)

    2012-01-01

    Polyethylene is one of the most widely used plastics, and over 60 million tons are produced worldwide every year. Polyethylene is obtained by the catalytic polymerization of ethylene in gas and liquid phase reactors. The gas phase processes are more advantageous, and use fluidized-bed reactors for production of polyethylene. Since they operate so close to the melting point of the polymer, agglomeration is an operational concern in all slurry and gas polymerization processes. Electrostatics and hot spot formation are the main factors that contribute to agglomeration in gas-phase processes. Electrostatic charges in gas phase polymerization fluidized bed reactors are known to influence the bed hydrodynamics, particle elutriation, bubble size, bubble shape etc. Accumulation of electrostatic charges in the fluidized-bed can lead to operational issues. In this work a first-principles electrostatic model is developed and coupled with a multi-fluid computational fluid dynamic (CFD) model to understand the effect of electrostatics on the dynamics of a fluidized-bed. The multi-fluid CFD model for gas-particle flow is based on the kinetic theory of granular flows closures. The electrostatic model is developed based on a fixed, size-dependent charge for each type of particle (catalyst, polymer, polymer fines) phase. The combined CFD model is first verified using simple test cases, validated with experiments and applied to a pilot-scale polymerization fluidized-bed reactor. The CFD model reproduced qualitative trends in particle segregation and entrainment due to electrostatic charges observed in experiments. For the scale up of fluidized bed reactor, filtered models are developed and implemented on pilot scale reactor.

  2. Mathematical Modelling of the Heald Shaft

    Directory of Open Access Journals (Sweden)

    Bílek Martin

    2016-12-01

    Full Text Available The manufacturers of weaving equipment recently endeavour to minimise the necessary designing plays in the weaving loom mechanisms. One of the mechanisms most exposed to stress is the shedding motion that defines the held-shaft stroke. Its end part is the heald shaft. The heald shaft constitutes a problematic assembly of the shedding motion. The design employed presently is characterised by dynamic impact loading caused by designing play in the suspension of healds into the heald shaft. During weaving cycle, the healds fly between the main beams of the heald shaft, producing a considerable force pulse. This paper is concerned with the description of dynamic behaviour of the existing design on the basis of mathematical modelling and verification of obtained results by means of experimental analysis.

  3. Mathematical Modeling of Spiral Heat Exchanger

    Directory of Open Access Journals (Sweden)

    Probal Guha , Vaishnavi Unde

    2014-04-01

    Full Text Available Compact Heat Exchangers (CHEs are increasingly being used on small and medium scale industries. Due to their compact size and efficient design, they facilitate more efficient heat transfer. Better heat transfer would imply lesser fuel consumption for the operations of the plant, giving improvement to overall efficiency. This reduction in consumption of fuel is a step towards sustainable development. This report exclusively deals with the study the spiral heat exchanger.The design considerations for spiral heat exchanger is that the flow within the spiral has been assumed as flow through a duct and by using Shah London empirical equation for Nusselt number design parameters are further optimized.This is accompanied by a detailed energy balance to generate a concise mathematical model

  4. Mathematical modelling on instability of shear fault

    Institute of Scientific and Technical Information of China (English)

    范天佑

    1996-01-01

    A study on mathematical modelling on instability of fault is reported.The fracture mechanics and fracture dynamics as a basis of the discussion,and the method of complex variable function (including the conformal mapping and approximate conformal mapping) are employed,and some analytic solutions of the problem in closed form are found.The fault body concept is emphasized and the characteristic size of fault body is introduced.The effect of finite size of the fault body and the effect of the fault propagating speed (especially the effect of the high speed) and their influence on the fault instability are discussed.These results further explain the low-stress drop phenomena observed in earthquake source.

  5. Some Mathematical Models for ELM Signal

    CERN Document Server

    XIE, Hua-sheng

    2012-01-01

    There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.

  6. Mathematical Model for the Continuous Vacuum Drying

    Institute of Scientific and Technical Information of China (English)

    DAI Hui-liang

    2002-01-01

    An improved mathematical model for the continuous vacuum drying of highly viscous and heatsensitive foodstuffs was proposed, The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh meat paste.

  7. Mathematical Modeling of the Origins of Life

    Science.gov (United States)

    Pohorille, Andrew

    2006-01-01

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

  8. Mathematics in Nature Modeling Patterns in the Natural World

    CERN Document Server

    Adam, John A

    2011-01-01

    From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem

  9. Thermohydraulic and nuclear modeling of natural fission reactors

    Science.gov (United States)

    Viggato, Jason Charles

    Experimental verification of proposed nuclear waste storage schemes in geologic repositories is not possible, however, a natural analog exists in the form of ancient natural reactors that existed in uranium-rich ores. Two billion years ago, the enrichment of natural uranium was high enough to allow a sustained chain reaction in the presence of water as a moderator. Several natural reactors occurred in Gabon, Africa and were discovered in the early 1970's. These reactors operated at low power levels for hundreds of thousands of years. Heated water generated from the reactors also leached uranium from the surrounding rock strata and deposited it in the reactor cores. This increased the concentration of uranium in the core over time and served to "refuel" the reactor. This has strong implications in the design of modern geologic repositories for spent nuclear fuel. The possibility of accidental fission events in man-made repositories exists and the geologic evidence from Oklo suggests how those events may progress and enhance local concentrations of uranium. Based on a review of the literature, a comprehensive code was developed to model the thermohydraulic behavior and criticality conditions that may have existed in the Oklo reactor core. A two-dimensional numerical model that incorporates modeling of fluid flow, temperatures, and nuclear fission and subsequent heat generation was developed for the Oklo natural reactors. The operating temperatures ranged from about 456 K to about 721 K. Critical reactions were observed for a wide range of concentrations and porosity values (9 to 30 percent UO2 and 10 to 20 percent porosity). Periodic operation occurred in the computer model prediction with UO2 concentrations of 30 percent in the core and 5 percent in the surrounding material. For saturated conditions and 30 percent porosity, the model predicted temperature transients with a period of about 5 hours. Kuroda predicted 3 to 4 hour durations for temperature transients

  10. Mathematical analysis of epidemiological models with heterogeneity

    Energy Technology Data Exchange (ETDEWEB)

    Van Ark, J.W.

    1992-01-01

    For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.

  11. 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.

  12. 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...

  13. Mathematical modeling of endovenous laser treatment (ELT

    Directory of Open Access Journals (Sweden)

    Wassmer Benjamin

    2006-04-01

    Full Text Available Abstract Background and objectives Endovenous laser treatment (ELT has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV and Small Saphenous Vein (SSV. Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA. Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm, a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm played only a minor influence on these results. Discussion and conclusion The parameters

  14. THATCH: A computer code for modelling thermal networks of high- temperature gas-cooled nuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Kroeger, P.G.; Kennett, R.J.; Colman, J.; Ginsberg, T. (Brookhaven National Lab., Upton, NY (United States))

    1991-10-01

    This report documents the THATCH code, which can be used to model general thermal and flow networks of solids and coolant channels in two-dimensional r-z geometries. The main application of THATCH is to model reactor thermo-hydraulic transients in High-Temperature Gas-Cooled Reactors (HTGRs). The available modules simulate pressurized or depressurized core heatup transients, heat transfer to general exterior sinks or to specific passive Reactor Cavity Cooling Systems, which can be air or water-cooled. Graphite oxidation during air or water ingress can be modelled, including the effects of added combustion products to the gas flow and the additional chemical energy release. A point kinetics model is available for analyzing reactivity excursions; for instance due to water ingress, and also for hypothetical no-scram scenarios. For most HTGR transients, which generally range over hours, a user-selected nodalization of the core in r-z geometry is used. However, a separate model of heat transfer in the symmetry element of each fuel element is also available for very rapid transients. This model can be applied coupled to the traditional coarser r-z nodalization. This report described the mathematical models used in the code and the method of solution. It describes the code and its various sub-elements. Details of the input data and file usage, with file formats, is given for the code, as well as for several preprocessing and postprocessing options. The THATCH model of the currently applicable 350 MW{sub th} reactor is described. Input data for four sample cases are given with output available in fiche form. Installation requirements and code limitations, as well as the most common error indications are listed. 31 refs., 23 figs., 32 tabs.

  15. Mathematical Modeling Social Responsibility for Dynamic Organizations

    Directory of Open Access Journals (Sweden)

    Farzaneh Chavoshbashi

    2012-03-01

    Full Text Available Dynamic organizations as accountable organizations, for transparency and accountability to its stakeholders to stakeholders for their toward performance there should express their commitment to social responsibility are through their values and ensure that this commitment throughout the organization are now and thus will have a social responsibility for their mutual benefit, so there is more and more coherent in their ethical approach takes advantage and the community and stakeholders and the organization will have better performance and strengths. Because of interest in social responsibility, in this paper dynamic model is presented for Corporate Social Responsibility of Bionic organization. Model presented a new model is inspired by chaos theory and natural systems theory based on bifurcation in creation to be all natural systems, realizing the value of responsibility as one of the fundamental values of social and institutional development that the relationship between business and work environment in the global market economy and range will be specified. First Social Responsibility factors identified, then experts and scholars determine the weight of the components and technical coefficient for modeling and paired comparison has been done using MATLAB mathematical Software.

  16. Cocaine addiction and personality: a mathematical model.

    Science.gov (United States)

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

    2010-05-01

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

  17. Mathematical Model for the Mineralization of Bone

    Science.gov (United States)

    Martin, Bruce

    1994-01-01

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

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

    Science.gov (United States)

    Rahimpour, M R; Asgari, A

    2008-05-01

    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.

  19. A mathematical model of glutathione metabolism

    Directory of Open Access Journals (Sweden)

    James S Jill

    2008-04-01

    Full Text Available Abstract Background Glutathione (GSH plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism. Approach We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data. Conclusion We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.

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

    Science.gov (United States)

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

    2016-01-01

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

  1. Mathematical model insights into arsenic detoxification

    Directory of Open Access Journals (Sweden)

    Nijhout H Frederik

    2011-08-01

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

  2. Application of Mathematical Modeling Activities in Costarican High School Education

    Directory of Open Access Journals (Sweden)

    Karen Porras-Lizano

    2015-01-01

    Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.

  3. Mathematical model of electrotaxis in osteoblastic cells.

    Science.gov (United States)

    Vanegas-Acosta, J C; Garzón-Alvarado, D A; Zwamborn, A P M

    2012-12-01

    Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF strengths and different configurations of both electrical and chemical stimuli. Accordingly, we found that the cell migration speed is described as the combination of an electrical and a chemical term. Cell migration is faster when both stimuli orient cell migration towards the same direction. In contrast, a reduced speed is obtained when the EF vector is opposed to the direction of the chemical stimulus. Numerical relations were obtained to quantify the cell migration speed at each configuration. Additional calculations for the cell colonization of a substrate also show mediation of the EF strength. Therefore, the term electro-osteoconduction is introduced to account the electrically induced cell colonization. Since numerical results compare favorably with experimental evidence, the model is suitable to be extended to other types of cells, and to numerically explore the influence of EF during wound healing. Copyright © 2012 Elsevier B.V. All rights reserved.

  4. BISON and MARMOT Development for Modeling Fast Reactor Fuel Performance

    Energy Technology Data Exchange (ETDEWEB)

    Gamble, Kyle Allan Lawrence [Idaho National Lab. (INL), Idaho Falls, ID (United States); Williamson, Richard L. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Schwen, Daniel [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Yongfeng [Idaho National Lab. (INL), Idaho Falls, ID (United States); Novascone, Stephen Rhead [Idaho National Lab. (INL), Idaho Falls, ID (United States); Medvedev, Pavel G. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2015-09-01

    BISON and MARMOT are two codes under development at the Idaho National Laboratory for engineering scale and lower length scale fuel performance modeling. It is desired to add capabilities for fast reactor applications to these codes. The fast reactor fuel types under consideration are metal (U-Pu-Zr) and oxide (MOX). The cladding types of interest include 316SS, D9, and HT9. The purpose of this report is to outline the proposed plans for code development and provide an overview of the models added to the BISON and MARMOT codes for fast reactor fuel behavior. A brief overview of preliminary discussions on the formation of a bilateral agreement between the Idaho National Laboratory and the National Nuclear Laboratory in the United Kingdom is presented.

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

    Science.gov (United States)

    Çelik, H. Coskun

    2017-01-01

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

  6. Modelling Mathematical Reasoning in Physics Education

    Science.gov (United States)

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

    2012-01-01

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

  7. Mathematics Teacher TPACK Standards and Development Model

    Science.gov (United States)

    Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

    2009-01-01

    What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

  8. CFD Simulation on Ethylene Furnace Reactor Tubes

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Different mathematical models for ethylene furnace reactor tubes were reviewed. On the basis of these models a new mathematical simulation approach for reactor tubes based on computational fluid dynamics (CFD) technique was presented. This approach took the flow, heat transfer, mass transfer and thermal cracking reactions in the reactor tubes into consideration. The coupled reactor model was solved with the SIMPLE algorithm. Some detailed information about the flow field, temperature field and concentration distribution in the reactor tubes was obtained, revealing the basic characteristics of the hydrodynamic phenomena and reaction behavior in the reactor tubes. The CFD approach provides the necessary information for conclusive decisions regarding the production optimization, the design and improvement of reactor tubes, and the new techniques implementation.

  9. Two-dimensional model for circulating fluidized-bed reactors

    Energy Technology Data Exchange (ETDEWEB)

    Schoenfelder, H.; Kruse, M.; Werther, J. [Technical Univ. Hamburg-Harburg, Hamburg (Germany). Dept. of Chemical Engineering

    1996-07-01

    Circulating fluidized bed reactors are widely used for the combustion of coal in power stations as well as for the cracking of heavy oil in the petroleum industry. A two-dimensional reactor model for circulating fluidized beds (CFB) was studied based on the assumption that at every location within the riser, a descending dense phase and a rising lean phase coexist. Fluid mechanical variables may be calculated from one measured radial solids flux profile (upward and downward). The internal mass-transfer behavior is described on the basis of tracer gas experiments. The CFB reactor model was tested against data from ozone decomposition experiments in a CFB cold flow model (15.6-m height, 0.4-m ID) operated in the ranges 2.5--4.5 m/s and 9--45 kg/(m{sup 2}{center_dot}s) of superficial gas velocity and solids mass flux, respectively. Based on effective reaction rate constants determined from the ozone exit concentration, the model was used to predict the spatial reactant distribution within the reactor. Model predictions agreed well with measurements.

  10. A mathematical model of embodied consciousness.

    Science.gov (United States)

    Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth

    2017-09-07

    We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.

  11. Simple mathematical models of gene regulatory dynamics

    CERN Document Server

    Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S

    2016-01-01

    This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...

  12. A mathematical model of forgetting and amnesia

    Directory of Open Access Journals (Sweden)

    Jaap M. J. Murre

    2013-02-01

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

  13. Mathematical model I. Electron and quantum mechanics

    Science.gov (United States)

    Gadre, Nitin Ramchandra

    2011-03-01

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

  14. Mathematical model I. Electron and quantum mechanics

    Directory of Open Access Journals (Sweden)

    Nitin Ramchandra Gadre

    2011-03-01

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

  15. Mathematical modeling of Chikungunya fever control

    Science.gov (United States)

    Hincapié-Palacio, Doracelly; Ospina, Juan

    2015-05-01

    Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.

  16. A mathematical model of a computational problem solving system

    Science.gov (United States)

    Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

    2015-05-01

    This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.

  17. CFD Modeling of Melt Spreading on the Reactor Cavity Floor

    Energy Technology Data Exchange (ETDEWEB)

    Yeon, Wan Sik; Bang, Kwang Hyun [Korea Maritime University, Busan (Korea, Republic of); Cho, Young Jo; Lee, Jae Gon [Korea Hydro and Nuclear Power Co., Daejeon (Korea, Republic of)

    2010-05-15

    In the very unlikely event of a severe reactor accident involving core melt and reactor pressure vessel failure, it is important to provide an accident management strategy that would allow the molten core material to cool down, resolidify and bring the core debris to a stable coolable state for Light Water Reactors (LWRs). One approach to achieve a stable coolable state is to quench the core melt after its relocation from the reactor pressure vessel into the reactor cavity. This approach typically requires a large cavity floor area on which a large amount of core melt spreads well and forms a shallow melt thickness for small thermal resistance across the melt pool. Spreading of high temperature (approx3000 K), low superheat (approx200 K) core melt over a wide cavity floor has been a key question to the success of the ex-vessel core coolability and it has brought a number of experimental work (CORINE, ECOKATS, VULCANO) and analytical work (CORFLOW, MELTSPREAD, THEMA). These computational models are currently able to predict well the spreading of stimulant materials but yet have shown a limitation for prototypic core melt of UO{sub 2}+ZrO{sub 2} mixture. A computational model for the melt spreading requires a multiphase treatment of liquid melt, solidified melt, and air. Also solidification and thermal radiation physics should be included. The present work uses ANSYS-CFX code to simulate core melt spreading on the reactor cavity. The CFX code is a general-purpose multiphase code and the present work is focused on exploring the code's capability to model melt spreading problem in a step by step approach

  18. Mathematical Modeling of Photochemical Air Pollution.

    Science.gov (United States)

    McRae, Gregory John

    Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes

  19. Mathematical modeling of biomass fuels formation process.

    Science.gov (United States)

    Gaska, Krzysztof; Wandrasz, Andrzej J

    2008-01-01

    The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.

  20. MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR

    Directory of Open Access Journals (Sweden)

    S. YU. Buryak

    2014-03-01

    Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes

  1. 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...

  2. 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...

  3. Model biases in high-burnup fast reactor simulations

    Energy Technology Data Exchange (ETDEWEB)

    Touran, N.; Cheatham, J.; Petroski, R. [TerraPower LLC, 11235 S.E. 6th St, Bellevue, WA 98004 (United States)

    2012-07-01

    A new code system called the Advanced Reactor Modeling Interface (ARMI) has been developed that loosely couples multiscale, multiphysics nuclear reactor simulations to provide rapid, user-friendly, high-fidelity full systems analysis. Incorporating neutronic, thermal-hydraulic, safety/transient, fuel performance, core mechanical, and economic analyses, ARMI provides 'one-click' assessments of many multi-disciplined performance metrics and constraints that historically require iterations between many diverse experts. The capabilities of ARMI are implemented in this study to quantify neutronic biases of various modeling approximations typically made in fast reactor analysis at an equilibrium condition, after many repetitive shuffles. Sensitivities at equilibrium that result in very high discharge burnup are considered ( and >20% FIMA), as motivated by the development of the Traveling Wave Reactor. Model approximations discussed include homogenization, neutronic and depletion mesh resolution, thermal-hydraulic coupling, explicit control rod insertion, burnup-dependent cross sections, fission product model, burn chain truncation, and dynamic fuel performance. The sensitivities of these approximations on equilibrium discharge burnup, k{sub eff}, power density, delayed neutron fraction, and coolant temperature coefficient are discussed. (authors)

  4. A mathematical model and simulation results of plasma enhanced chemical vapor deposition of silicon nitride films

    Science.gov (United States)

    Konakov, S. A.; Krzhizhanovskaya, V. V.

    2015-01-01

    We developed a mathematical model of Plasma Enhanced Chemical Vapor Deposition (PECVD) of silicon nitride thin films from SiH4-NH3-N2-Ar mixture, an important application in modern materials science. Our multiphysics model describes gas dynamics, chemical physics, plasma physics and electrodynamics. The PECVD technology is inherently multiscale, from macroscale processes in the chemical reactor to atomic-scale surface chemistry. Our macroscale model is based on Navier-Stokes equations for a transient laminar flow of a compressible chemically reacting gas mixture, together with the mass transfer and energy balance equations, Poisson equation for electric potential, electrons and ions balance equations. The chemical kinetics model includes 24 species and 58 reactions: 37 in the gas phase and 21 on the surface. A deposition model consists of three stages: adsorption to the surface, diffusion along the surface and embedding of products into the substrate. A new model has been validated on experimental results obtained with the "Plasmalab System 100" reactor. We present the mathematical model and simulation results investigating the influence of flow rate and source gas proportion on silicon nitride film growth rate and chemical composition.

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

    OpenAIRE

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

    2016-01-01

    Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of technology modified the educational process, thus generating a meaningful impact as presented by studies carried out by Galbraith and Haines (2000). They d...

  6. Reactor

    Science.gov (United States)

    Evans, Robert M.

    1976-10-05

    1. A neutronic reactor having a moderator, coolant tubes traversing the moderator from an inlet end to an outlet end, bodies of material fissionable by neutrons of thermal energy disposed within the coolant tubes, and means for circulating water through said coolant tubes characterized by the improved construction wherein the coolant tubes are constructed of aluminum having an outer diameter of 1.729 inches and a wall thickness of 0.059 inch, and the means for circulating a liquid coolant through the tubes includes a source of water at a pressure of approximately 350 pounds per square inch connected to the inlet end of the tubes, and said construction including a pressure reducing orifice disposed at the inlet ends of the tubes reducing the pressure of the water by approximately 150 pounds per square inch.

  7. Study on Modeling Technology in Digital Reactor System

    Institute of Scientific and Technical Information of China (English)

    刘晓平; 罗月童; 童莉莉

    2004-01-01

    Modeling is the kernel part of a digital reactor system. As an extensible platform for reactor conceptual design, it is very important to study modeling technology and develop some kind of tools to speed up preparation of all classical computing models. This paper introduces the background of the project and basic conception of digital reactor. MCAM is taken as an example for modeling and its related technologies used are given. It is an interface program for MCNP geometry model developed by FDS team (ASIPP & HUT), and designed to run on windows system. MCAM aims at utilizing CAD technology to facilitate creation of MCNP geometry model. There have been two ways for MCAM to utilize CAD technology:(1) Making use of user interface technology in aid of generation of MCNP geometry model;(2) Making use of existing 3D CAD model to accelerate creation of MCNP geometry model. This paper gives an overview of MCAM's major function. At last, several examples are given to demonstrate MCAM's various capabilities.

  8. Mathematical model of radon activity measurements

    Energy Technology Data Exchange (ETDEWEB)

    Paschuk, Sergei A.; Correa, Janine N.; Kappke, Jaqueline; Zambianchi, Pedro, E-mail: sergei@utfpr.edu.br, E-mail: janine_nicolosi@hotmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Denyak, Valeriy, E-mail: denyak@gmail.com [Instituto de Pesquisa Pele Pequeno Principe, Curitiba, PR (Brazil)

    2015-07-01

    Present work describes a mathematical model that quantifies the time dependent amount of {sup 222}Rn and {sup 220}Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of {sup 222}Rn and {sup 220}Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since {sup 220}Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to {sup 222}Rn, only. Furthermore, the model also addresses the activity of {sup 220}Rn and {sup 222}Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure. (author)

  9. Symmetrization of mathematical model of charge transport in semiconductors

    Directory of Open Access Journals (Sweden)

    Alexander M. Blokhin

    2002-11-01

    Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.

  10. A basic mathematical and numerical model for gas injection

    NARCIS (Netherlands)

    Molenaar, J.

    1996-01-01

    In this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.

  11. A basic mathematical and numerical model for gas injection

    NARCIS (Netherlands)

    J. Molenaar (Gijs)

    1996-01-01

    textabstractIn this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.

  12. Generalized Mathematical Model for Hot Rolling Process of Plate

    Institute of Scientific and Technical Information of China (English)

    Zhenshan CUI; Bingye XU

    2003-01-01

    A generalized mathematical model is developed to predict the changes of temperature, rolling pressure, strain,strain rate, and austenite grain size for plate hot rolling and cooling processes. The model is established mainly by incorporating analytical an

  13. A mathematical model of the Mafia game

    CERN Document Server

    Migdal, Piotr

    2010-01-01

    Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set of actions (e.g. lynching during day). The mafia members have additional powers (knowing each other, killing during night) whereas the citizens are more numerous. We propose a simple mathematical model of the game, which is essentially a pure death process with discrete time. We find closed-form formulas for mafia winning chances $w(n,m)$ as well as for evolution of the game. Moreover, we investigate discrete properties of results, as well as its continuous-time approximation. I turns out that a relatively small number of the mafia members $m$ (among $n$ players) give $50:50$ winning chances, i.e. $m\\approx\\sqrt{n}$. Furthermore, the game strongly depends on the parity of the total number of players.

  14. A MATHEMATICAL MODELING OF CAMPUS INFORMATION SYSTEM

    Directory of Open Access Journals (Sweden)

    S. STALIN KUMAR

    2016-07-01

    Full Text Available An H-magic labeling in a H-decomposable graph G is a bijection f : V (G ∪ E(G → {1, 2, ..., p + q} such that for every copy H in the decomposition, \\sum\\limits_{v∈V (H}{f(v}+\\sum\\limits_{e∈E(H}{ f(e} is constant. f is said to be H-V -super magic if f(V (G = {1, 2, ..., p}. Suppose that V (G = U(G ∪ W(G with |U(G| = m and |W(G| = n. Then f is said to be H-V -super-strong magic labeling if f(U(G = {1, 2, ..., m} and f(W(G = {m + 1, m + 2, ...,(m + n = p}. A graph that admits a H-V -super-strong magic labeling is called a H-V -super-strong magic decomposable graph. In this paper, we pay our attention to provide a mathematical modeling of campus information system.

  15. Mathematical modelling for nanotube bundle oscillators

    Science.gov (United States)

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

    2009-07-01

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

  16. About the aims, objects and problems in Brazilian research on Mathematical Modeling in Mathematics Education

    Directory of Open Access Journals (Sweden)

    Universidade Estadual do Oeste do Paraná

    2012-12-01

    Full Text Available This paper presents an analysis of scientific communications published in the IV Mathematical Modeling National Conference (CNMEM in the Brazilian abbreviation, which took place in 2005. The analysis consists of a meta-analytical and content qualitative approach, aided by the software Atlas T.i. The data collected was originated in the above mentioned conference which is the first of the three which will be analyzed in the study that aims to unveil the research on Mathematical Modeling in Brazil. The categories established in this paper and which will be interpreted are: a Meta-study on Mathematics Modeling; b Modeling application; c Articulation between Modeling and other theories, and d Modeling and teachers education.

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

    Science.gov (United States)

    Fitamo, T; Boldrin, A; Dorini, G; Boe, K; Angelidaki, I; Scheutz, C

    2016-12-01

    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 strategies for controlling and optimising the co-digestion process. The model parameters were maintained in the same way as the original dynamic bioconversion model, albeit with minor adjustments, to simulate the co-digestion of food and garden waste with mixed sludge from a wastewater treatment plant 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 scenario analysis demonstrated that increasing the amount of mixed sludge in the co-substrate had a marginal effect on the reactor performance. In contrast, increasing the amount of food waste and garden waste resulted in improved performance.

  18. MODELING THE ELECTROLYTIC DECHLORINATION OF TRICHLOROETHYLENE IN A GRANULAR GRAPHITE-PACKED REACTOR

    Science.gov (United States)

    A comprehensive reactor model was developed for the electrolytic dechlorination of trichloroethylene (TCE) at a granular-graphite cathode. The reactor model describes the dynamic processes of TCE dechlorination and adsorption, and the formation and dechlorination of all the major...

  19. Economic mathematical methods and forecasting models

    OpenAIRE

    K. Karpovska-Skoryk

    2000-01-01

    In the article the questions of the expert system, based on the fuzzy mathematics, are discussed. It is pointed out that usage of such a system for medical insurance in the conditions of the Ukrainian economy is very convenient.

  20. Quantum Gravity Mathematical Models and Experimental Bounds

    CERN Document Server

    Fauser, Bertfried; Zeidler, Eberhard

    2007-01-01

    The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...

  1. Parameter estimation and accuracy matching strategies for 2-D reactor models

    Science.gov (United States)

    Nowak, U.; Grah, A.; Schreier, M.

    2005-11-01

    The mathematical modelling of a special modular catalytic reactor kit leads to a system of partial differential equation in two space dimensions. As customary, this model contains uncertain physical parameters, which may be adapted to fit experimental data. To solve this nonlinear least-squares problem we apply a damped Gauss-Newton method. A method of lines approach is used to evaluate the associated model equations. By an a priori spatial discretization, a large DAE system is derived and integrated with an adaptive, linearly implicit extrapolation method. For sensitivity evaluation we apply an internal numerical differentiation technique, which reuses linear algebra information from the model integration. In order not to interfere with the control of the Gauss-Newton iteration these computations are done usually very accurately and, therefore, with substantial cost. To overcome this difficulty, we discuss several accuracy adaptation strategies, e.g., a master-slave mode. Finally, we present some numerical experiments.

  2. 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.

  3. Methods and models in mathematical biology deterministic and stochastic approaches

    CERN Document Server

    Müller, Johannes

    2015-01-01

    This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

  4. Retrospective Study on Mathematical Modeling Based on Computer Graphic Processing

    Science.gov (United States)

    Zhang, Kai Li

    Graphics & image making is an important field in computer application, in which visualization software has been widely used with the characteristics of convenience and quick. However, it was thought by modeling designers that the software had been limited in it's function and flexibility because mathematics modeling platform was not built. A non-visualization graphics software appearing at this moment enabled the graphics & image design has a very good mathematics modeling platform. In the paper, a polished pyramid is established by multivariate spline function algorithm, and validate the non-visualization software is good in mathematical modeling.

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

    Science.gov (United States)

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

    2015-11-01

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

  6. Sodium fast reactor gaps analysis of computer codes and models for accident analysis and reactor safety.

    Energy Technology Data Exchange (ETDEWEB)

    Carbajo, Juan (Oak Ridge National Laboratory, Oak Ridge, TN); Jeong, Hae-Yong (Korea Atomic Energy Research Institute, Daejeon, Korea); Wigeland, Roald (Idaho National Laboratory, Idaho Falls, ID); Corradini, Michael (University of Wisconsin, Madison, WI); Schmidt, Rodney Cannon; Thomas, Justin (Argonne National Laboratory, Argonne, IL); Wei, Tom (Argonne National Laboratory, Argonne, IL); Sofu, Tanju (Argonne National Laboratory, Argonne, IL); Ludewig, Hans (Brookhaven National Laboratory, Upton, NY); Tobita, Yoshiharu (Japan Atomic Energy Agency, Ibaraki-ken, Japan); Ohshima, Hiroyuki (Japan Atomic Energy Agency, Ibaraki-ken, Japan); Serre, Frederic (Centre d' %C3%94etudes nucl%C3%94eaires de Cadarache %3CU%2B2013%3E CEA, France)

    2011-06-01

    This report summarizes the results of an expert-opinion elicitation activity designed to qualitatively assess the status and capabilities of currently available computer codes and models for accident analysis and reactor safety calculations of advanced sodium fast reactors, and identify important gaps. The twelve-member panel consisted of representatives from five U.S. National Laboratories (SNL, ANL, INL, ORNL, and BNL), the University of Wisconsin, the KAERI, the JAEA, and the CEA. The major portion of this elicitation activity occurred during a two-day meeting held on Aug. 10-11, 2010 at Argonne National Laboratory. There were two primary objectives of this work: (1) Identify computer codes currently available for SFR accident analysis and reactor safety calculations; and (2) Assess the status and capability of current US computer codes to adequately model the required accident scenarios and associated phenomena, and identify important gaps. During the review, panel members identified over 60 computer codes that are currently available in the international community to perform different aspects of SFR safety analysis for various event scenarios and accident categories. A brief description of each of these codes together with references (when available) is provided. An adaptation of the Predictive Capability Maturity Model (PCMM) for computational modeling and simulation is described for use in this work. The panel's assessment of the available US codes is presented in the form of nine tables, organized into groups of three for each of three risk categories considered: anticipated operational occurrences (AOOs), design basis accidents (DBA), and beyond design basis accidents (BDBA). A set of summary conclusions are drawn from the results obtained. At the highest level, the panel judged that current US code capabilities are adequate for licensing given reasonable margins, but expressed concern that US code development activities had stagnated and that the

  7. 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.

  8. Crystal Plasticity Model of Reactor Pressure Vessel Embrittlement in GRIZZLY

    Energy Technology Data Exchange (ETDEWEB)

    Chakraborty, Pritam [Idaho National Laboratory (INL), Idaho Falls, ID (United States); Biner, Suleyman Bulent [Idaho National Laboratory (INL), Idaho Falls, ID (United States); Zhang, Yongfeng [Idaho National Laboratory (INL), Idaho Falls, ID (United States); Spencer, Benjamin Whiting [Idaho National Laboratory (INL), Idaho Falls, ID (United States)

    2015-07-01

    The integrity of reactor pressure vessels (RPVs) is of utmost importance to ensure safe operation of nuclear reactors under extended lifetime. Microstructure-scale models at various length and time scales, coupled concurrently or through homogenization methods, can play a crucial role in understanding and quantifying irradiation-induced defect production, growth and their influence on mechanical behavior of RPV steels. A multi-scale approach, involving atomistic, meso- and engineering-scale models, is currently being pursued within the GRIZZLY project to understand and quantify irradiation-induced embrittlement of RPV steels. Within this framework, a dislocation-density based crystal plasticity model has been developed in GRIZZLY that captures the effect of irradiation-induced defects on the flow stress behavior and is presented in this report. The present formulation accounts for the interaction between self-interstitial loops and matrix dislocations. The model predictions have been validated with experiments and dislocation dynamics simulation.

  9. Simulation of MILD combustion using Perfectly Stirred Reactor model

    KAUST Repository

    Chen, Z.

    2016-07-06

    A simple model based on a Perfectly Stirred Reactor (PSR) is proposed for moderate or intense low-oxygen dilution (MILD) combustion. The PSR calculation is performed covering the entire flammability range and the tabulated chemistry approach is used with a presumed joint probability density function (PDF). The jet, in hot and diluted coflow experimental set-up under MILD conditions, is simulated using this reactor model for two oxygen dilution levels. The computed results for mean temperature, major and minor species mass fractions are compared with the experimental data and simulation results obtained recently using a multi-environment transported PDF approach. Overall, a good agreement is observed at three different axial locations for these comparisons despite the over-predicted peak value of CO formation. This suggests that MILD combustion can be effectively modelled by the proposed PSR model with lower computational cost.

  10. Teaching Writing and Communication in a Mathematical Modeling Course

    Science.gov (United States)

    Linhart, Jean Marie

    2014-01-01

    Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

  11. An Assessment Model for Proof Comprehension in Undergraduate Mathematics

    Science.gov (United States)

    Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron

    2012-01-01

    Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

  12. A COMPARISON OF DIFFERENT MODELING APPROACHES FOR THE SIMULATION OF THE TRANSIENT AND STEADY-STATE BEHAVIOR OF CONTINUOUS EMULSION POLYMERIZATIONS IN PULSED TUBULAR REACTORS

    Directory of Open Access Journals (Sweden)

    C. Sayer

    2002-03-01

    Full Text Available Dynamic mathematical models are developed to simulate styrene emulsion polymerization reactions carried out in pulsed tubular reactors. Two different modeling approaches, the tanks-in-series model and the axial dispersion model, are compared. The models developed were validated with experimental data from the literature and used to study the dynamics during transient periods, e.g., the start-up of the reactor and the response to disturbances. The effect of the Peclet number on process variables such as conversion and particle concentration was also verified.

  13. Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

    Science.gov (United States)

    Wright, Vince

    2014-01-01

    Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

  14. Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

    Science.gov (United States)

    Wright, Vince

    2014-01-01

    Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

  15. The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

    Science.gov (United States)

    Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

    2017-05-01

    The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

  16. A review of mathematical modeling of the zinc/bromine flow cell and battery

    Science.gov (United States)

    Evans, T. I.; White, R. E.

    1987-11-01

    Mathematical models which have been developed to study various aspects of the zinc/bromine cell and stack of cells are reviewed. Development of these macroscopic models begins with a material balance, a transport equation which includes a migration term for charged species in an electric field, and an electrode kinetic expression. Various types of models are discussed: partial differential equation models that can be used to predict current and potential distributions, an algebraic model that includes shunt currents and associated energy losses and can be used to determine the optimum resistivity of an electrolyte, and ordinary differential equation models that can be used to predict the energy efficiency of the cell as a function of the state of charge. These models have allowed researchers to better understand the physical phenomena occurring within parallel plate electrochemical flow reactors and have been instrumental in the improvement of the zinc/bromine cell design. Suggestions are made for future modeling work.

  17. Mathematical modelling of friction-vibration interactions of nuclear fuel rods

    Directory of Open Access Journals (Sweden)

    Zeman V.

    2016-06-01

    Full Text Available Nuclear fuel rods (FRs are transverselly linked to each other by three spacer grid cells at several vertical levels inside a fuel assembly (FA. Vibration of FA components, caused by the motion of FA support plates in the reactor core, generates variable contact forces between FRs and spacer grid cells. Friction effects in contact surfaces have an influence on the expected lifetime period of nuclear FA in terms of FR cladding fretting wear. This paper introduces an original approach to mathematical modelling and simulation analysis of FR nonlinear vibrations and fretting wear taking into consideration friction forces at all levels of spacer grids.

  18. Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory

    Directory of Open Access Journals (Sweden)

    Daniele Molinini

    2014-06-01

    Full Text Available The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context.

  19. Economic-mathematical methods and models under uncertainty

    CERN Document Server

    Aliyev, A G

    2013-01-01

    Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp

  20. A New Activity-Based Cost (ABC) Mathematical Model

    Institute of Scientific and Technical Information of China (English)

    JIANG Shuo; SONG Lei

    2003-01-01

    Along with the product price competition growing intensely, it is apparently important for reasonably distributing and counting cost. But, in sharing indirect cost, traditional cost accounting unveils the limitations increasingly, especially in authenticity of cost information. And the accounting theory circles and industry circles begin seeking one kind of new accurate cost calculation method, and the activity-based cost (ABC) method emerges as the times require. In this paper, we will build its mathematical model by the basic principle of ABC, and will improve its mathematical model further. We will establish its comparison mathematical model and make the ABC method go a step further to its practical application.

  1. Mathematical Model of Asynchronous Motor with Embedded Combined Braking Device

    Directory of Open Access Journals (Sweden)

    V. Solencov

    2013-01-01

    Full Text Available The paper presents a conclusion of a mathematical model pertaining to asynchronous motor with embedded combined braking device on the basis of electromechanical brake and electromagnetic slip coupling. The mathematical model has been obtained in an orthogonal coordinate system a, b, which is fixed with respect to the asymmetric part of the asynchronous motor with embedded combined braking device. The model makes it possible to investigate transient processes in various asynchronous motors with embedded braking devices.

  2. Mathematical Model of Extrinsic Blood Coagulation Cascade Dynamic System

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The blood coagulation system is very important to life. This paper presents a mathematical blood coagulation model for the extrinsic pathway. This model simulates clotting factor VIII, which plays an important role in the coagulation mechanism. The mathematical model is used to study the equilibrium stability, orbit structure, attractors and global stability behavior, with conclusions in accordance with the physiological phenomena. Moreover, the results provide information about blood related illnesses, which can be used for further study of the coagulation mechanism.

  3. Modeling of Flow in Nuclear Reactor Fuel Cell Outlet

    Directory of Open Access Journals (Sweden)

    František URBAN

    2010-12-01

    Full Text Available Safe and effective load of nuclear reactor fuel cells demands qualitative and quantitative analysis of relations between coolant temperature in fuel cell outlet temperature measured by thermocouple and middle temperature of coolant in thermocouple plane position. In laboratory at Insitute of thermal power engineering of the Slovak University of Technology in Bratislava was installed an experimental physical fuel cell model of VVER 440 nuclear power plant with V 213 nuclear reactors. Objective of measurements on physical model was temperature and velocity profiles analysis in the fuel cell outlet. In this paper the measured temperature and velocity profiles are compared with the results of CFD simulation of fuel cell physical model coolant flow.

  4. Modelling of an ASR countercurrent pyrolysis reactor with nonlinear kinetics

    Energy Technology Data Exchange (ETDEWEB)

    Chiarioni, A.; Reverberi, A.P.; Dovi, V.G. [Universita degli Studi di Genova (Italy). Dipartimento di Ingegneria Chimica e di Processo ' G.B. Bonino' ; El-Shaarawi, A.H. [National Water Research Institute, Burlington, Ont. (Canada)

    2003-10-01

    The main objective of this work is focused on the modelling of a steady-state reactor where an automotive shredder residue (ASR) is subject to pyrolysis. The gas and solid temperature inside the reactor and the relevant density profiles of both phases are simulated for fixed values of the geometry of the apparatus and a lumped kinetic model is adopted to take into account the high heterogeneity of the ASR material. The key elements for the simulation are the inlet solid temperature and the outlet gas temperature. The problem is modelled by a system of first-order boundary-value ordinary differential equations and it is solved by means of a relaxation technique owing to the nonlinearities contained in the chemical kinetic expression. (author)

  5. 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. 

  6. Mathematical modeling of urea transport in the kidney.

    Science.gov (United States)

    Layton, Anita T

    2014-01-01

    Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

  7. Development of an automated core model for nuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Mosteller, R.D.

    1998-12-31

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objective of this project was to develop an automated package of computer codes that can model the steady-state behavior of nuclear-reactor cores of various designs. As an added benefit, data produced for steady-state analysis also can be used as input to the TRAC transient-analysis code for subsequent safety analysis of the reactor at any point in its operating lifetime. The basic capability to perform steady-state reactor-core analysis already existed in the combination of the HELIOS lattice-physics code and the NESTLE advanced nodal code. In this project, the automated package was completed by (1) obtaining cross-section libraries for HELIOS, (2) validating HELIOS by comparing its predictions to results from critical experiments and from the MCNP Monte Carlo code, (3) validating NESTLE by comparing its predictions to results from numerical benchmarks and to measured data from operating reactors, and (4) developing a linkage code to transform HELIOS output into NESTLE input.

  8. Rotary Bed Reactor for Chemical-Looping Combustion with Carbon Capture. Part 1: Reactor Design and Model Development

    KAUST Repository

    Zhao, Zhenlong

    2013-01-17

    Chemical-looping combustion (CLC) is a novel and promising technology for power generation with inherent CO2 capture. Currently, almost all of the research has been focused on developing CLC-based interconnected fluidized-bed reactors. In this two-part series, a new rotary reactor concept for gas-fueled CLC is proposed and analyzed. In part 1, the detailed configuration of the rotary reactor is described. In the reactor, a solid wheel rotates between the fuel and air streams at the reactor inlet and exit. Two purging sectors are used to avoid the mixing between the fuel stream and the air stream. The rotary wheel consists of a large number of channels with copper oxide coated on the inner surface of the channels. The support material is boron nitride, which has high specific heat and thermal conductivity. Gas flows through the reactor at elevated pressure, and it is heated to a high temperature by fuel combustion. Typical design parameters for a thermal capacity of 1 MW have been proposed, and a simplified model is developed to predict the performances of the reactor. The potential drawbacks of the rotary reactor are also discussed. © 2012 American Chemical Society.

  9. Mathematics of tsunami: modelling and identification

    Science.gov (United States)

    Krivorotko, Olga; Kabanikhin, Sergey

    2015-04-01

    Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of

  10. Modelling Methane Production and Sulfate Reduction in Anaerobic Granular Sludge Reactor with Ethanol as Electron Donor

    Science.gov (United States)

    Sun, Jing; Dai, Xiaohu; Wang, Qilin; Pan, Yuting; Ni, Bing-Jie

    2016-10-01

    In this work, a mathematical model based on growth kinetics of microorganisms and substrates transportation through biofilms was developed to describe methane production and sulfate reduction with ethanol being a key electron donor. The model was calibrated and validated using experimental data from two case studies conducted in granule-based Upflow Anaerobic Sludge Blanket reactors. The results suggest that the developed model could satisfactorily describe methane and sulfide productions as well as ethanol and sulfate removals in both systems. The modeling results reveal a stratified distribution of methanogenic archaea, sulfate-reducing bacteria and fermentative bacteria in the anaerobic granular sludge and the relative abundances of these microorganisms vary with substrate concentrations. It also indicates sulfate-reducing bacteria can successfully outcompete fermentative bacteria for ethanol utilization when COD/SO42‑ ratio reaches 0.5. Model simulation suggests that an optimal granule diameter for the maximum methane production efficiency can be achieved while the sulfate reduction efficiency is not significantly affected by variation in granule size. It also indicates that the methane production and sulfate reduction can be affected by ethanol and sulfate loading rates, and the microbial community development stage in the reactor, which provided comprehensive insights into the system for its practical operation.

  11. A study of the isobutane dehydrogenation in a porous membrane catalytic reactor: design, use and modelling

    Energy Technology Data Exchange (ETDEWEB)

    Casanave, D.

    1996-01-26

    The aim of this study was to set up and model a catalytic fixed-bed membrane reactor for the isobutane dehydrogenation. The catalyst, developed at Catalysis Research Institute (IRC), was a silicalite-supported Pt-based catalyst. Their catalytic performances (activity, selectivity, stability) where found better adapted to the membrane reactor, when compared with commercial Pt or Cr based catalysts. The kinetic study of the reaction has been performed in a differential reactor and led to the determination of a kinetic law, suitable when the catalyst is used near thermodynamic equilibrium. The mass transfer mechanisms were determined in meso-porous and microporous membranes through both permeability and gas mixtures (iC{sub 4}/H{sub 2}/N{sub 2}) separation measurements. For the meso-porous {gamma}-alumina, the mass transfer is ensured by a Knudsen diffusion mechanism which can compete with surface diffusion for condensable gas like isobutane. The resulting permselectivity H{sub 2}/iC4 of this membrane is low ({approx} 4). For the microporous zeolite membrane, molecular sieving occurs due to steric hindrance, leading to higher permselectivity {approx}14. Catalyst/membrane associations were compared in terms of isobutane dehydrogenation performances, for both types of membranes (meso-porous and microporous) and for two different reactor configurations (co-current and counter-current sweep gas flow). The best experimental results were obtained with the zeolite membrane, when sweeping the outer compartment in a co-current flow. The equilibrium displacement observed with the {gamma}-alumina membrane was lower and mainly due to a dilution effect of the reaction mixture by the sweep gas. A mathematical model was developed, which correctly describes all the experimental results obtained with the zeolite membrane, when the co-current mode is used. (Abstract Truncated)

  12. 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.

  13. Mathematical modelling with case studies using Maple and Matlab

    CERN Document Server

    Barnes, B

    2014-01-01

    Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-

  14. Mathematical Modelling for Micropiles Embedded in Salt Rock

    Directory of Open Access Journals (Sweden)

    Rădan (Toader Georgiana

    2016-03-01

    Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

  15. VIPRE modeling of VVER-1000 reactor core for DNB analyses

    Energy Technology Data Exchange (ETDEWEB)

    Sung, Y.; Nguyen, Q. [Westinghouse Electric Corporation, Pittsburgh, PA (United States); Cizek, J. [Nuclear Research Institute, Prague, (Czech Republic)

    1995-09-01

    Based on the one-pass modeling approach, the hot channels and the VVER-1000 reactor core can be modeled in 30 channels for DNB analyses using the VIPRE-01/MOD02 (VIPRE) code (VIPRE is owned by Electric Power Research Institute, Palo Alto, California). The VIPRE one-pass model does not compromise any accuracy in the hot channel local fluid conditions. Extensive qualifications include sensitivity studies of radial noding and crossflow parameters and comparisons with the results from THINC and CALOPEA subchannel codes. The qualifications confirm that the VIPRE code with the Westinghouse modeling method provides good computational performance and accuracy for VVER-1000 DNB analyses.

  16. Mathematical modeling of electromechanical processes in a brushless DC motor

    Directory of Open Access Journals (Sweden)

    V.I. Tkachuk

    2014-03-01

    Full Text Available On the basis of initial assumptions, a mathematical model that describes electromechanical processes in a brushless DC electric motor with a salient-pole stator and permanent-magnet excitation is created.

  17. mathematical model for direct evaporative space cooling systems

    African Journals Online (AJOL)

    eobe

    MATHEMATICAL MODEL FOR DIRECT EVAPORATIVE SPACE COOLING. SYSTEMS ... Water is the working fluid in evaporative cooling thus it is ..... co o lin g efficien cy (%. ) Time (hrs) predicted experimental. 0. 10. 20. 30. 40. 50. 60. 70. 80.

  18. A Local Mathematical Model for EPR-Experiments

    OpenAIRE

    Philipp, W.; Hess, K.

    2002-01-01

    In this paper we give a detailed and simplified version of our original mathematical model published first in the Proceedings of the National Academy of Science. We hope that this will clarify some misinterpretations of our original paper.

  19. 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,...

  20. RECENT MATHEMATICAL STUDIES IN THE MODELING OF OPTICS AND ELECTROMAGNETICS

    Institute of Scientific and Technical Information of China (English)

    Gang Bao

    2004-01-01

    This work is concerned with mathematical modeling, analysis, and computation of optics and electromagnetics, motivated particularly by optical and microwave applications.The main technical focus is on Maxwell's equations in complex linear and nonlinear media.

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

    Science.gov (United States)

    Fischbein, Efraim; Baltsan, Madlen

    1999-01-01

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

  2. Key Concept Mathematics and Management Science Models

    Science.gov (United States)

    Macbeth, Thomas G.; Dery, George C.

    1973-01-01

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

  3. Key Concept Mathematics and Management Science Models

    Science.gov (United States)

    Macbeth, Thomas G.; Dery, George C.

    1973-01-01

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

  4. Mathematical Model of Silicon Oxidation in Microelectronics

    Directory of Open Access Journals (Sweden)

    V. A. Bondarev

    2006-01-01

    Full Text Available The paper involves analytical solutions and formulae for determination of the oxide film thickness in the silicon oxidation while using nitride mask. Calculations are based on solutions of a three-dimensional diffusion equation and new mathematical functions that are firstly defined by the author. Suitable analytical and numerical solutions based on the diffusion equation have not yet been obtained

  5. The mathematical and computer modeling of the worm tool shaping

    Science.gov (United States)

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

    2017-06-01

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

  6. 2nd Tbilisi-Salerno Workshop on Modeling in Mathematics

    CERN Document Server

    Ricci, Paolo; Tavkhelidze, Ilia

    2017-01-01

    This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.

  7. A practical course in differential equations and mathematical modeling

    CERN Document Server

    Ibragimov , Nail H

    2009-01-01

    A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

  8. A mathematical look at a physical power prediction model

    DEFF Research Database (Denmark)

    Landberg, L.

    1998-01-01

    This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...

  9. Designing visual displays and system models for safe reactor operations

    Energy Technology Data Exchange (ETDEWEB)

    Brown-VanHoozer, S.A.

    1995-12-31

    The material presented in this paper is based on two studies involving the design of visual displays and the user`s prospective model of a system. The studies involve a methodology known as Neuro-Linguistic Programming and its use in expanding design choices from the operator`s perspective image. The contents of this paper focuses on the studies and how they are applicable to the safety of operating reactors.

  10. The mathematical model realization algorithm of high voltage cable

    OpenAIRE

    2006-01-01

    At mathematical model realization algorithm is very important to know the account order of necessary relations and how it presents. Depending of loads or signal sources connection in selected points of mathematical model its very important to know as to make the equations in this point that it was possible to determine all unknown variables in this point. The number of equations which describe this point must to coincide with number of unknown variables, and matrix which describes factor...

  11. Mathematical Model of Moving Heat-Transfer Agents

    Directory of Open Access Journals (Sweden)

    R. I. Yesman

    2010-01-01

    Full Text Available A mathematical model of moving heat-transfer agents which is applied in power systems and plants has been developed in the paper. A paper presents the mathematical model as a closed system of differential convective heat-transfer equations that includes a continuity equation, a motion equation, an energy equation.Various variants of boundary conditions on the surfaces of calculation flow and heat exchange zone are considered in the paper.

  12. Mathematical and computational modeling in biology at multiple scales

    OpenAIRE

    Tuszynski, Jack A; Winter, Philip; White, Diana; Tseng, Chih-Yuan; Sahu, Kamlesh K.; Gentile, Francesco; Spasevska, Ivana; Omar, Sara Ibrahim; Nayebi, Niloofar; Churchill, Cassandra DM; Klobukowski, Mariusz; El-Magd, Rabab M Abou

    2014-01-01

    A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields f...

  13. Mathematical modeling of a V-stack piezoelectric aileron actuation

    Directory of Open Access Journals (Sweden)

    Ioan URSU

    2016-12-01

    Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.

  14. Análisis para la modelación y optimización geométrica de un reactor tipo tornillo sin-fin empleando el método de grafos dicromáticos//Analysis for geometric modeling and optimization of a worm type reactor using the method of dichromatic graph

    Directory of Open Access Journals (Sweden)

    Armando Díaz-Concepción

    2015-09-01

    Full Text Available En el presente trabajo se realiza la modelación, simulación y optimización de un reactor utilizado en las plantas para la obtención de un alimento animal, sobre la base de la predigestión del bagacillo de caña y el hidróxido de calcio en presencia de vapor denominado PREDICAL utilizando grafos dicromáticos. Se obtuvo el modelo matemático para el diseño del reactor, donde se vinculan las variables geométricas y tecnológicas. El modelo formulado permitió la optimización de la variable costo a partir de minimizar la variable geométrica diámetro exterior del reactor. Palabras claves: modelación reactor tipo tornillo sinfin, grafos dicromáticos, modelo matemático________________________________________________________________________________AbstractThe present work performs modeling, simulation and optimization of a reactor used in plants for the obtencion of animal feed. It's made on the basis of pre-digestion of cane bagasse and calcium hydroxide in the presence of steam called PREDICAL and using dichromatic graphs. It was achieved the mathematical model for the design of the reactor, where are linked geometric and technological variables. The model developed allowed cost optimization based on minimize the geometric variable outside diameter of the reactor. Key words: worm type reactor modeling, dichromatic graphs, mathematical model.

  15. Mechanical-mathematical modeling for landslide process

    Science.gov (United States)

    Svalova, V.

    2009-04-01

    500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.

  16. Mathematical modelling and numerical simulation of oil pollution problems

    CERN Document Server

    2015-01-01

    Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics,  together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems.   The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...

  17. Modeling simultaneous carbon and nitrogen removal (SCNR) in anaerobic/anoxic reactor treating domestic wastewater.

    Science.gov (United States)

    Mendes, Carlos; Esquerre, Karla; Queiroz, Luciano Matos

    2016-07-15

    This paper presents a mathematical model based on the Anaerobic Digestion Model No. 1 (ADM1) to simulate the effects of nitrate concentration and hydraulic retention time (HRT) on the simultaneous carbon and nitrogen removal (SCNR) in anaerobic/anoxic reactor treating domestic wastewater. The model was calibrated using previously published experimental data obtained from anaerobic batch tests for different COD/ [Formula: see text] ratios. Model simulations were performed to predict the SCNR in a completely mixed reactor (CSTR) operating under mesophilic conditions (35 °C). Six different scenarios were evaluated to investigate the performance of the SCNR based on typical influent characteristics of domestic wastewater. The variables analyzed were chemical oxygen demand (COD) removal, nitrate concentration, methane production, nitrogen gas, volatile fatty acids (VFA) concentration, pH and percentage of COD used by the denitrifying and methanogenic microorganisms. The HRT was decreased stepwise from 15 to 4 h. The results indicate that Scenario (S5) with a COD/ [Formula: see text] ratio equal to 10 and an HRT equal to 15 h ensures the occurrence of the stable SCNR. Furthermore, the accumulation of denitrification intermediates and a significant reduction in the biogas production when the organic matter is limited was verified.

  18. Problems in experimental and mathematical investigations of the accidental thermalhydraulic processes in RBMK nuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Nigmatulin, B.I.; Tikhonenko, L.K. [Engineering Centre (EREC) for Nuclear Plants Safety, Electrogorsk (Russian Federation); Blinkov, V.N. [Aviation Institute, Kharkov (Ukraine)] [and others

    1995-09-01

    In this paper the thermalhydraulic scheme and peculiarities of the boiling water graphite-moderated channel-type reactor RBMK are presented and discussed shortly. The essential for RBMK transient regimes, accidental situations and accompanying thermalhydraulic phenomena and processes are formulated. These data are presented in the form of cross reference matrix (version 1) for system computer codes verification. The paper includes qualitative analysis of the computer codes and integral facilities which have been used or can be used for RBMK transients and accidents investigations. The stability margins for RBMK-1000 and RBMK-1500 are shown.

  19. Mathematical analysis and uncertain models of a nitrification process

    Energy Technology Data Exchange (ETDEWEB)

    Harmand, J.; Steyer, J.P.; Queinnec, I.; Bernet, N.

    1995-12-31

    The non linear model of a Continuous Strirred Tank Reactor (CSTR) for nitrogen removal, derived from mass balance consideration, can be linearized around a nominal steady state. The analysis of the linear model in terms of stability, observability and controllability allows to highlight the structural properties of the model. Disturbances and uncertainties can then be explicitly expressed in the linear model, such that it completes the modelling in view of a future control scheme of the process. (authors) 13 refs.

  20. Some Aspects of Mathematical Model of Collaborative Learning

    Science.gov (United States)

    Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

    2012-01-01

    There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

  1. Environmental impact assessment of the nuclear reactor at Vinca, based on the data on emission of radioactivity from the literature: A modeling approach

    Directory of Open Access Journals (Sweden)

    Gršić Z.

    2015-01-01

    Full Text Available Research activities of Vinca Institite have been based on two heavy water research reactors: 10 MW one, RA and zero power RB. Reactor RA was operational from 1962 to 1982. In 2010, spent fuel have been sent to the country of origin, and reactor now is in decommissioning. During operational phase of the reactor there were no recorded accidental releases into the environment just operational ones. Results of the environmental impact assessment, of the assumed emission of radionuclides, from the ventilation of nuclear reactor "RA" in Vinca, to the atmospheric boundary layer are presented in this paper. Evaluation was done by using the Gaussian straight-line diffusion model and taking into account characteristics of the reactor ventilation system, the assumed emission release of radioactivity (from the literature, site-specific meteorological data for six-year period and local topography around nuclear reactor, and corresponding dose factors for inventory of radionuclides. Based on the described approach, and assuming that the range of appropriate meteorological data for six year period for the application of described mathematical model is enough for this kind of analysis, it can be concluded that the nuclear reactor "RA", in the course of its work from 1962 to 1982, had no influence on the surrounding environment through the air above regulatory limits. [Projekat Ministarstva nauke Republike Srbije, br. III 45003

  2. Once-through CANDU reactor models for the ORIGEN2 computer code

    Energy Technology Data Exchange (ETDEWEB)

    Croff, A.G.; Bjerke, M.A.

    1980-11-01

    Reactor physics calculations have led to the development of two CANDU reactor models for the ORIGEN2 computer code. The model CANDUs are based on (1) the existing once-through fuel cycle with feed comprised of natural uranium and (2) a projected slightly enriched (1.2 wt % /sup 235/U) fuel cycle. The reactor models are based on cross sections taken directly from the reactor physics codes. Descriptions of the reactor models, as well as values for the ORIGEN2 flux parameters THERM, RES, and FAST, are given.

  3. 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.

  4. Mathematics

    CERN Document Server

    Eringen, A Cemal

    2013-01-01

    Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

  5. Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

    Science.gov (United States)

    Michelsen, Claus

    2015-01-01

    Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

  6. EVALUATION OF PLANING CRAFT MANEUVERABILITY USING MATHEMATICAL MODELING

    Directory of Open Access Journals (Sweden)

    Sajad Hajizadeh

    2016-03-01

    Full Text Available Ship transportation is increasing globally as is risk of collision especially in congested areas is a main concern. Numerical modeling method is major simulation method to predict ship maneuverability. Ship maneuvering in calm water is an important topic to avoid collisions and leads to safe navigation. Therefore reliable ship maneuvering simulations are required for incident analysis and prevention. In recent time within the research community orientated towards ship hydrodynamics an increasing attention has been paid to simultaneous solution of the maneuvering of planing ship problem. The maneuverability of planing crafts has been the subject of many research projects during the last few decades. To assess the maneuverability of planing crafts at the early design stage, reliable simulation models are required. Traditionally, these tools have used empiric descriptions of the forces and moments on the planing craft’s hull. Ship maneuvering calculations, horizontal plane motion control and development of maneuvering simulators need a mathematical description of ship maneuvering. In the recent years, different mathematical models are suggested for maneuvering of displacement vessels that are capable of estimation of vessel maneuvers with acceptable precision. But simulation of planing craft maneuverability through mathematical model is not common yet and is the subject of future research. Maneuvering of planing crafts is influenced greatly by action of rudder. But research efforts have been to include the rudder action in the mathematical models of planing ship maneuvering. In this paper a mathematical model is developed for planing craft maneuvering that includes the rudder forces and moments. Different maneuvers are executed through the mathematical model. Simulations are validated by model tests. Finally the influence of rudder angle on maneuverability of planing ship is studied. The mathematical model and hydrodynamic coefficients presented

  7. Compositional Fragmentation Model for the Oxidation of Sulfide Particles in a Flash Reactor

    Science.gov (United States)

    Parra-Sánchez, Víctor Roberto; Pérez-Tello, Manuel; Duarte-Ruiz, Cirilo Andrés; Sohn, Hong Yong

    2014-04-01

    A mathematical model to predict the size distribution and chemical composition of a cloud of sulfide particles during high-temperature oxidation in a flash reactor is presented. The model incorporates the expansion and further fragmentation of the reacting particles along their trajectories throughout the reaction chamber. A relevant feature of the present formulation is its flexibility to treat a variety of flash reacting systems, such as the flash smelting and flash converting processes. This is accomplished by computing the chemical composition of individual particles and the size distribution and overall composition of the particle cloud in separate modules, which are coupled through a database of particle properties previously stored on disk. The flash converting of solid copper mattes is considered as an example. The model predictions showed good agreement with the experimental data collected in a large laboratory reactor in terms of particle size distribution and sulfur remaining in the population of particles. The cumulative contribution and distribution coefficients are introduced to quantify the relationship between specific particle sizes in the feed and those in the reacted products upon oxidation, the latter of which has practical implications on the amount and chemical composition of dust particles produced during the industrial operation.

  8. The development of mathematical creativity through model-eliciting activities

    Directory of Open Access Journals (Sweden)

    Helena M. Wessels

    2012-03-01

    Full Text Available The ability to think creatively and solve problems is regarded as crucial for economic and personal success. The traditional approach in classrooms is not conducive to mathematical creativity, and prospective teachers should be exposed to alternative problem solving activities through which mathematical knowledge, competencies and creativity can be developed. Research studies have pointed out the possibilities and successes of a modelling approach in which complex, open problems or model-eliciting problems are used to develop meaningful mathematical knowledge and prepare learners for everyday life, as well as for tertiary studies and their occupations. Model-eliciting activities (MEAs do not only develop mathematical knowledge, but also creativity. Five hundred and one preservice Foundation Phase teachers completed different model-eliciting activities (MEAs in a longitudinal project over a period of two years. The purpose was to develop and consolidate their own mathematical knowledge, and at the same time develop creativity and modelling competencies. The ultimate purpose of the project is to prepare preservice teachers to use mathematical modelling to develop creativity in young children aged six to nine. Through solving MEAs learners also build and consolidate their mathematical knowledge and improve their own problem-solving abilities. A framework with four criteria for the identification of creativity was successfully used to evaluate levels of creativity in the solutions offered to the MEAs. Preservice teachers’ final models displayed reasonably consistent levels of creativity regarding the four criteria. Their willingness to solve MEAs and create multiple, original and useful – therefore creative – solutions also increased over the period of their exposure to modelling tasks.

  9. Modelling of gas-liquid reactors - stability and dynamic behaviour of a hydroformylation reactor, influence of mass transfer in the kinetics controlled regime

    NARCIS (Netherlands)

    Elk, E.P. van; Borman, P.C.; Kuipers, J.A.M.; Versteeg, G.F.

    2001-01-01

    On behalf of the development of new hydroformylation reactors, a research project was initiated to examine the dynamics of hydroformylation processes. The current paper presents the results of applying the rigorous reactor model and the approximate reactor model on a new, to be developed, hydroformy

  10. Mathematical Models of Beam and Rails for the Simulation Programs

    Directory of Open Access Journals (Sweden)

    V. A. Trudonoshin

    2015-01-01

    Full Text Available The article considers a mathematical model of the beam adapted for use in general-purpose software systems to analyze dynamic characteristics. The elastic properties of the beam tension, bending and torsion are taken into account. Such a model significantly expands the functional capabilities of the complexes. The mathematical model of the beam designed for the finite element method is taken as a basis. Then its adaptation is carried out taking into account the beam joint to the arbitrary points of a rigid solid, thereby having a model suitable to analyze objects with lumped parameters. Beam parameters are the material parameters, the geometric characteristics, and the coordinates of joint points to the solids.The paper describes in detail the algorithm of computations performed at each step of numerical integration of the systems of ordinary differential equations, and presents an equivalent diagram of the mathematical model of the beam. Mathematical models of elastic rail guides, cylindrical and prismatic, derived from the mathematical model of the beam are more functional compared to the models based on the kinematic equations.The prismatic rail guide (V-guide, unlike the beam, does not counteract the translational motion of solids along it, i.e. only works in torsion and bending, and a deforming part of the rail guide length is variable. The cylindrical rail guide works in bending only. These differences can be easily implemented by modifying the equations of the mathematical model of the beam. Using these models allows us to connect solids by two or more rail guides, and it does not lead to the degeneration of the Jacobi matrix (unlike models based on kinematic equations. The models are implemented in PA8 and PA9 software and methodological support complexes for analysis of dynamic objects developed at the Department of CAD in Bauman MSTU.

  11. Linearized model for the hydrodynamic stability investigation of molten fuel jets into the coolant of a Liquid Metal Fast Breeder Reactor (LMFBR)

    Science.gov (United States)

    Hartel, K.

    1986-02-01

    The hydrodynamic stability of liquid jets in a liquid continuum, both characterized by low viscosity was analyzed. A linearized mathematical model was developed. This model enables the length necessary for fragmentation of a vertical, symmetric jet of molten fuel by hydraulic forces in the coolant of a liquid metal fast breeder reactor to be evaluated. On the basis of this model the FRAG code for numerical calculation of the hydrodynamic fragmentation mechanism was developed.

  12. Hdr reactor containment fire modeling with Br12

    Energy Technology Data Exchange (ETDEWEB)

    Rockett, J.A.; Keski-Rahkonen, O.; Heikkilae, L.

    1992-01-01

    Fire tests at the German test reactor, HDR, were simulated using a Japanese zone model code, BRI2. Eight and ten room models of the containment building were developed. Critical phenomena occurring during simulation were explored. BRI2 can be used for this type of work but care must be exercised where a side wind increases entrainment by the fire plume. Horizontal vents were described by effective vertical vents. The effect of location of the vent to the ambient was found critical during severely oxygen limited burning. (Copyright (c) Valtion teknillinen tutkimuskeskus (VTT) 1992.)

  13. Mathematical Modeling of the Induced Mutation Process in Bacterial Cells

    Science.gov (United States)

    Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.

    2010-01-01

    A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.

  14. High Flux Isotope Reactor system RELAP5 input model

    Energy Technology Data Exchange (ETDEWEB)

    Morris, D.G.; Wendel, M.W.

    1993-01-01

    A thermal-hydraulic computational model of the High Flux Isotope Reactor (HFIR) has been developed using the RELAP5 program. The purpose of the model is to provide a state-of-the art thermal-hydraulic simulation tool for analyzing selected hypothetical accident scenarios for a revised HFIR Safety Analysis Report (SAR). The model includes (1) a detailed representation of the reactor core and other vessel components, (2) three heat exchanger/pump cells, (3) pressurizing pumps and letdown valves, and (4) secondary coolant system (with less detail than the primary system). Data from HFIR operation, component tests, tests in facility mockups and the HFIR, HFIR specific experiments, and other pertinent experiments performed independent of HFIR were used to construct the model and validate it to the extent permitted by the data. The detailed version of the model has been used to simulate loss-of-coolant accidents (LOCAs), while the abbreviated version has been developed for the operational transients that allow use of a less detailed nodalization. Analysis of station blackout with core long-term decay heat removal via natural convection has been performed using the core and vessel portions of the detailed model.

  15. 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...... where the co-contaminants were oxidized. The results of the model further indicate that contradicting findings in the literature about the effects of BTEX on the degradation of MTBE are mainly due to differences in the study methodologies. Effects such as short-term toxicity of BTEX and the lack...

  16. BUILDING MATHEMATICAL MODELS IN DYNAMIC PROGRAMMING

    Directory of Open Access Journals (Sweden)

    LIANA RODICA PATER

    2012-05-01

    Full Text Available In short, we can say that dynamic programming is a method of optimization of systems, using their mathematical representation in phases or sequences or as we say, periods. Such systems are common in economic studies at the implementation of programs on the most advanced techniques, such as for example that involving cosmic navigation. Another concept that is involved in the study of dynamic programs is the economic horizon (number of periods or phases that a dynamic program needs. This concept often leads to the examination of the convergence of certain variables on infinite horizon. In many cases from the real economy by introducing updating, dynamic programs can be made convergent.

  17. Plasma Reactors and Plasma Thrusters Modeling by Ar Complete Global Models

    Directory of Open Access Journals (Sweden)

    Chloe Berenguer

    2012-01-01

    Full Text Available A complete global model for argon was developed and adapted to plasma reactor and plasma thruster modeling. It takes into consideration ground level and excited Ar and Ar+ species and the reactor and thruster form factors. The electronic temperature, the species densities, and the ionization percentage, depending mainly on the pressure and the absorbed power, have been obtained and commented for various physical conditions.

  18. Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis.

    Science.gov (United States)

    Olivieri, Giuseppe; Russo, Maria Elena; Marzocchella, Antonio; Salatino, Piero

    2011-01-01

    A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular-supported biofilm: biofilm growth and detachment, gas-liquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady-state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas-liquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady-state scenario with transcritical and saddle-node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011.

  19. Investigation of the Air-Argon-Steel-Slag Flow in an Industrial RH Reactor with VOF-DPM Coupled Model

    Science.gov (United States)

    Chen, Gujun; He, Shengping; Li, Yugang

    2017-08-01

    A coupled three-dimensional volume of fluid method-discrete phase model (VOF-DPM) is developed to investigate the air-argon-steel-slag flow in an industrial Rheinsahl-Heraeus (RH) reactor while considering the expansion of argon bubbles. The simulated results of mixing time and recirculation flow rate of molten steel, and the flow pattern and local velocity of water agree well with the measured results reported in the literature. Comparison of the results with and without consideration of the expansion of bubbles indicates that the expansion of bubbles has an enormous impact on the multiphase flow in the industrial RH reactor. The proposed mathematical model presents a more realistic free surface in the RH vacuum vessel.

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

    Science.gov (United States)

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

    2016-09-01

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

  1. An evaluation of mathematical models for predicting skin permeability.

    Science.gov (United States)

    Lian, Guoping; Chen, Longjian; Han, Lujia

    2008-01-01

    A number of mathematical models have been proposed for predicting skin permeability, mostly empirical and very few are deterministic. Early empirical models use simple lipophilicity parameters. The recent trend is to use more complicated molecular structure descriptors. There has been much debate on which models best predict skin permeability. This article evaluates various mathematical models using a comprehensive experimental dataset of skin permeability for 124 chemical compounds compiled from various sources. Of the seven models compared, the deterministic model of Mitragotri gives the best prediction. The simple quantitative structure permeability relationships (QSPR) model of Potts and Guy gives the second best prediction. The two models have many features in common. Both assume the lipid matrix as the pathway of transdermal permeation. Both use octanol-water partition coefficient and molecular size. Even the mathematical formulae are similar. All other empirical QSPR models that use more complicated molecular structure descriptors fail to provide satisfactory prediction. The molecular structure descriptors in the more complicated QSPR models are empirically related to skin permeation. The mechanism on how these descriptors affect transdermal permeation is not clear. Mathematically it is an ill-defined approach to use many colinearly related parameters rather than fewer independent parameters in multi-linear regression.

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

    Science.gov (United States)

    Bezruchko, Boris P.; Smirnov, Dmitry A.

    Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.

  3. Mathematical model of layered metallurgical furnaces and units

    Science.gov (United States)

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

    2016-09-01

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

  4. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  5. What Is Known about Elementary Grades Mathematical Modelling

    Directory of Open Access Journals (Sweden)

    Micah S. Stohlmann

    2016-01-01

    Full Text Available Mathematical modelling has often been emphasized at the secondary level, but more research is needed at the elementary level. This paper serves to summarize what is known about elementary mathematical modelling to guide future research. A targeted and general literature search was conducted and studies were summarized based on five categories: content of mathematical modelling intervention, assessment data collected, unit of analysis studied, population, and effectiveness. It was found that there were three main units of analysis into which the studies could be categorized: representational and conceptual competence, models created, and student beliefs. The main findings from each of these units of analysis are discussed along with future research that is needed.

  6. Analysis of mathematical model for micromechanical vibratory wheel gyroscope

    Institute of Scientific and Technical Information of China (English)

    LUO Yue-sheng; FAN Chong-jin; TAN Zhen-fan

    2003-01-01

    By the sketch of structure of MVWG,the working laws of this kind of gyroscope were explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.

  7. Predictive control applied to an evaporator mathematical model

    Directory of Open Access Journals (Sweden)

    Daniel Alonso Giraldo Giraldo

    2010-07-01

    Full Text Available This paper outlines designing a predictive control model (PCM applied to a mathematical model of a falling film evaporator with mechanical steam compression like those used in the dairy industry. The controller was designed using the Connoisseur software package and data gathered from the simulation of a non-linear mathematical model. A control law was obtained from minimising a cost function sublect to dynamic system constraints, using a quadratic programme (QP algorithm. A linear programming (LP algorithm was used for finding a sub-optimal operation point for the process in stationary state.

  8. Dependability breakeven point mathematical model for production - quality strategy support

    Science.gov (United States)

    Vilcu, Adrian; Verzea, Ion; Chaib, Rachid

    2016-08-01

    This paper connects the field of dependability system with the production-quality strategies through a new mathematical model based on breakeven points. The novelties consist in the identification of the parameters of dependability system which, in safety control, represents the degree to which an item is capable of performing its required function at any randomly chosen time during its specified operating period disregarding non-operation related influences, as well as the analysis of the production-quality strategies, defining a mathematical model based on a new concept - dependability breakeven points, model validation on datasets and shows the practical applicability of this new approach.

  9. Solutions manual to accompany finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

    A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

  10. MELCOR Model Development of High Temperature Gas-cooled Reactor

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Changyong; Huh, Changwook [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)

    2013-05-15

    The High Temperature Gas-cooled Reactor is one of the major challenging issues on the development of licensing technology for HTGR. The safety evaluation tools of HTGR can be developed in two ways - development of new HTGR-specific codes or revision of existing codes. The KINS is considering using existing analytic tools to the extent feasible, with appropriate modifications for the intended purpose. The system-level MELCOR code is traditionally used for LWR safety analysis, which is capable of performing thermal-fluid and accident analysis, including fission-product transport and release. Recently, this code is being modified for the NGNP HTGR by the NRC. In this study, the MELCOR input model for HTGR with Reactor Cavity Cooling System (RCCS) was developed and the steady state performance was analyzed to evaluate the applicability in HTGR. HTGR model with design characteristics of GT-MHR was developed using MELCOR 2.1 code to validate the applicability of MELCOR code to HTGR. In addition, the steady state of GT-MHR was analyzed with the developed model. It was evaluated to predict well the design parameters of GT-MHR. The developed model can be used as the basis for accident analysis of HTGR with further update of packages such as Radio Nuclide (RN) package.

  11. Meso-scale modeling of irradiated concrete in test reactor

    Energy Technology Data Exchange (ETDEWEB)

    Giorla, A. [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Vaitová, M. [Czech Technical University, Thakurova 7, 166 29 Praha 6 (Czech Republic); Le Pape, Y., E-mail: lepapeym@ornl.gov [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Štemberk, P. [Czech Technical University, Thakurova 7, 166 29 Praha 6 (Czech Republic)

    2015-12-15

    Highlights: • A meso-scale finite element model for irradiated concrete is developed. • Neutron radiation-induced volumetric expansion is a predominant degradation mode. • Confrontation with expansion and damage obtained from experiments is successful. • Effects of paste shrinkage, creep and ductility are discussed. - Abstract: A numerical model accounting for the effects of neutron irradiation on concrete at the mesoscale is detailed in this paper. Irradiation experiments in test reactor (Elleuch et al., 1972), i.e., in accelerated conditions, are simulated. Concrete is considered as a two-phase material made of elastic inclusions (aggregate) subjected to thermal and irradiation-induced swelling and embedded in a cementitious matrix subjected to shrinkage and thermal expansion. The role of the hardened cement paste in the post-peak regime (brittle-ductile transition with decreasing loading rate), and creep effects are investigated. Radiation-induced volumetric expansion (RIVE) of the aggregate cause the development and propagation of damage around the aggregate which further develops in bridging cracks across the hardened cement paste between the individual aggregate particles. The development of damage is aggravated when shrinkage occurs simultaneously with RIVE during the irradiation experiment. The post-irradiation expansion derived from the simulation is well correlated with the experimental data and, the obtained damage levels are fully consistent with previous estimations based on a micromechanical interpretation of the experimental post-irradiation elastic properties (Le Pape et al., 2015). The proposed modeling opens new perspectives for the interpretation of test reactor experiments in regards to the actual operation of light water reactors.

  12. Control Rod Driveline Reactivity Feedback Model for Liquid Metal Reactors

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Young-Min; Jeong, Hae-Yong; Chang, Won-Pyo; Cho, Chung-Ho; Lee, Yong-Bum

    2008-01-15

    The thermal expansion of the control rod drivelines (CRDL) is one important passive mitigator under all unprotected accident conditions in the metal and oxide cores. When the CRDL are washed by hot sodium in the coolant outlet plenum, the CRDL thermally expands and causes the control rods to be inserted further down into the active core region, providing a negative reactivity feedback. Since the control rods are attached to the top of the vessel head and the core attaches to the bottom of the reactor vessel (RV), the expansion of the vessel wall as it heats will either lower the core or raise the control rods supports. This contrary thermal expansion of the reactor vessel wall pulls the control rods out of the core somewhat, providing a positive reactivity feedback. However this is not a safety factor early in a transient because its time constant is relatively large. The total elongated length is calculated by subtracting the vessel expansion from the CRDL expansion to determine the net control rod expansion into the core. The system-wide safety analysis code SSC-K includes the CRDL/RV reactivity feedback model in which control rod and vessel expansions are calculated using single-nod temperatures for the vessel and CRDL masses. The KALIMER design has the upper internal structures (UIS) in which the CRDLs are positioned outside the structure where they are exposed to the mixed sodium temperature exiting the core. A new method to determine the CRDL expansion is suggested. Two dimensional hot pool thermal hydraulic model (HP2D) originally developed for the analysis of the stratification phenomena in the hot pool is utilized for a detailed heat transfer between the CRDL mass and the hot pool coolant. However, the reactor vessel wall temperature is still calculated by a simple lumped model.

  13. Mathematical modeling of a rotary hearth coke calciner

    Directory of Open Access Journals (Sweden)

    Hilde C. Meisingset

    1995-10-01

    Full Text Available A mathematical model of a rotary hearth coke calciner is developed. The model is based on first principles including the most important dynamic phenomena. The model is a thermodynamic model involving heat and mass transfer and chemical reactions. Fundamental mass and energy balance equations for the coke phase, the gas phase and the lining are formulated. For the gas phase, a stationary model is used. The equations are solved numerically, and simulated temperature profiles are shown in this paper.

  14. Mathematical Models of the Sinusoidal Screen Family

    Directory of Open Access Journals (Sweden)

    Tajana Koren

    2011-06-01

    Full Text Available In this paper we will define a family of sinusoidal screening elements and explore the possibilities of their application in graphic arts, securities printing and design solutions in photography and typography editing. For this purpose mathematical expressions of sinusoidal families were converted into a Postscript language. The introduction of a random variable results in a countless number of various mutations which cannot be repeated without knowing the programming code itself. The use of the family of screens in protection of securities is thus of great importance. Other possible application of modulated sinusoidal screens is related to the large format color printing. This paper will test the application of sinusoidal screens in vector graphics, pixel graphics and typography. The development of parameters in the sinusoidal screen element algorithms gives new forms defined within screening cells with strict requirements of coverage implementation. Individual solutions include stochastic algorithms, as well as the autonomy of screening forms in regard to multicolor printing channels.

  15. Mathematics

    CERN Document Server

    Stein, Sherman K

    2010-01-01

    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  16. Discrete element modelling of pebble packing in pebble bed reactors

    Energy Technology Data Exchange (ETDEWEB)

    Suikkanen, Heikki, E-mail: heikki.suikkanen@lut.fi; Ritvanen, Jouni, E-mail: jouni.ritvanen@lut.fi; Jalali, Payman, E-mail: payman.jalali@lut.fi; Kyrki-Rajamäki, Riitta, E-mail: riitta.kyrki-rajamaki@lut.fi

    2014-07-01

    Highlights: • A discrete element method code is developed for pebble bed reactor analyses. • Methods are established to extract packing information at various spatial scales. • Packing simulations inside annular core geometry are done varying input parameters. • The restitution coefficient has the strongest effect on the resulting packing density. • Detailed analyses reveal local densification especially near the walls. - Abstract: It is important to understand the packing characteristics and behaviour of the randomly packed pebble bed to further analyse the reactor physical and thermal-hydraulic behaviour and to design a safe and economically feasible pebble bed reactor. The objective of this work was to establish methods to model and analyse the pebble packing in detail to provide useful tools and data for further analyses. Discrete element method (DEM) is a well acknowledged method for analysing granular materials, such as the fuel pebbles in a pebble bed reactor. In this work, a DEM computer code was written specifically for pebble bed analyses. Analysis methods were established to extract data at various spatial scales from the pebble beds resulting from the DEM simulations. A comparison with available experimental data was performed to validate the DEM implementation. To test the code implementation in full-scale reactor calculations, DEM packing simulations were done in annular geometry with 450,000 pebbles. Effects of the initial packing configuration, friction and restitution coefficients and pebble size distribution to the resulting pebble bed were investigated. The packing simulations revealed that from the investigated parameters the restitution coefficient had the largest effect on the resulting average packing density while other parameters had smaller effects. Detailed local packing density analysis of pebble beds with different average densities revealed local variations especially strong in the regions near the walls. The implemented DEM

  17. An integration scheme for stiff solid-gas reactor models

    Directory of Open Access Journals (Sweden)

    Bjarne A. Foss

    2001-04-01

    Full Text Available Many dynamic models encounter numerical integration problems because of a large span in the dynamic modes. In this paper we develop a numerical integration scheme for systems that include a gas phase, and solid and liquid phases, such as a gas-solid reactor. The method is based on neglecting fast dynamic modes and exploiting the structure of the algebraic equations. The integration method is suitable for a large class of industrially relevant systems. The methodology has proven remarkably efficient. It has in practice performed excellent and been a key factor for the success of the industrial simulator for electrochemical furnaces for ferro-alloy production.

  18. MATHEMATIC MODEL FOR SITY BUS SCHEDULING IN YOGYAKARTA

    Directory of Open Access Journals (Sweden)

    Sahid Sahid

    2016-05-01

    Full Text Available Various methods can be used to construct a mathematical model of the transportation problems. One model that can be used is a linear model. Several studies have used a linear model to get the schedule and the optimal route of bus trips. This research will build a mathematical model of a city bus transportation problems in DIY using linear models. Linear model is built to get the condition density city bus passengers on shifts respectively that morning, noon, and evening. After finding a suitable model, applied to the bus passengers data in Yogyakarta. From these results it can be seen the optimum conditions in terms of density, because the condition of the city bus at this time that quiet enthusiasts. Besides, the optimum density at each shift in the morning is 11 passengers, 10 passengers during the day, and evening 9 passengers.   Keywords: transportation problems, the linear model, the optimal route, density

  19. MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM

    Directory of Open Access Journals (Sweden)

    Olha Sushchenko

    2017-07-01

    Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.

  20. Mathematical modelling as basis for efficient enterprise management

    Directory of Open Access Journals (Sweden)

    Kalmykova Svetlana

    2017-01-01

    Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.

  1. Invention software support by integrating function and mathematical modeling

    NARCIS (Netherlands)

    Chechurin, L.S.; Wits, Wessel Willems; Bakker, H.M.

    2015-01-01

    New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a

  2. Invention software support by integrating function and mathematical modeling

    NARCIS (Netherlands)

    Chechurin, L.S.; Wits, W.W.; Bakker, H.M.

    2015-01-01

    New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a

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

    Science.gov (United States)

    Millat, Thomas; Winzer, Klaus

    2017-03-01

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

  4. Mathematical 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.

  5. Applicability of mathematical modeling to problems of environmental physiology

    Science.gov (United States)

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

    1988-01-01

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

  6. The Singing Wineglass: An Exercise in Mathematical Modelling

    Science.gov (United States)

    Voges, E. L.; Joubert, S. V.

    2008-01-01

    Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

  7. Use of mathematical modeling in nuclear measurements projects

    Energy Technology Data Exchange (ETDEWEB)

    Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A. [AREVA/CANBERRA Nuclear Measurements Business Unit, Saint Quentin-en-Yvelines 78182 (France); Chany, P. [AREVA/BE Nuclear Sites Value Development AREVA NC Marcoule, BP 76170, 30206 Bagnols Sur Ceze (France); Devita, A. [AREVA/BE MELOX, BP 124, 30206 Bagnols Sur Ceze (France)

    2011-07-01

    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)

  8. Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling

    NARCIS (Netherlands)

    Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.

    2004-01-01

    A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use

  9. Analysis of rear end impact using mathematical human modelling

    NARCIS (Netherlands)

    Happee, R.; Meijer, R.; Horst, M.J. van der; Ono, K.; Yamazaki, K.

    2000-01-01

    At TNO an omni-directional mathematical human body model has been developed. Until now this human model has been validated for frontal and lateral loading using response data of volunteer and post mortem human subject (PMHS) sled tests. For rearward loading it has been validated for high speed impac

  10. Mathematical modelling in blood coagulation : simulation and parameter estimation

    NARCIS (Netherlands)

    W.J.H. Stortelder (Walter); P.W. Hemker (Piet); H.C. Hemker

    1997-01-01

    textabstractThis paper describes the mathematical modelling of a part of the blood coagulation mechanism. The model includes the activation of factor X by a purified enzyme from Russel's Viper Venom (RVV), factor V and prothrombin, and also comprises the inactivation of the products formed. In this

  11. Metaphors and Models in Translation between College and Workplace Mathematics

    Science.gov (United States)

    Williams, Julian; Wake, Geoff

    2007-01-01

    We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

  12. Metaphors and Models in Translation between College and Workplace Mathematics

    Science.gov (United States)

    Williams, Julian; Wake, Geoff

    2007-01-01

    We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

  13. Mathematical modeling of steel fiber concrete under dynamic impact

    Science.gov (United States)

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

    2015-01-01

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

  14. Mathematical and computational modeling simulation of solar drying Systems

    Science.gov (United States)

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

  15. A Mathematical Model for Comparing Holland's Personality and Environmental Codes.

    Science.gov (United States)

    Kwak, Junkyu Christopher; Pulvino, Charles J.

    1982-01-01

    Presents a mathematical model utilizing three-letter codes of personality patterns determined from the Self Directed Search. This model compares personality types over time or determines relationships between personality types and person-environment interactions. This approach is consistent with Holland's theory yet more comprehensive than one- or…

  16. Mathematical models of a diffusion-convection in porous media

    Directory of Open Access Journals (Sweden)

    Anvarbek M. Meirmanov

    2012-06-01

    Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.

  17. Mathematical model of two-phase flow in accelerator channel

    Directory of Open Access Journals (Sweden)

    О.Ф. Нікулін

    2010-01-01

    Full Text Available  The problem of  two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in  counter jet mill accelerator channel design.

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

    Science.gov (United States)

    McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

    2013-10-01

    This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

  19. Mathematically Modeling Parameters Influencing Surface Roughness in CNC Milling

    Directory of Open Access Journals (Sweden)

    Engin Nas

    2012-01-01

    Full Text Available In this study, steel AISI 1050 is subjected to process of face milling in CNC milling machine and such parameters as cutting speed, feed rate, cutting tip, depth of cut influencing the surface roughness are investigated experimentally. Four different experiments are conducted by creating different combinations for parameters. In conducted experiments, cutting tools, which are coated by PVD method used in forcing steel and spheroidal graphite cast iron are used. Surface roughness values, which are obtained by using specified parameters with cutting tools, are measured and correlation between measured surface roughness values and parameters is modeled mathematically by using curve fitting algorithm. Mathematical models are evaluated according to coefficients of determination (R2 and the most ideal one is suggested for theoretical works. Mathematical models, which are proposed for each experiment, are estipulated.

  20. Random curds as mathematical models of fractal rhythm in architecture

    Directory of Open Access Journals (Sweden)

    Ćirović Ivana

    2014-01-01

    Full Text Available The author Carl Bovill has suggested and described a method for generating rhythm in architecture with the help of random curds, as they are the mathematical models of unpredictable and uneven groupings which he recognizes in natural shapes and in natural processes. He specified the rhythm generated in this way as the fractal rhythm. Random curds can be generated by a simple process of curdling, as suggested by B. Mandelbrot. This paper examines the way in which the choice of probability for every stage or level of the curdling process, and the number of stages in the procedure of curdling, affect the characteristics of the obtained fractal object as a potential mathematical model of rhythm in the design process. At the same time, this paper examines the characteristics of rhythm in architecture which determine whether the obtained fractal object will be accepted as an appropriate mathematical model of the observed rhythm.