Railway bogie vibration analysis by mathematical simulation model and a scaled four-wheel railway bogie set

Science.gov (United States)

Visayataksin, Noppharat; Sooklamai, Manon

2018-01-01

The bogie is the part that connects and transfers all the load from the vehicle body onto the railway track; interestingly the interaction between wheels and rails is the critical point for derailment of the rail vehicles. However, observing or experimenting with real bogies on rail vehicles is impossible due to the operational rules and safety concerns. Therefore, this research aimed to develop a vibration analysis set for a four-wheel railway bogie by constructing a four-wheel bogie with scale of 1:4.5. The bogie structures, including wheels and axles, were made from an aluminium alloy, equipped with springs and dampers. The bogie was driven by an electric motor using 4 round wheels instead of 2 straight rails, with linear velocity between 0 to 11.22 m/s. The data collected from the vibration analysis set was compared to the mathematical simulation model to investigate the vibration behavior of the bogie, especially the hunting motion. The results showed that vibration behavior from a scaled four-wheel railway bogie set significantly agreed with the mathematical simulation model in terms of displacement and hunting frequency. The critical speed of the wheelset was found by executing the mathematical simulation model at 13 m/s.

Comparison among mathematical models of the photovoltaic cell for computer simulation purposes

Science.gov (United States)

Tofoli, Fernando Lessa; Pereira, Denis de Castro; Josias De Paula, Wesley; Moreira Vicente, Eduardo; Vicente, Paula dos Santos; Braga, Henrique Antonio Carvalho

2017-07-01

This paper presents a comparison among mathematical models used in the simulation of solar photovoltaic modules that can be easily integrated with power electronic converters. In order to perform the analysis, three models available in literature and also the physical model of the module in software PSIM® are used. Some results regarding the respective I × V and P × V curves are presented, while some advantages and eventual limitations are discussed. Besides, a DC-DC buck converter performs maximum power point tracking by using perturb and observe method, while the performance of each one of the aforementioned models is investigated.

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

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

A mathematical model for the simulation of thermal transients in the water loop of IPEN

International Nuclear Information System (INIS)

Pontedeiro, A.C.

1980-01-01

A mathematical model for simulation of thermal transients in the water loop at the Instituto de Pesquisas Energeticas e Nucleares, Sao Paulo, Brasil, is developed. The model is based on energy equations applied to the components of the experimental water loop. The non-linear system of first order diferencial equations and of non-linear algebraic equations obtained through the utilization of the IBM 'System/360-Continous System Modeling Program' (CSMP) is resolved. An optimization of the running time of the computer is made and a typical simulation of the water loop is executed. (Author) [pt

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

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

Science.gov (United States)

Pawar, Sumedh; Sharma, Atul

2018-01-01

This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

Mathematical modelling and simulation of the thermal performance of a solar heated indoor swimming pool

Directory of Open Access Journals (Sweden)

Mančić Marko V.

2014-01-01

Full Text Available Buildings with indoor swimming pools have a large energy footprint. The source of major energy loss is the swimming pool hall where air humidity is increased by evaporation from the pool water surface. This increases energy consumption for heating and ventilation of the pool hall, fresh water supply loss and heat demand for pool water heating. In this paper, a mathematical model of the swimming pool was made to assess energy demands of an indoor swimming pool building. The mathematical model of the swimming pool is used with the created multi-zone building model in TRNSYS software to determine pool hall energy demand and pool losses. Energy loss for pool water and pool hall heating and ventilation are analyzed for different target pool water and air temperatures. The simulation showed that pool water heating accounts for around 22%, whereas heating and ventilation of the pool hall for around 60% of the total pool hall heat demand. With a change of preset controller air and water temperatures in simulations, evaporation loss was in the range 46-54% of the total pool losses. A solar thermal sanitary hot water system was modelled and simulated to analyze it's potential for energy savings of the presented demand side model. The simulation showed that up to 87% of water heating demands could be met by the solar thermal system, while avoiding stagnation. [Projekat Ministarstva nauke Republike Srbije, br. III 42006: Research and development of energy and environmentally highly effective polygeneration systems based on using renewable energy sources

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,...

Mathematical simulation of oil reservoir properties

International Nuclear Information System (INIS)

Ramirez, A.; Romero, A.; Chavez, F.; Carrillo, F.; Lopez, S.

2008-01-01

The study and computational representation of porous media properties are very important for many industries where problems of fluid flow, percolation phenomena and liquid movement and stagnation are involved, for example, in building constructions, ore processing, chemical industries, mining, corrosion sciences, etc. Nevertheless, these kinds of processes present a noneasy behavior to be predicted and mathematical models must include statistical analysis, fractal and/or stochastic procedures to do it. This work shows the characterization of sandstone berea core samples which can be found as a porous media (PM) in natural oil reservoirs, rock formations, etc. and the development of a mathematical algorithm for simulating the anisotropic characteristics of a PM based on a stochastic distribution of some of their most important properties like porosity, permeability, pressure and saturation. Finally a stochastic process is used again to simulated the topography of an oil reservoir

Steel heat treating: mathematical modelling and numerical simulation of a problem arising in the automotive industry

Directory of Open Access Journals (Sweden)

Jose Manuel Diaz Moreno

2017-12-01

Full Text Available We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile. The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue. The high hardness is due to the phase transformation of steel accompanying the rapid cooling. This work takes into account both heating-cooling stage and viscoplastic model. Once the general mathematical formulation is derived, we can perform some numerical simulations.

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...

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

2002-01-01

A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

Mathematical model of compact type evaporator

Science.gov (United States)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

Hard and soft mathematical models for simulation in some analytical chemical system. Modelos matematicos duros y blandos para la simulacion de sistemas quimicos analiticos

Energy Technology Data Exchange (ETDEWEB)

Lacalle, P.

1989-07-01

In order to determine ion-metallic species with xantene derivates as reagents, different mathematical models in some ion-pair spectrophotometric system have been applied haro mathematical models-based in physical-chemical laws-versus soft mathematical models-empirical and ranoom-have been compared explicits mathematical functions for simulation and optimization of the studied system have been obtained. That optimization has been done using some derivaties methods. Stochastics models in time-dependent systems have been applied. (Author)

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

An Equivalent Electrical Circuit Model of Proton Exchange Membrane Fuel Cells Based on Mathematical Modelling

Directory of Open Access Journals (Sweden)

Dinh An Nguyen

2012-07-01

Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.

Mathematics of large eddy simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Berselli, L.C. [Pisa Univ. (Italy). Dept. of Applied Mathematics ' ' U. Dini' ' ; Iliescu, T. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Mathematics; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics

2006-07-01

Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive development and has matured into a highly-developed computational technology. It uses the tools of turbulence theory and the experience gained from practical computation. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations. The authors give a mathematically informed and detailed treatment of an interesting selection of models, focusing on issues connected with understanding and expanding the correctness and universality of LES. This volume offers a useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations. Non-mathematicians will appreciate it as a reference that introduces them to current tools and advances in the mathematical theory of LES. (orig.)

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise

Science.gov (United States)

Lau, Kevin D.; Asrress, Kaleab N.; Redwood, Simon R.; Figueroa, C. Alberto

2016-01-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. PMID:26945076

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise.

Science.gov (United States)

Arthurs, Christopher J; Lau, Kevin D; Asrress, Kaleab N; Redwood, Simon R; Figueroa, C Alberto

2016-05-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. Copyright © 2016 the American Physiological Society.

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...

Mathematics Career Simulations: An Invitation

Science.gov (United States)

Sinn, Robb; Phipps, Marnie

2013-01-01

A simulated academic career was combined with inquiry-based learning in an upper-division undergraduate mathematics course. Concepts such as tenure, professional conferences and journals were simulated. Simulation procedures were combined with student-led, inquiry-based classroom formats. A qualitative analysis (ethnography) describes the culture…

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

A mathematical model for postirradiation immunity

International Nuclear Information System (INIS)

Smirnova, O.A.

1988-01-01

A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases

MATHEMATICAL MODEL FOR THE SIMULATION OF WATER QUALITY IN RIVERS USING THE VENSIM PLE® SOFTWARE

Directory of Open Access Journals (Sweden)

Julio Cesar de S. I. Gonçalves

2013-06-01

Full Text Available Mathematical modeling of water quality in rivers is an important tool for the planning and management of water resources. Nevertheless, the available models frequently show structural and functional limitations. With the objective of reducing these drawbacks, a new model has been developed to simulate water quality in rivers under unsteady conditions; this model runs on the Vensim PLE® software and can also be operated for steady-state conditions. The following eighteen water quality variables can be simulated: DO, BODc, organic nitrogen (No, ammonia nitrogen (Na, nitrite (Ni, nitrate (Nn, organic and inorganic phosphorus (Fo and Fi, respectively, inorganic solids (Si, phytoplankton (F, zooplankton (Z, bottom algae (A, detritus (D, total coliforms (TC, alkalinity (Al., total inorganic carbon (TIC, pH, and temperature (T. Methane as well as nitrogen and phosphorus compounds that are present in the aerobic and anaerobic layers of the sediment can also be simulated. Several scenarios were generated for computational simulations produced using the new model by using the QUAL2K program, and, when possible, analytical solutions. The results obtained using the new model strongly supported the results from the QUAL family and analytical solutions.

Mathematical Modelling of Unmanned Aerial Vehicles

Directory of Open Access Journals (Sweden)

Saeed Sarwar

2013-04-01

Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV

Mathematical modelling of unmanned aerial vehicles

International Nuclear Information System (INIS)

Sarwar, S.; Rehman, S.U.

2013-01-01

UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)

Mathematical Simulation of High-Conversion Binary Copolymerization

Institute of Scientific and Technical Information of China (English)

JiangWei; QinJiguang

2005-01-01

A new model for mathematical simulation of high-conversion binary copolymerization was established by combination of the concept of the three stage polymerization model (TSPM) proposed by Qin et al. for bulk free radical homopolymerization with the North equation to describe high-conversion copolymerization reaction exhibiting a strong gel effect, and the mathematical expressions of this new model were derived. Like TSPM, the new model also assmnes that the whole course of binary copolymerization can be divided into three different stages: low conversion, gel effect and glass effect stages. In addition, the reaction rate constants and the initiator efficiency at each copolymerization stage do not vary with conversion. Based on the expressions derived, a plot method for determining the overall rate constants and critical conversions was proposed. The literature data on conversion history for styrene (St)-methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDMA)-MMA copolymerizations were treated to examine the model, which shows that the model is satisfactory.

Stochastic modeling analysis and simulation

CERN Document Server

Nelson, Barry L

1995-01-01

A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se

Mathematical modeling of reciprocating pump

International Nuclear Information System (INIS)

Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo

2015-01-01

A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.

Model reduction for circuit simulation

CERN Document Server

Hinze, Michael; Maten, E Jan W Ter

2011-01-01

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the devi

An Integrated Approach to Mathematical Modeling: A Classroom Study.

Science.gov (United States)

Doerr, Helen M.

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

A mathematical model for camera calibration based on straight lines

Directory of Open Access Journals (Sweden)

Antonio M. G. Tommaselli

2005-12-01

Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.

Mathematical modeling of a convective textile drying process

Directory of Open Access Journals (Sweden)

G. Johann

2014-12-01

Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.

Mathematical model simulation of a diesel spill in the Potomac River

International Nuclear Information System (INIS)

Feng, S.S.; Nicolette, J.P.; Markarian, R.K.

1995-01-01

A mathematical modeling technique was used to simulate the transport and fate of approximately 400,000 gallons of spilled diesel fuel and its impact on the aquatic biota in the Potomac River and Sugarland Run. Sugarland Run is a tributary about 21 miles upstream from Washington, DC. The mass balance model predicted the dynamic (spatial and temporal) distribution of spilled oil. The distributions were presented in terms of surface oil slick and sheen, dissolved and undissolved total petroleum hydrocarbons (TPH) in the water surface, water column, river sediments, shoreline and atmosphere. The processes simulated included advective movement, dispersion, dissolution, evaporation, volatilization, sedimentation, shoreline deposition, biodegradation, and removal of oil from cleanup operations. The model predicted that the spill resulted in a water column dissolved TPH concentration range of 0.05 to 18.6 ppm in Sugarland Run. The spilled oil traveled 10 miles along Sugarland Run before it reached the Potomac River. At the Potomac River, the water column TPH concentration was predicted to have decreased to the range of 0.0 to 0.43 ppm. These levels were consistent with field samples. To assess biological injury, the model used 4, 8, 24, 48, and 96-hr LC values in computing the fish injury caused by the fuel oil. The model used the maximum running average of dissolved TPH and exposure time to predict levels of fish mortality in the range of 38 to 40% in Sugarland Run. This prediction was consistent with field fisheries surveys. The model also computed the amount of spilled oil that adsorbed and settled into the river sediments

Some Fundamental Issues of Mathematical Simulation in Biology

Science.gov (United States)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Mathematical and physical modeling of rainfall in centrifuge

OpenAIRE

CAICEDO, Bernardo; THOREL, Luc; TRISTANCHO, Julian

2015-01-01

Rainfall simulation in centrifuge models is important for modelling soil-atmosphere interactions. However, the presence of Coriolis force, drag forces, evaporation and wind within the centrifuge may affect the distribution of rainfall over the model. As a result, development of appropriate centrifuge rain simulators requires a demanding process of experimental trial and error. This paper highlights the key factors involved in controlling rainfall in centrifuge simulations, develops a mathemat...

On the mathematical modeling of memristors

KAUST Repository

Radwan, Ahmed G.

2012-10-06

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

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

Mathematical Modeling 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…

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

DEFF Research Database (Denmark)

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

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

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical 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...

A mathematical framework for agent based models of complex biological networks.

Science.gov (United States)

Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2011-07-01

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

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.

Mathematical modeling of laser lipolysis

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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

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

Science.gov (United States)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization

Development of a selection support expert system of mathematical models for dynamic simulation of liquid-vapor two-phase flow

International Nuclear Information System (INIS)

Gofuku, Akio; Shimizu, Kenji; Sugano, Keiji; Morimoto, Takashi; Yoshikawa, Hidekazu; Wakabayashi, Jiro

1992-01-01

This paper deals with computerized supporting techniques of a numerical simulation of complex and large-scale engineering systems like nuclear power plants. As an example of the intelligent support systems of dynamic simulation, a prototype expert system is developed on an expert system development tool to support the selection of mathematical model which is a first step of numerical simulation and is required both wide expert knowledge and high-level decision making. The expert system supports the selection of liquid-vapor two phase flow models (fluid model and constitutive equations) consistent with simulation purpose and condition in the case of thermal-hydraulic simulation of nuclear power plants. The possibility of the expert system is examined for various selection support cases by both investigation of the appropriateness of the selection support logic and comparison between support results and decision results of several experts. (author)

Introduction to mathematical models and methods

Energy Technology Data Exchange (ETDEWEB)

Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)

2012-07-17

Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.

Structured Mathematical Modeling of Industrial Boiler

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Abdullah Nur Aziz

2014-04-01

Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.

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…

A mathematical model, algorithm, and package of programs for simulation and prompt estimation of the atmospheric dispersion of radioactive pollutants

International Nuclear Information System (INIS)

Nikolaev, V.I.; Yatsko, S.N.

1995-01-01

A mathematical model and a package of programs are presented for simulating the atmospheric turbulent diffusion of contaminating impurities from land based and other sources. Test calculations and investigations of the effect of various factors are carried out

Mathematical Modeling and Numerical Simulation of CO2 Removal by Using Hollow Fiber Membrane Contactors

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Mohammad Mesbah

2017-10-01

Full Text Available Abstract In this study, a mathematical model is proposed for CO2 separation from N2/CO2 mixtureusing a hollow fiber membrane contactor by various absorbents. The contactor assumed as non-wetted membrane; radial and axial diffusions were also considered in the model development. The governing equations of the model are solved via the finite element method (FEM. To ensure the accuracy of the developed model, the simulation results were validated using the reported experimental data for potassium glycinate (PG, monoethanol amine (MEA, and methyldiethanol amine (MDEA. The results of the proposed model indicated that PG absorbent has the highest removal efficiency of CO2, followed by potassium threonate (PT, MEA, amino-2-methyl-1-propanol (AMP, diethanol amine (DEA, and MDEA in sequence. In addition, the results revealed that the CO2 removal efficiency was favored by absorbent flow rate and liquid temperature, while the gas flow rate has a reverse effect. The simulation results proved that the hollow fiber membrane contactors have a good potential in the area of CO2 capture.

A Mathematical Model of Hourly Solar Radiation in Varying Weather Conditions for a Dynamic Simulation of the Solar Organic Rankine Cycle

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Taehong Sung

2015-07-01

Full Text Available A mathematical model of hourly solar radiation with weather variability is proposed based on the simple sky model. The model uses a superposition of trigonometric functions with short and long periods. We investigate the effects of the model variables on the clearness (kD and the probability of persistence (POPD indices and also evaluate the proposed model for all of the kD-POPD weather classes. A simple solar organic Rankine cycle (SORC system with thermal storage is simulated using the actual weather conditions, and then, the results are compared with the simulation results using the proposed model and the simple sky model. The simulation results show that the proposed model provides more accurate system operation characteristics than the simple sky model.

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...

A Mathematical Model, Implementation and Study of a Swarm System

OpenAIRE

Varghese, Blesson; McKee, Gerard

2013-01-01

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...

Vehicle dynamics modeling and simulation

CERN Document Server

Schramm, Dieter; Bardini, Roberto

2014-01-01

The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context different levels of complexity will be presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models on the basis of real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.

Calibration of mathematical models for simulation of thermal, seepage and mechanical behaviour of boom clay

International Nuclear Information System (INIS)

Baldi, G.; Borsetto, M.; Hueckel, T.

1987-01-01

This report presents results of research on the verification of the validity of a generalized thermo-elastoplastic-hydraulic mathematical model elaborated at Ismes for description of the behaviour of boom clay. The model is described in Section 2. Experimental results performed at Ismes for the identification of the material constants in athermal and thermal drained conditions are then presented. Procedures for the identification are described in Section 4. The undrained consolidated constant total stress heating test is then discussed. The undrained test shows the possibility of clay yielding due to effective pressure decrease during heating, caused by water pressure growth. The test has been simulated numerically, confirming the interpretation of the experiment. Further simulation of plane strain and plane stress central heating axisymmetric problem shows again a formation of a yielded clay zone around the heater. Interpretation of the results and recommendations for further research are given

A mathematical model for the dynamic simulation of low size cogeneration gas turbines within smart microgrids

International Nuclear Information System (INIS)

Bracco, Stefano; Delfino, Federico

2017-01-01

Microturbines represent a suitable technology to be adopted in smart microgrids since they are characterized by affordable capital and maintenance costs, high reliability and flexibility, and low environmental impact; moreover, they can be fed by fossil fuels or biofuels. They can operate in cogeneration and trigeneration mode, thus permitting to attain high global efficiency values of the energy conversion system from primary energy to electrical and thermal energy; from the electrical point of view, microturbines can operate connected to the distribution grid but also in islanded mode, thus enabling their use in remote areas without electrification. The paper describes the mathematical model that has been developed to simulate in off-design and transient conditions the operation of a 65 kW_e_l cogeneration microturbine installed within a smart microgrid. The dynamic simulation model is characterized by a flexible architecture that permits to simulate other different size single-shaft microturbines. The paper reports the main equations of the model, focusing on the architecture of the simulator and the microturbine control system; furthermore the most significant results derived from the validation phase are reported too, referring to the microturbine installed in the Smart Polygeneration Microgrid of the Savona Campus at the University of Genoa in Italy. - Highlights: • Dynamic simulation model of a cogeneration microturbine. • Off-design and transient performances of the microturbine. • Simulator validated on the Smart Polygeneration Microgrid at the Savona Campus.

Tracer kinetic modelling of receptor data with mathematical metabolite correction

International Nuclear Information System (INIS)

Burger, C.; Buck, A.

1996-01-01

Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabilites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabilite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K 1 -k 4 ) were refitted with reasonable identifiability when using mathematical metabolite correciton. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the 11 C iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. (orig./MG)

Mathematical 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.

Mathematical modeling in wound healing, bone regeneration and tissue engineering.

Science.gov (United States)

Geris, Liesbet; Gerisch, Alf; Schugart, Richard C

2010-12-01

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

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 ...

Experiments with mathematical models to simulate hepatitis A population dynamics under different levels of endemicity

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Mariana Alves de Guimaraens

Full Text Available Heterogeneous access to sanitation services is a characteristic of communities in Brazil. This heterogeneity leads to different patterns of hepatitis A endemicity: areas with low infection rates have higher probability of outbreaks, and areas with higher infection rates have high prevalence and low risk of outbreaks. Here we develop a mathematical model to study the effect of variable exposure to infection on the epidemiological dynamics of hepatitis A. Differential equations were used to simulate population dynamics and were numerically solved using the software StellaTM. The model uses parameters from serological surveys in the Greater Metropolitan Rio de Janeiro, in areas with different sanitation conditions. Computer simulation experiments show that the range of infection rates observed in these communities are characteristic of high and low levels of hepatitis A endemicity. We also found that the functional relationship between sanitation and exposure to infection is an important component of the model. The analysis of the public health impact of partial sanitation requires a better understanding of this relationship.

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…

Mathematical modeling of efficient protocols to control glioma growth.

Science.gov (United States)

Branco, J R; Ferreira, J A; de Oliveira, Paula

2014-09-01

In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.

Mathematical model for dissolved oxygen prediction in Cirata ...

African Journals Online (AJOL)

This paper presents the implementation and performance of mathematical model to predict theconcentration of dissolved oxygen in Cirata Reservoir, West Java by using Artificial Neural Network (ANN). The simulation program was created using Visual Studio 2012 C# software with ANN model implemented in it. Prediction ...

Mathematical modeling of a V-stack piezoelectric aileron actuation

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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.

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

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

Science.gov (United States)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

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

Science.gov (United States)

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

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

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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.

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.

Hybrid modelling framework by using mathematics-based and information-based methods

International Nuclear Information System (INIS)

Ghaboussi, J; Kim, J; Elnashai, A

2010-01-01

Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

DEFF Research Database (Denmark)

Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.

2017-01-01

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...

Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties.

Science.gov (United States)

Stamatakos, Georgios S; Dionysiou, Dimitra D

2009-10-21

The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the "summarize and jump" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed.

Mathematical model of the reactor coolant pump

International Nuclear Information System (INIS)

Kozuh, M.

1989-01-01

The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Mathematical modelling of tissue formation in chondrocyte filter cultures.

Science.gov (United States)

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

2011-12-17

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

MATHEMATICAL MODEL MANIPULATOR ROBOTS

Directory of Open Access Journals (Sweden)

O. N. Krakhmalev

2015-12-01

Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

The mathematical model of thread unrolling from a bobbin

Directory of Open Access Journals (Sweden)

S. M. Tenenbaum

2014-01-01

Full Text Available I. Introduction The subject of research in this work is a process of thread unrolling from a bobbin. The mathematical model of this process considering motion of thread peace on a bobbin and unrolled peace is proposed. The dimension of system of differential equations for this model is constant during deploying.The relevance to simulate this process for design of Heliogyro-like solar sails (Heliogyro [1], BMSTU-Sail [2] is proved. The paper briefly characterizes a blade for such solar sail as a simulation object. It proves the possibility for using a flexible thread model for a long blade because of very small blade thickness (less than 10 μm [3] relative to blade width and the phenomena of Koriolis forces [4] that lead to buckling failure of blade flatness.The major features of the proposed model are:-- simulated as a motion of the thread piece both being on a bobbin and its unrolled peace;-- splitting a thread length into nodes does not depend on the demand to ensure a sufficient number of nodes on a single thread turn on the coil;-- because of avoiding a problem of contact between the thread and bobbin a stable integration of motion equations is provided by the conventional Runge-Kutta method of fourth order with a constant step [5];-- in the course of solution the number of freedom degrees (number of motion equation is constant, thereby simplifying a calculation algorithm.The closest mathematical model is proposed in [6].The scientific novelty of this research is the approach to solving the problem of unrolling thread from a bobbin using a constant number of motion equations while preserving real kinematics coiling process.II. Problem formulationIn this section the problem of unrolling thread with length L from a bobbin of radius r is posed while any kind of forces are acting on the unrolled peace of thread. Moreover, the law of bobbin rotation φ(t assumed to be known with the proviso that the model can be modified if φ(t is the result of

Assessing the accuracy of mathematical models used in thermoelectric simulation: Thermal influence of insulated air zone and radiation heat

International Nuclear Information System (INIS)

Gao, Junling; Du, Qungui; Chen, Min; Li, Bo; Zhang, Dongwen

2015-01-01

An accurate mathematical model of thermoelectric modules (TEMs) provides the basis for the analysis and design of thermoelectric conversion system. TEM models from the literature are only valid for the heat transfer of N-type and P-type thermoelectric couples without considering air around the actual thermoelectric couples of TEMs. In fact, air space imposes significant influence on the model computational accuracy, especially for a TEM with large air space inside. In this study, heat transfer analyses of air between the TEM cold and hot plates were carried out in order to propose a new mathematical model that minimises simulation errors. This model was applied to analyse characteristic parameters of two typical TEMs, and the ratio of cross-sectional area of air space to thermocouples were 48.2% and 80.0%, respectively. The average relative errors in simulation decreased from 5.2% to 2.8% and from 12.8% to 3.7%, respectively. It is noted that our new model gives result more accurate than models from the literature provided that higher temperature difference occurs between hot side and cold side of TEM. Thus, the proposed model is of theoretical significance in guiding future design of TEMs for high-power or large-temperature-difference thermoelectric conversion systems. - Highlights: • Built a new accurate model for thermoelectric modules with inner air heat transfer. • Analysed the influence on heat transfer of the air within the TEM ∗ . • Reduced simulation errors for high-power thermoelectric conversion systems. • Two typical TEMs were measured with a good agreement with theoretical results. • ∗ TEM is the abbreviation of thermoelectric module

Modeling and Simulation of Low Voltage Arcs

NARCIS (Netherlands)

Ghezzi, L.; Balestrero, A.

2010-01-01

Modeling and Simulation of Low Voltage Arcs is an attempt to improve the physical understanding, mathematical modeling and numerical simulation of the electric arcs that are found during current interruptions in low voltage circuit breakers. An empirical description is gained by refined electrical

Mathematical modelling, variational formulation and numerical simulation of the energy transfer process in a gray plate in the presence of a thermal radiant source

International Nuclear Information System (INIS)

Gama, R.M.S. da.

1992-05-01

The energy transfer process in a gray, opaque and rigid plate, heated by an external thermal radiant source, is considered. The source is regarded as a spherical black body, with radius a (a → 0) and uniform heat generation, placed above the plate. A mathematical model is constructed, assuming that the heat transfer from/to the plate takes place by thermal radiation. The obtained mathematical model is nonlinear. Is presented a suitable variational principle which is employed for simulating some particular cases. (author)

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

Science.gov (United States)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Mathematical modeling based evaluation and simulation of boron removal in bioelectrochemical systems

Energy Technology Data Exchange (ETDEWEB)

Ping, Qingyun [Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States); Abu-Reesh, Ibrahim M. [Department of Chemical Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha (Qatar); He, Zhen, E-mail: zhenhe@vt.edu [Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States)

2016-11-01

Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level < 2 mg L{sup −} {sup 1}. The ratio between the anolyte and the catholyte flow rates should be kept > 22.2 in order to avoid boron accumulation in the anolyte effluent. - Highlights: • Mathematical models are developed to understand boron removal in BES. • Boron removal can be driven by electromigration induced by current generation. • Diffusion induced by a salt concentration gradient also contributes to boron removal. • Osmosis and current driven convection transport play diverse roles in different BES.

Mathematical Model of Age Aggression

OpenAIRE

Golovinski, P. A.

2013-01-01

We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...

Adaptation of Boynton's mathematical model to hydrogen isotope separation column by cryogenic distillation

International Nuclear Information System (INIS)

Kinoshita, Masahiro; Naruse, Yuji

1981-08-01

Boynton's mathematical simulation procedure for multi-component distillation calculations has the advantage that the Jacobian matrix is calculated analytically. The purpose of the present study is to adapt this procedure to hydrogen isotope separation columns by cryogenic distillation. The Boynton's model is modified so that the model can incorporate decay heat of tritium, nonideality of the hydrogen isotope solutions, multiple feeds and multiple sidestreams. Basic equations are derived and the mathematical simulation procedure is briefly explained. (author)

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

Directory of Open Access Journals (Sweden)

Davide Verotta

2017-01-01

Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.

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....

Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties

Directory of Open Access Journals (Sweden)

Georgios S. Stamatakos

2009-10-01

Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code. However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

Science.gov (United States)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

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.

Mathematical modeling, analysis and Markov Chain Monte Carlo simulation of Ebola epidemics

Science.gov (United States)

Tulu, Thomas Wetere; Tian, Boping; Wu, Zunyou

Ebola virus infection is a severe infectious disease with the highest case fatality rate which become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed. The existence as well as uniqueness of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both Euler method and one of the top ten most influential algorithm known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least real data has been fitted to the model, showing that it can used to predict the dynamic of Ebola epidemic.

Mathematical models and numerical simulation in electromagnetism

CERN Document Server

Bermúdez, Alfredo; Salgado, Pilar

2014-01-01

The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory  based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

A mathematical model of combustion kinetics of municipal solid ...

African Journals Online (AJOL)

Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the ...

Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

Science.gov (United States)

Sgouralis, Ioannis; Layton, Anita T

2015-06-01

In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

Mathematical modeling and dynamic simulation of a class of drive systems with permanent magnet synchronous motors

Directory of Open Access Journals (Sweden)

Mikhov M.

2009-12-01

Full Text Available The performance of a two-coordinate drive system with permanent magnet synchronous motors is analyzed and discussed in this paper. Both motors have been controlled in brushless DC motor mode in accordance with the rotor positions. Detailed study has been carried out by means of mathematical modeling and computer simulation for the respective transient and steady-state regimes at various load and work conditions. The research carried out as well as the results obtained can be used in the design, optimization and tuning of such types of drive systems. They could be also applied in the teaching process.

Mathematical Modeling Using MATLAB

National Research Council Canada - National Science Library

Phillips, Donovan

1998-01-01

.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

The new version of the Institute of Numerical Mathematics Sigma Ocean Model (INMSOM) for simulation of Global Ocean circulation and its variability

Science.gov (United States)

Gusev, Anatoly; Fomin, Vladimir; Diansky, Nikolay; Korshenko, Evgeniya

2017-04-01

In this paper, we present the improved version of the ocean general circulation sigma-model developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The previous version referred to as INMOM (Institute of Numerical Mathematics Ocean Model) is used as the oceanic component of the IPCC climate system model INMCM (Institute of Numerical Mathematics Climate Model (Volodin et al 2010,2013). Besides, INMOM as the only sigma-model was used for simulations according to CORE-II scenario (Danabasoglu et al. 2014,2016; Downes et al. 2015; Farneti et al. 2015). In general, INMOM results are comparable to ones of other OGCMs and were used for investigation of climatic variations in the North Atlantic (Gusev and Diansky 2014). However, detailed analysis of some CORE-II INMOM results revealed some disadvantages of the INMOM leading to considerable errors in reproducing some ocean characteristics. So, the mass transport in the Antarctic Circumpolar Current (ACC) was overestimated. As well, there were noticeable errors in reproducing thermohaline structure of the ocean. After analysing the previous results, the new version of the OGCM was developed. It was decided to entitle is INMSOM (Institute of Numerical Mathematics Sigma Ocean Model). The new title allows one to distingwish the new model, first, from its older version, and second, from another z-model developed in the INM RAS and referred to as INMIO (Institute of Numerical Mathematics and Institute of Oceanology ocean model) (Ushakov et al. 2016). There were numerous modifications in the model, some of them are as follows. 1) Formulation of the ocean circulation problem in terms of full free surface with taking into account water amount variation. 2) Using tensor form of lateral viscosity operator invariant to rotation. 3) Using isopycnal diffusion including Gent-McWilliams mixing. 4) Using atmospheric forcing computation according to NCAR methodology (Large and Yeager 2009). 5

Models and simulations

International Nuclear Information System (INIS)

Lee, M.J.; Sheppard, J.C.; Sullenberger, M.; Woodley, M.D.

1983-09-01

On-line mathematical models have been used successfully for computer controlled operation of SPEAR and PEP. The same model control concept is being implemented for the operation of the LINAC and for the Damping Ring, which will be part of the Stanford Linear Collider (SLC). The purpose of this paper is to describe the general relationships between models, simulations and the control system for any machine at SLAC. The work we have done on the development of the empirical model for the Damping Ring will be presented as an example

Mathematical simulation of point defect interaction with grain boundaries

International Nuclear Information System (INIS)

Bojko, V.S.

1987-01-01

Published works, where the interaction of point defects and grain boundaries was studied by mathematical simulation methods, have been analysed. Energetics of the vacancy formation both in nuclei of large-angle special grain boundaries and in lattice regions adjoining them has been considered. The data obtained permit to explain specific features of grain-boundary diffusion processes. Results of mathematical simulation of the interaction of impurity atoms and boundaries have been considered. Specific features of the helium atom interaction with large-angle grain boundaries are analysed as well

Dynamic models of staged gasification processes. Documentation of gasification simulator; Dynamiske modeller a f trinopdelte forgasningsprocesser. Dokumentation til forgasser simulator

Energy Technology Data Exchange (ETDEWEB)

NONE

2005-02-15

In connection with the ERP project 'Dynamic modelling of staged gasification processes' a gasification simulator has been constructed. The simulator consists of: a mathematical model of the gasification process developed at Technical University of Denmark, a user interface programme, IGSS, and a communication interface between the two programmes. (BA)

Mathematical Modeling: A Structured Process

Science.gov (United States)

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Simulating individual-based models of epidemics in hierarchical networks

NARCIS (Netherlands)

Quax, R.; Bader, D.A.; Sloot, P.M.A.

2009-01-01

Current mathematical modeling methods for the spreading of infectious diseases are too simplified and do not scale well. We present the Simulator of Epidemic Evolution in Complex Networks (SEECN), an efficient simulator of detailed individual-based models by parameterizing separate dynamics

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

Science.gov (United States)

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

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.

Multiphase flow experiments, mathematical modeling and numerical simulation of the water - gas - solute movement

Science.gov (United States)

Li, Y.; Ma, X.; Su, N.

2013-12-01

The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.

Spherical Detector Device Mathematical Modelling with Taking into Account Detector Module Symmetry

International Nuclear Information System (INIS)

Batyj, V.G.; Fedorchenko, D.V.; Prokopets, S.I.; Prokopets, I.M.; Kazhmuradov, M.A.

2005-01-01

Mathematical Model for spherical detector device accounting to symmetry properties is considered. Exact algorithm for simulation of measurement procedure with multiple radiation sources is developed. Modelling results are shown to have perfect agreement with calibration measurements

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.

A mathematical model of radiation effect on the immunity system

International Nuclear Information System (INIS)

Smirnova, O.A.

1984-01-01

A mathematical model, simulating the effect of ionizing radiation on the dynamics of humoral immune reaction is suggested. It represents the system of nonlinear differential equations and is realized in the form of program in Fortran computer language. The model describes the primary immune reaction of nonirradiated organism on T-independent antigen, reflects the postradiation lymphopoiesis dynamics in nonimmunized mammals, simulates the processes of injury and recovery of the humoral immunity system under the combined effect of ionizing radiation and antigenic stimulation. The model can be used for forecasting imminity state in irradiated mammals

Mathematical and physical modeling of thermal stratification phenomena in steel ladles

Science.gov (United States)

Putan, V.; Vilceanu, L.; Socalici, A.; Putan, A.

2018-01-01

By means of CFD numerical modeling, a systematic analysis of the similarity between steel ladles and hot-water model regarding natural convection phenomena was studied. The key similarity criteria we found to be dependent on the dimensionless numbers Fr and βΔT. These similarity criteria suggested that hot-water models with scale in the range between 1/5 and 1/3 and using hot water with temperature of 45 °C or higher are appropriate for simulating natural convection in steel ladles. With this physical model, thermal stratification phenomena due to natural convection in steel ladles were investigated. By controlling the cooling intensity of water model to correspond to the heat loss rate of steel ladles, which is governed by Fr and βΔT, the temperature profiles measured in the water bath of the model were to deduce the extent of thermal stratification in liquid steel bath in the ladles. Comparisons between mathematically simulated temperature profiles in the prototype steel ladles and those physically simulated by scaling-up the measured temperatures profiles in the water model showed good agreement. This proved that it is feasible to use a 1/5 scale water model with 45 °C hot water to simulate natural convection in steel ladles. Therefore, besides mathematical CFD models, the physical hot-water model provided an additional means of studying fluid flow and heat transfer in steel ladles.

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

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

Mathematical Modeling and Simulation Introduction for Scientists and Engineers

CERN Document Server

Velten, Kai

2008-01-01

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra—all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently di

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

Science.gov (United States)

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

Modeling, simulation and optimization of bipedal walking

CERN Document Server

Berns, Karsten

2013-01-01

The model-based investigation of motions of anthropomorphic systems is an important interdisciplinary research topic involving specialists from many fields such as Robotics, Biomechanics, Physiology, Orthopedics, Psychology, Neurosciences, Sports, Computer Graphics and Applied Mathematics. This book presents a study of basic locomotion forms such as walking and running is of particular interest due to the high demand on dynamic coordination, actuator efficiency and balance control. Mathematical models and numerical simulation and optimization techniques are explained, in combination with experimental data, which can help to better understand the basic underlying mechanisms of these motions and to improve them. Example topics treated in this book are Modeling techniques for anthropomorphic bipedal walking systems Optimized walking motions for different objective functions Identification of objective functions from measurements Simulation and optimization approaches for humanoid robots Biologically inspired con...

SEIR model simulation for Hepatitis B

Science.gov (United States)

Side, Syafruddin; Irwan, Mulbar, Usman; Sanusi, Wahidah

2017-09-01

Mathematical modelling and simulation for Hepatitis B discuss in this paper. Population devided by four variables, namely: Susceptible, Exposed, Infected and Recovered (SEIR). Several factors affect the population in this model is vaccination, immigration and emigration that occurred in the population. SEIR Model obtained Ordinary Differential Equation (ODE) non-linear System 4-D which then reduces to 3-D. SEIR model simulation undertaken to predict the number of Hepatitis B cases. The results of the simulation indicates the number of Hepatitis B cases will increase and then decrease for several months. The result of simulation using the number of case in Makassar also found the basic reproduction number less than one, that means, Makassar city is not an endemic area of Hepatitis B.

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...

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

Science.gov (United States)

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

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

Science.gov (United States)

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

2017-08-01

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

Simulation of a coal-fired power plant using mathematical programming algorithms in order to optimize its efficiency

International Nuclear Information System (INIS)

Tzolakis, G.; Papanikolaou, P.; Kolokotronis, D.; Samaras, N.; Tourlidakis, A.; Tomboulides, A.

2012-01-01

Since most of the world's electric energy production is mainly based on fossil fuels and need for better efficiency of the energy conversion systems is imminent, mathematical programming algorithms were applied for the simulation and optimization of a detailed model of an existing lignite-fired power plant in Kozani, Greece (KARDIA IV). The optimization of its overall thermal efficiency, using as control variables the mass flow rates of the steam turbine extractions and the fuel consumption, was performed with the use of the simulation and optimization software gPROMS. The power plant components' mathematical models were imported in software by the authors and the results showed that further increase to the overall thermal efficiency of the plant can be achieved (a 0.55% absolute increase) through reduction of the HP turbine's and increase of the LP turbine's extractions mass flow rates and the parallel reduction of the fuel consumption by 2.05% which also results to an equivalent reduction of the greenhouse gasses. The setup of the mathematical model and the flexibility of gPROMS, make this software applicable to various power plants. - Highlights: ► Modeling and simulation of the flue gases circuit of a specific plant. ► Designing of modules in gPROMS FO (Foreign Objects). ► Simulation of the complete detailed plant with gPROMS. ► Optimization using a non-linear optimization algorithm of the plant's efficiency.

IMPROVEMENT OF SLAB REHEATING PROCESS AT USIMINAS THROUGH MATHEMATICAL SIMULATION

Directory of Open Access Journals (Sweden)

Antônio Adel dos Santos

2012-09-01

Full Text Available Basic characteristics and application examples of the mathematical simulator for reheating process in walking-beam type furnaces, that has been developed and applied to Usiminas plate mill line at Ipatinga, are shown in this paper. This is a bi-dimensional mathematical model solved by the finite volume method, validated by temperature measurements inside the slab during heating and coded as a visual tool. Among these applications, the following can be highlighted: (i determination of suitable furnace zone temperatures and residence times for processing steels by accelerated cooling technology; (ii determination of slab average temperature at discharging as well as at each zone exit, supplying data to be fed to the automation system at the comissioning stage; (iii analyses of slab thermal distribution through the reheating process, enabling operational optimization

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

DEFF Research Database (Denmark)

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

2016-01-01

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

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

Science.gov (United States)

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Mathematical modeling with multidisciplinary applications

CERN Document Server

Yang, Xin-She

2013-01-01

Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

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

Science.gov (United States)

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Applied impulsive mathematical models

CERN Document Server

Stamova, Ivanka

2016-01-01

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

Development of a mathematical model simulating the multiply connected automatic control system of a coal-fired power unit equipped with a direct-injection dust feed system

Energy Technology Data Exchange (ETDEWEB)

V.A. Shorokhov; A.P. Smol' nikov; D.A. Kurochkin; N.N. Komarova; A.S. Mar' yasov; A.R. Gudovich; S.N. Bartosh [ZAO SibKOTES, Krasnoyarsk (Russian Federation)

2009-07-01

Matters relating to development and identification of a mathematical model for simulating a power unit and its individual systems are discussed. Results obtained from a large series of the active experiments on an operating power unit are presented.

Mathematical Formulation Requirements and Specifications for the Process Models

Energy Technology Data Exchange (ETDEWEB)

Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

2010-11-01

The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments

Mathematical Formulation Requirements and Specifications for the Process Models

International Nuclear Information System (INIS)

Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

2010-01-01

The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments naturally

Multi-band effective mass approximations advanced mathematical models and numerical techniques

CERN Document Server

Koprucki, Thomas

2014-01-01

This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...

A Primer for Mathematical Modeling

Science.gov (United States)

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

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

Science.gov (United States)

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Chancroid transmission dynamics: a mathematical modeling approach.

Science.gov (United States)

Bhunu, C P; Mushayabasa, S

2011-12-01

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.

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

Science.gov (United States)

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

2013-11-18

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

MATHEMATICAL MODEL OF CATALYTIC PROCESSES AT MODIFIED ELECTRODES

Directory of Open Access Journals (Sweden)

Femila Mercy Rani Joseph

Full Text Available A mathematical modeling of electrocatalytic processes taking place at modified electrodes is discussed. In this paper we obtained the approximate analytical solutions for the nonlinear equations under non steady state conditions using homotopy perturbation method. Simple and approximate polynomial expressions for the concentration of reactant, product and charge carrier were obtained in terms of diffusion coefficient and rate constant. In this work the numerical simulation of the problem is reported using Scilab program. In this manuscript analytical results are compared with simulation results and satisfactory agreement is noted.

Mathematical modelling of membrane separation

DEFF Research Database (Denmark)

Vinther, Frank

This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

Mathematical model for spreading dynamics of social network worms

International Nuclear Information System (INIS)

Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin

2012-01-01

In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks

Exploring Iconic Interpretation and Mathematics Teacher Development through Clinical Simulations

Science.gov (United States)

Dotger, Benjamin; Masingila, Joanna; Bearkland, Mary; Dotger, Sharon

2015-01-01

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Mathematical model on Alzheimer's disease.

Science.gov (United States)

Hao, Wenrui; Friedman, Avner

2016-11-18

Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.

Description of mathematical models and computer programs

International Nuclear Information System (INIS)

1977-01-01

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

Simulation of Electric Faults in Doubly-Fed Induction Generators Employing Advanced Mathematical Modelling

DEFF Research Database (Denmark)

Martens, Sebastian; Mijatovic, Nenad; Holbøll, Joachim

2015-01-01

in many areas of electrical machine analysis. However, for fault investigations, the phase-coordinate representation has been found more suitable. This paper presents a mathematical model in phase coordinates of the DFIG with two parallel windings per rotor phase. The model has been implemented in Matlab...

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

Science.gov (United States)

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

Verification of temporal-causal network models by mathematical analysis

Directory of Open Access Journals (Sweden)

Jan Treur

2016-04-01

Full Text Available Abstract Usually dynamic properties of models can be analysed by conducting simulation experiments. But sometimes, as a kind of prediction properties can also be found by calculations in a mathematical manner, without performing simulations. Examples of properties that can be explored in such a manner are: whether some values for the variables exist for which no change occurs (stationary points or equilibria, and how such values may depend on the values of the parameters of the model and/or the initial values for the variables whether certain variables in the model converge to some limit value (equilibria and how this may depend on the values of the parameters of the model and/or the initial values for the variables whether or not certain variables will show monotonically increasing or decreasing values over time (monotonicity how fast a convergence to a limit value takes place (convergence speed whether situations occur in which no convergence takes place but in the end a specific sequence of values is repeated all the time (limit cycle Such properties found in an analytic mathematical manner can be used for verification of the model by checking them for the values observed in simulation experiments. If one of these properties is not fulfilled, then there will be some error in the implementation of the model. In this paper some methods to analyse such properties of dynamical models will be described and illustrated for the Hebbian learning model, and for dynamic connection strengths in social networks. The properties analysed by the methods discussed cover equilibria, increasing or decreasing trends, recurring patterns (limit cycles, and speed of convergence to equilibria.

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

Development of computer program for simulation of an ice bank system operation, Part I: Mathematical modelling

Energy Technology Data Exchange (ETDEWEB)

Halasz, Boris; Grozdek, Marino; Soldo, Vladimir [Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucica 5, 10 000 Zagreb (Croatia)

2009-09-15

Since the use of standard engineering methods in the process of an ice bank performance evaluation offers neither adequate flexibility nor accuracy, the aim of this research was to provide a powerful tool for an industrial design of an ice storage system allowing to account for the various design parameters and system arrangements over a wide range of time varying operating conditions. In this paper the development of a computer application for the prediction of an ice bank system operation is presented. Static, indirect, cool thermal storage systems with external ice on coil building/melting were considered. The mathematical model was developed by means of energy and mass balance relations for each component of the system and is basically divided into two parts, the model of an ice storage system and the model of a refrigeration unit. Heat transfer processes in an ice silo were modelled by use of empirical correlations while the performance of refrigeration unit components were based on manufacturers data. Programming and application design were made in Fortran 95 language standard. Input of data is enabled through drop down menus and dialog boxes, while the results are presented via figures, diagrams and data (ASCII) files. In addition, to demonstrate the necessity for development of simulation program a case study was performed. Simulation results clearly indicate that no simple engineering methods or rule of thumb principles could be utilised in order to validate performance of an ice bank system properly. (author)

Mathematical modeling and multicriterion optimization for photonuclear production of the 67cu isotope

International Nuclear Information System (INIS)

Dikij, N.P.; Rudychev, Y.V.; Fedorchenko, D.V.; Khazhmuradov, M.A.

2014-01-01

This paper considers a method for 67 Cu isotope production using electron bremsstrahlung by the 68 Zn(gamma, p) 67 Cu reaction. The facility for 67 Cu isotope production contains an electron accelerator, electron-gamma converter and zinc target. To optimize this facility we developed three-dimensional model of the converter and the target. Using this model, we performed the mathematical modeling of zinc target irradiation and thermal-hydraulic processes inside the target for various parameters of the electron beam and converter configurations. For mathematical modeling of radiation processes we used the MCNPX software. Thermal-hydraulic simulation utilized the commercial SolidWorks software with Flow Simulation module. Mathematical modeling revealed that efficient 67 Cu isotope production needs smaller beam diameter and higher electron energy. Under these conditions target heat power also increases, thus additional cooling is necessary. If the beam diameter and the electron energy are fixed the most effective method to satisfy the operating parameters and retain an efficient isotope yield is to optimize photonuclear spectra of the target by variation of converter thickness. We developed an algorithm for multicriterion optimization and performed the optimization of the facility with account to coupled radiation and heat transfer processes.

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

Science.gov (United States)

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Mathematical modeling based evaluation and simulation of boron removal in bioelectrochemical systems.

Science.gov (United States)

Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen

2016-11-01

Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level 22.2 in order to avoid boron accumulation in the anolyte effluent. Copyright © 2016 Elsevier B.V. All rights reserved.

Computerized mathematical model for prediction of resin/fiber composite properties

International Nuclear Information System (INIS)

Lowe, K.A.

1985-01-01

A mathematical model has been developed for the design and optimization of resin formulations. The behavior of a fiber-reinforced cured resin matrix can be predicted from constituent properties of the formulation and fiber when component interaction is taken into account. A computer implementation of the mathematical model has been coded to simulate resin/fiber response and generate expected values for any definable properties of the composite. The algorithm is based on multistage regression techniques and the manipulation of n-order matrices. Excellent correlation between actual test values and predicted values has been observed for physical, mechanical, and qualitative properties of resin/fiber composites. Both experimental and commercial resin systems with various fiber reinforcements have been successfully characterized by the model. 6 references, 3 figures, 2 tables

Mathematical models in cell biology and cancer chemotherapy

CERN Document Server

Eisen, Martin

1979-01-01

The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on...

Comparison of two mathematical models of the kite for Laddermill sail simulation

NARCIS (Netherlands)

Podgaets, A.R.; Ockels, W.J.

2007-01-01

Laddermill sail is an innovative approach to propel the ship with the power generated by kites. The first Laddermill system is currently being designed however existing mathematical models of the system produce different optimal recommendations. Thus a decision has been made to step back and to take

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

Wilkinson, Michael H.F.

2006-01-01

Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic

A model management system for combat simulation

OpenAIRE

Dolk, Daniel R.

1986-01-01

The design and implementation of a model management system to support combat modeling is discussed. Structured modeling is introduced as a formalism for representing mathematical models. A relational information resource dictionary system is developed which can accommodate structured models. An implementation is described. Structured modeling is then compared to Jackson System Development (JSD) as a methodology for facilitating discrete event simulation. JSD is currently better at representin...

Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.

Science.gov (United States)

Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo

2017-02-01

New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

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L. V. Ursulyak

2017-12-01

Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity

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

Science.gov (United States)

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

2018-04-11

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

A mathematical model of insulin resistance in Parkinson's disease.

Science.gov (United States)

Braatz, Elise M; Coleman, Randolph A

2015-06-01

This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Evolvable mathematical models: A new artificial Intelligence paradigm

Science.gov (United States)

Grouchy, Paul

We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.

Hill’s and Huxley’s muscle models - tools for simulations in biomechanics

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Jovanović Kosta

2015-01-01

Full Text Available Numerous mathematical models of human skeletal muscles have been developed. However, none of them is adopted as a general one and each of them is suggested for some specific purpose. This topic is essential in humanoid robotics, since we firstly need to understand how human moves and acts in order to exploit human movement patterns in robotics and design human like actuators. Simulations in biomechanics are intensively used in research of locomotion, safe human-robot interaction, development of novel robotic actuators, biologically inspired control algorithms, etc. This paper presents two widely adopted muscle models (Hill’s and Huxley’s model, elaborates their features and demonstrates trade-off between their accuracy and efficiency of computer simulations. The simulation setup contains mathematical representation of passive muscle structures as well as mathematical model of an elastic tendon as a series elastic actuation element. Advanced robot control techniques point out energy consumption as one of the key issues. Therefore, energy store and release mechanism in elastic elements in both tendon and muscle, based on the simulation models, are considered. [Projekat Ministarstva nauke Republike Srbije, br. TR35003 and br. OS175016

The behavior of adaptive bone-remodeling simulation models

NARCIS (Netherlands)

H.H. Weinans (Harrie); R. Huiskes (Rik); H.J. Grootenboer

1992-01-01

textabstractThe process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule

Mathematical modeling of left ventricular dimensional changes in mice during aging

Directory of Open Access Journals (Sweden)

Yang Tianyi

2012-12-01

Full Text Available Abstract Cardiac aging is characterized by diastolic dysfunction of the left ventricle (LV, which is due in part to increased LV wall stiffness. In the diastolic phase, myocytes are relaxed and extracellular matrix (ECM is a critical determinant to the changes of LV wall stiffness. To evaluate the effects of ECM composition on cardiac aging, we developed a mathematical model to predict LV dimension and wall stiffness changes in aging mice by integrating mechanical laws and our experimental results. We measured LV dimension, wall thickness, LV mass, and collagen content for wild type (WT C57/BL6J mice of ages ranging from 7.3 months to those of 34.0 months. The model was established using the thick wall theory and stretch-induced tissue growth to an isotropic and homogeneous elastic composite with mixed constituents. The initial conditions of the simulation were set based on the data from the young mice. Matlab simulations of this mathematical model demonstrated that the model captured the major features of LV remodeling with age and closely approximated experimental results. Specifically, the temporal progression of the LV interior and exterior dimensions demonstrated the same trend and order-of-magnitude change as our experimental results. In conclusion, we present here a validated mathematical model of cardiac aging that applies the thick-wall theory and stretch-induced tissue growth to LV remodeling with age.

Mathematical modeling of alcohol distillation columns

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Ones Osney Pérez

2011-04-01

Full Text Available New evaluation modules are proposed to extend the scope of a modular simulator oriented to the sugar cane industry, called STA 4.0, in a way that it can be used to carry out x calculation and analysis in ethanol distilleries. Calculation modules were developed for the simulation of the columns that are combined in the distillation area. Mathematical models were supported on materials and energy balances, equilibrium relations and thermodynamic properties of the ethanol-water system. Ponchon-Savarit method was used for the evaluation of the theoretical stages in the columns. A comparison between the results using Ponchon- Savarit method and those obtained applying McCabe-Thiele method was done for a distillation column. These calculation modules for ethanol distilleries were applied to a real case for validation.

Mathematical 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.

Pest control through viral disease: mathematical modeling and analysis.

Science.gov (United States)

Bhattacharyya, S; Bhattacharya, D K

2006-01-07

This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappain(1,infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing kappa values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented.

Modeling and Simulation of a Modified Quadruple Tank System

DEFF Research Database (Denmark)

Mohd. Azam, Sazuan Nazrah; Jørgensen, John Bagterp

2015-01-01

to model and control. In this paper, a modified quadruple-tank system has been described, all the important variables has been outlined and a mathematical model has been presented. We developed deterministic and stochastic models using differential equations and simulate the models using Matlab...

Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems

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Fedotov A.

2017-02-01

Full Text Available The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.

Evaluation of Mathematical Models for Tankers’ Maneuvering Motions

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Erhan AKSU

2017-03-01

Full Text Available In this study, the maneuvering performance of two tanker ships, KVLCC1 and KVLCC2 which have different stern forms are predicted using a system-based method. Two different 3 DOF (degrees of freedom mathematical models based on the MMG(Maneuvering Modeling Group concept areappliedwith the difference in representing lateral force and yawing moment by second and third order polynomials respectively. Hydrodynamic coefficients and related parameters used in the mathematical models of the same scale models of KVLCC1 and KVLCC2 ships are estimated by using experimental data of NMRI (National Maritime Research Institute. The simulations of turning circle with rudder angle ±35o , zigzag(±10o /±10o and zigzag (±20o /±20o maneuvers are carried out and compared with free running model test data of MARIN (Maritime Research Institute Netherlands in this study. As a result of the analysis, it can be summarised that MMG model based on the third order polynomial is superior to the one based on the second order polynomial in view of estimation accuracy of lateral hull force and yawing moment.

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.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data

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Kansuporn eSriyudthsak

2016-05-01

Full Text Available The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data.

Science.gov (United States)

Sriyudthsak, Kansuporn; Shiraishi, Fumihide; Hirai, Masami Yokota

2016-01-01

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

The thyroid cancer policy model: A mathematical simulation model of papillary thyroid carcinoma in The U.S. population.

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Carrie Lubitz

Full Text Available Thyroid cancer affects over ½ million people in the U.S. and the incidence of thyroid cancer has increased worldwide at a rate higher than any other cancer, while survival has remained largely unchanged. The aim of this research was to develop, calibrate and verify a mathematical disease model to simulate the natural history of papillary thyroid cancer, which will serve as a platform to assess the effectiveness of clinical and cancer control interventions.Herein, we modeled the natural pre-clinical course of both benign and malignant thyroid nodules with biologically relevant health states from normal to detected nodule. Using established calibration techniques, optimal parameter sets for tumor growth characteristics, development rate, and detection rate were used to fit Surveillance Epidemiology and End Results (SEER incidence data and other calibration targets.Model outputs compared to calibration targets demonstrating sufficient calibration fit and model validation are presented including primary targets of SEER incidence data and size distribution at detection of malignancy. Additionally, we show the predicted underlying benign and malignant prevalence of nodules in the population, the probability of detection based on size of nodule, and estimates of growth over time in both benign and malignant nodules.This comprehensive model provides a dynamic platform employable for future comparative effectiveness research. Future model analyses will test and assess various clinical management strategies to improve patient outcomes related to thyroid cancer and optimize resource utilization for patients with thyroid nodules.

Mathematical Modeling of an Active-Fiber Composite Energy Harvester with Interdigitated Electrodes

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A. Jemai

2014-01-01

Full Text Available The use of active-fiber composites (AFC instead of traditional ceramic piezoelectric materials is motivated by flexibility and relatively high actuation capacity. Nevertheless, their energy harvesting capabilities remain low. As a first step toward the enhancement of AFC’s performances, a mathematical model that accurately simulates the dynamic behavior of the AFC is proposed. In fact, most of the modeling approaches found in the literature for AFC are based on finite element methods. In this work, we use homogenization techniques to mathematically describe piezoelectric properties taking into consideration the composite structure of the AFC. We model the interdigitated electrodes as a series of capacitances and current sources linked in parallel; then we integrate these properties into the structural model of the AFC. The proposed model is incorporated into a vibration based energy harvesting system consisting of a cantilever beam on top of which an AFC patch is attached. Finally, analytical solutions of the dynamic behavior and the harvested voltage are proposed and validated with finite element simulations.

Equivalence of two models in single-phase multicomponent flow simulations

KAUST Repository

Wu, Yuanqing

2016-02-28

In this work, two models to simulate the single-phase multicomponent flow in reservoirs are introduced: single-phase multicomponent flow model and two-phase compositional flow model. Because the single-phase multicomponent flow is a special case of the two-phase compositional flow, the two-phase compositional flow model can also simulate the case. We compare and analyze the two models when simulating the single-phase multicomponent flow, and then demonstrate the equivalence of the two models mathematically. An experiment is also carried out to verify the equivalence of the two models.

Equivalence of two models in single-phase multicomponent flow simulations

KAUST Repository

Wu, Yuanqing; Sun, Shuyu

2016-01-01

In this work, two models to simulate the single-phase multicomponent flow in reservoirs are introduced: single-phase multicomponent flow model and two-phase compositional flow model. Because the single-phase multicomponent flow is a special case of the two-phase compositional flow, the two-phase compositional flow model can also simulate the case. We compare and analyze the two models when simulating the single-phase multicomponent flow, and then demonstrate the equivalence of the two models mathematically. An experiment is also carried out to verify the equivalence of the two models.

Simulation and similarity using models to understand the world

CERN Document Server

Weisberg, Michael

2013-01-01

In the 1950s, John Reber convinced many Californians that the best way to solve the state's water shortage problem was to dam up the San Francisco Bay. Against massive political pressure, Reber's opponents persuaded lawmakers that doing so would lead to disaster. They did this not by empirical measurement alone, but also through the construction of a model. Simulation and Similarity explains why this was a good strategy while simultaneously providing an account of modeling and idealization in modern scientific practice. Michael Weisberg focuses on concrete, mathematical, and computational models in his consideration of the nature of models, the practice of modeling, and nature of the relationship between models and real-world phenomena. In addition to a careful analysis of physical, computational, and mathematical models, Simulation and Similarity offers a novel account of the model/world relationship. Breaking with the dominant tradition, which favors the analysis of this relation through logical notions suc...

Causal Bayes Model of Mathematical Competence in Kindergarten

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Božidar Tepeš

2016-06-01

Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.

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

Science.gov (United States)

Peper, Abraham

2004-08-21

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

Stochastic models: theory and simulation.

Energy Technology Data Exchange (ETDEWEB)

Field, Richard V., Jr.

2008-03-01

Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

A mathematical model for batch and continuous thickening of flocculent suspensions in vessels with varying section

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Damasceno, J.J.R.; Karlesen, K.H.

2001-10-01

The phenomenological theory of continuous thickening of flocculated suspensions in an ideal cylindrical thickener is extended to vessels having varying cross-section, including divergent or convergent conical vessels. The purpose of this contribution is to draw attention to the corresponding mathematical model, whose key ingredient is a strongly degenerate parabolic partial differential equation. For ideal (non-flocculated) suspensions, which do not form co compressible sediments, the mathematical model reduces to the kinematic approach by Anestis, who developed a method of construction of exact solution by the method of characteristics. The difficulty lies in the fact that characteristics and iso-concentration lines, unlike the conventional Kynch model for cylindrical vessels, do not coincide, and one has to resort to numerical methods to simulate the thickening process. A numerical algorithm is presented and employed for simulations of continuous thickening. Implications of the mathematical model are also demonstrated by steady-state calculations, which lead to new possibilities in thickener design. (author)

Mathematical modeling of sleep state dynamics in a rodent model of shift work

Directory of Open Access Journals (Sweden)

Michael J. Rempe

2018-06-01

Full Text Available Millions of people worldwide are required to work when their physiology is tuned for sleep. By forcing wakefulness out of the body’s normal schedule, shift workers face numerous adverse health consequences, including gastrointestinal problems, sleep problems, and higher rates of some diseases, including cancers. Recent studies have developed protocols to simulate shift work in rodents with the intention of assessing the effects of night-shift work on subsequent sleep (Grønli et al., 2017. These studies have already provided important contributions to the understanding of the metabolic consequences of shift work (Arble et al., 2015; Marti et al., 2016; Opperhuizen et al., 2015 and sleep-wake-specific impacts of night-shift work (Grønli et al., 2017. However, our understanding of the causal mechanisms underlying night-shift-related sleep disturbances is limited. In order to advance toward a mechanistic understanding of sleep disruption in shift work, we model these data with two different approaches. First we apply a simple homeostatic model to quantify differences in the rates at which sleep need, as measured by slow wave activity during slow wave sleep (SWS rises and falls. Second, we develop a simple and novel mathematical model of rodent sleep and use it to investigate the timing of sleep in a simulated shift work protocol (Grønli et al., 2017. This mathematical framework includes the circadian and homeostatic processes of the two-process model, but additionally incorporates a stochastic process to model the polyphasic nature of rodent sleep. By changing only the time at which the rodents are forced to be awake, the model reproduces some key experimental results from the previous study, including correct proportions of time spent in each stage of sleep as a function of circadian time and the differences in total wake time and SWS bout durations in the rodents representing night-shift workers and those representing day-shift workers

Mathematical model for optimization of multilayer submerged-arc welding of frame equipment of power units

International Nuclear Information System (INIS)

Pankov, V.V.; Chernyshev, G.G.; Kozlov, N.E.

1987-01-01

A mathematical model for optimization of multilayer submerged arc welding of frame equipment of power units is constructed. The variation-energy method permits to construct the universal mathematical model for strengthening formation of a single bead; the method is reasonable for simulation of a multilayer welded joint. Minimization of the distance between maximum and minimum layer height of a built-up metal is the necessary condition for qualitative formation of the multilayer joint. One can calculate in real time scale the optimal vector of maximally ten parameters under the multilayer welding condition immediately after change in the grooving width using the developed mathematical model of optimization

Mathematical simulation of cascade-probabilistic functions for charged particles

International Nuclear Information System (INIS)

Kupchishin, A.A.; Kupchishin, A.I.; Smygaleva, T.A.

1998-01-01

Analytical expressions for cascade-probabilistic functions (CPF) for electrons, protons, α-particles and ions with taking into account energy losses are received. Mathematical analysis of these functions is carried out and main properties of function are determined. Algorithms of CPF are developed and their computer calculation were conducted. Regularities in behavior of function in dependence on initial particles energy, atomic number and registration depth are established. Book is intended to specialists on mathematical simulation of radiation defects, solid state physics, elementary particle physics and applied mathematics. There are 3 chapters in the book: 1. Cascade-probabilistic functions for electrons; 2. CPF for protons and α-particles; 3. CPF with taking unto account energy losses of ions. (author)

Computer Modeling and Simulation

Energy Technology Data Exchange (ETDEWEB)

Pronskikh, V. S. [Fermilab

2014-05-09

Verification and validation of computer codes and models used in simulation are two aspects of the scientific practice of high importance and have recently been discussed by philosophers of science. While verification is predominantly associated with the correctness of the way a model is represented by a computer code or algorithm, validation more often refers to model’s relation to the real world and its intended use. It has been argued that because complex simulations are generally not transparent to a practitioner, the Duhem problem can arise for verification and validation due to their entanglement; such an entanglement makes it impossible to distinguish whether a coding error or model’s general inadequacy to its target should be blamed in the case of the model failure. I argue that in order to disentangle verification and validation, a clear distinction between computer modeling (construction of mathematical computer models of elementary processes) and simulation (construction of models of composite objects and processes by means of numerical experimenting with them) needs to be made. Holding on to that distinction, I propose to relate verification (based on theoretical strategies such as inferences) to modeling and validation, which shares the common epistemology with experimentation, to simulation. To explain reasons of their intermittent entanglement I propose a weberian ideal-typical model of modeling and simulation as roles in practice. I suggest an approach to alleviate the Duhem problem for verification and validation generally applicable in practice and based on differences in epistemic strategies and scopes

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

Science.gov (United States)

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

Directory of Open Access Journals (Sweden)

Nadia Said

Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

Science.gov (United States)

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

Science.gov (United States)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

A mathematical model of a three-gap thyratron simulating turn-on

International Nuclear Information System (INIS)

Barnes, M. J.; Wait, G.D.

1993-06-01

Kicker magnets are required for all ring-to-ring transfers in the 5 rings of the proposed KAON factory synchrotron. The kick must rise/fall from 1% to 99% of full strength during the time interval of gaps created in the beam (80 ns to 160 ns) so that the beam can be extracted with minimum losses. Approximately one-third of the injection and extraction kicker magnets will operate continuously at a rate of 50 pulses per second: the others operate at 10 pulses per second. The kicker magnet PFN voltages will be in the range 50kV to 80kV, hence multi-gap thyratrons will be used for the injection and extraction kicker systems. Displacement current arising from turn-on of a multi-gap thyratron flows in the external circuit and can thus increase the effective rise-time of the kick. A mathematical model of a three-gap thyratron, which includes the drift spaces, has been developed for simulating turn-on, and is described in this paper. The thyratron model has been used to investigate ways to suppress the effects of displacement current on the kick, and to reduce thyratron switching loss. A ferrite saturating inductor may be connected adjacent to each thyratron to reduce switching loss, so that thyratron life can be extended and the kick rise-time improved. This inductor can also be used to reduce the effect of anode displacement current during turn-on of a multi-gap thyratron. The research has culminated in a predicted kick rise time (1% to 99%) of less than 50 ns for a TRIUMF 10 cell prototype kicker magnet. The proposed improvements are currently being implemented on our prototype kicker system. (author). 15 refs., 11 figs

An aqueous physical and mathematical modelling of ultrasonic degassing of molten metals

International Nuclear Information System (INIS)

Meidani, A.R.N.; Hasan, M.

1999-01-01

A comprehensive mathematical model, combined with an aqueous physical modelling, have been developed to simulate the ultrasonic degassing of a gassy liquid. The mathematical model forms a set of coupled, highly nonlinear and stiff differential equations. Therefore, the modified Gear method, which is a good numerical scheme for solving extremely fast moving boundary problems is applied. The threshold pressure and the effects of ultrasonic specifications on rectified diffusion of the dissolved air in water with different initial concentrations are studied. The results show that the air bubble grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume reaches several times of its initial value in a fraction of second and the gas bubble may float to the surface due to the buoyancy force. A parametric study on the present model is carried out. The results of aqueous physical modelling for bubble growth are compared to the results of the mathematical model which show a reasonable agreement between the experiments and the predictions. (author)

MATHEMATICAL MODELING AND SIMULATION OF AUTOMATIC CONTROL FOR QUINTUPLE EFFECT EVAPORATION OF CENTRAL SUGAR “EL PALMAR” IN VENEZUELA

Directory of Open Access Journals (Sweden)

Lisoviett Pérez Pinto

2015-04-01

Full Text Available In this paper, the mathematical modeling and simulation of the automatic control of the quintuple effect of evaporation of a sugar mill “El Palmar” in Venezuela is made. The multiple effect consist of 5 evaporators Robert type, with equal characteristics, connected in series. Starting from the desired operating conditions and control requirements: level in each evaporator vessel, cane syrup concentration and pressure in the fifth evaporator vessel using mass balances, balance on solids for each evaporator and energy to the barometric condenser is present at the output of the fifth vessel, the nonlinear model of the process is obtained, resulting in a system of multiple inputs and multiple outputs, with strong interactions between variables. In the design of the system of the automatic process control, we are interested in maintaining the variables that characterize the performance of it and they are regulated in an operating point; we proceed to linearize the model around an equilibrium point, resulting in a new model in terms of the variables variations around an environment from that point. Then, it is processed the model obtained in terms of input and output relations, based on the characterization of it in terms of variables and transfer relationships in the complex frequency domain. Finally, the evaporation process is simulated, establishing the adequacy of the model to the real process.

Principles of object-oriented modeling and simulation with Modelica 2.1

CERN Document Server

Fritzson, Peter

2004-01-01

A timely introduction to the latest modeling and simulation techniques. Object-oriented modeling is a fast-growing area of modeling and simulation that provides a structured, computer-supported way of doing mathematical and equation-based modeling. Modelica is today's most promising modeling language in that it effectively unifies and generalizes previous object-oriented modeling languages and provides a sound basis for the basic concepts. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1 introduces the latest methods of object-oriented component-based system modeling and

Mathematical modelling and simulation of the operation in sugar and alcohol industry: 2 - evaporation; Modelagem matematica e simulacao das operacoes da industria de acucar e alcool: 2 - evaporacao

Energy Technology Data Exchange (ETDEWEB)

Chiappetta, A; Giudici, R; Nascimento, C A.O. do [Sao Paulo Univ., SP (Brazil). Escola Politecnica

1987-12-31

A mathematical model is presented for steady-state simulation of multiple-effects evaporators systems used for concentration of sugar solution. The model basis are the fundamental energy and mass balances equations, as well as empirical correlations for the problem being handled. The evaporation system simulation is performed with an executive program which allows different process configurations. For one typical case, some process parameters (volumetric rate and concentration of feed;exhaust steam temperature) influences on syrup concentration and solution temperature were studied. (author) 8 figs., 2 refs.

A mathematical model of transport and regional uptake of radioactive gases in the human respiratory system

Science.gov (United States)

Baek, Inseok

The purpose of this research is to describe the development of a mathematical model of diffusion, convection, and lateral transport into the airway wall and alveolar absorption for inhaled radioactive gases in the human conductive and respiratory airways based on a Single Path Trumpet-bell model (SPM). Mathematical simulation models have been used successfully to study transport, absorption into the blood through alveoli, and lung tissue uptake of soluble and nonreactive radioactive gases. Results from such simulations also show clearly that inhaled radioactive gases are absorbed into the lung tissues as well as into the blood through the alveoli. In contrast to previous reports in the literature, the present study found that blood uptake through alveoli is much greater than that calculated previously. Regional depositions in the lung from inhaled radioactive gases are presented as the result of this simulation. The committed effective dose to lung tissue due to submersion in radioactive clouds has been newly defined using the results of this simulation.

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…

Modeling and Simulation for Safeguards

International Nuclear Information System (INIS)

Swinhoe, Martyn T.

2012-01-01

The purpose of this talk is to give an overview of the role of modeling and simulation in Safeguards R and D and introduce you to (some of) the tools used. Some definitions are: (1) Modeling - the representation, often mathematical, of a process, concept, or operation of a system, often implemented by a computer program; (2) Simulation - the representation of the behavior or characteristics of one system through the use of another system, especially a computer program designed for the purpose; and (3) Safeguards - the timely detection of diversion of significant quantities of nuclear material. The role of modeling and simulation are: (1) Calculate amounts of material (plant modeling); (2) Calculate signatures of nuclear material etc. (source terms); and (3) Detector performance (radiation transport and detection). Plant modeling software (e.g. FACSIM) gives the flows and amount of material stored at all parts of the process. In safeguards this allow us to calculate the expected uncertainty of the mass and evaluate the expected MUF. We can determine the measurement accuracy required to achieve a certain performance.

Mathematical modelling and TMCP simulation for optimisation of steel behaviour

International Nuclear Information System (INIS)

Siwecki, T.

2001-01-01

Physically based mathematical models for prediction of steel behaviour and microstructure evolution in connection with thermal and thermomechanical controlled processing (TMCP) development in Swedish Institute for Metals Research are discussed. The models can be used for computer predictions of recrystallization and grain growth of austenite after deformation, precipitation or dissolution of microalloying carbonitride in austenite, flow stress during hot working, phase transformation behaviour during accelerated cooling as well as the final microstructure and mechanical properties. The database, which contains information about steel behaviour for a large number of HSLA steels, is also presented. Optimization of TMCP parameters for improving the properties of the steel are discussed in relation to the microstructure and mechanical properties. The effect of TMCP parameters (reheating temperature, rolling schedules and finish rolling temperature as well as accelerated control cooling) on steel properties was studied in laboratory scale. (author)

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Mathematical model of one-man air revitalization system

Science.gov (United States)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Modelling, simulation and validation of the industrial robot

Directory of Open Access Journals (Sweden)

Aleksandrov Slobodan Č.

2014-01-01

Full Text Available In this paper, a DH model of industrial robot, with anthropomorphic configuration and five degrees of freedom - Mitsubishi RV2AJ, is developed. The model is verified on the example robot Mitsubishi RV2AJ. In paper detailed represented the complete mathematical model of the robot and the parameters of the programming. On the basis of this model, simulation of robot motion from point to point is performed, as well as the continuous movement of the pre-defined path. Also, programming of industrial robots identical to simulation programs is made, and comparative analysis of real and simulated experiment is shown. In the final section, a detailed analysis of robot motion is described.

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

An introduction to mathematical modeling of infectious diseases

CERN Document Server

Li, Michael Y

2018-01-01

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Geomechanical problems of an underground storage of spent nuclear fuel and their mathematic modelling

Directory of Open Access Journals (Sweden)

Antonín Hájek

2007-01-01

Full Text Available The paper is devoted to the use of mathematical modelling for analysis of the thermo-mechanical (T-M processes, which are relevant for the assessment of underground repositories of the spent nuclear fuel. Wes shall discuss mathematical formulation, numerical methods and parallel alghorithms, which are capable to solve large-scale complicated and coupled 3D problems. Particularly, we show an application of the described methods and parallel computer simulations for analysis of model problems concerning the Swedish KBS3 concept of underground repository.

Fermentation process diagnosis using a mathematical model

Energy Technology Data Exchange (ETDEWEB)

Yerushalmi, L; Volesky, B; Votruba, J

1988-09-01

Intriguing physiology of a solvent-producing strain of Clostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active transport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.

Mathematical modeling of a steam generator for sensor fault detection

International Nuclear Information System (INIS)

Prock, J.

1988-01-01

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The ''parity-space'' algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytical redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals. (author)

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

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

The irradiance and temperature dependent mathematical model for estimation of photovoltaic panel performances

International Nuclear Information System (INIS)

Barukčić, M.; Ćorluka, V.; Miklošević, K.

2015-01-01

Highlights: • The temperature and irradiance dependent model for the I–V curve estimation is presented. • The purely mathematical model based on the analysis of the I–V curve shape is presented. • The model includes the Gompertz function with temperature and irradiance dependent parameters. • The input data are extracted from the data sheet I–V curves. - Abstract: The temperature and irradiance dependent mathematical model for photovoltaic panel performances estimation is proposed in the paper. The base of the model is the mathematical function of the photovoltaic panel current–voltage curve. The model of the current–voltage curve is based on the sigmoid function with temperature and irradiance dependent parameters. The temperature and irradiance dependencies of the parameters are proposed in the form of analytic functions. The constant parameters are involved in the analytical functions. The constant parameters need to be estimated to get the temperature and irradiance dependent current–voltage curve. The mathematical model contains 12 constant parameters and they are estimated by using the evolutionary algorithm. The optimization problem is defined for this purpose. The optimization problem objective function is based on estimated and extracted (measured) current and voltage values. The current and voltage values are extracted from current–voltage curves given in datasheet of the photovoltaic panels. The new procedure for estimation of open circuit voltage value at any temperature and irradiance is proposed in the model. The performance of the proposed mathematical model is presented for three different photovoltaic panel technologies. The simulation results indicate that the proposed mathematical model is acceptable for estimation of temperature and irradiance dependent current–voltage curve and photovoltaic panel performances within temperature and irradiance ranges

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

Science.gov (United States)

Pirbodaghi, Tohid

2017-08-01

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

MATHEMATICS EDUCATION FOR LOGISTICS ENGINEERING

OpenAIRE

BÉLA ILLÉS; GABRIELLA BOGNÁR

2012-01-01

Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’ performance at the end of each semester for these courses. Our goal is to overview a few questions on mathematics as a core subject of engineering.

Mathematical modeling of wiped-film evaporators

International Nuclear Information System (INIS)

Sommerfeld, J.T.

1976-05-01

A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes

Modeling and simulation for fewer-axis grinding of complex surface

Science.gov (United States)

Li, Zhengjian; Peng, Xiaoqiang; Song, Ci

2017-10-01

As the basis of fewer-axis grinding of complex surface, the grinding mathematical model is of great importance. A mathematical model of the grinding wheel was established, and then coordinate and normal vector of the wheel profile could be calculated. Through normal vector matching at the cutter contact point and the coordinate system transformation, the grinding mathematical model was established to work out the coordinate of the cutter location point. Based on the model, interference analysis was simulated to find out the right position and posture of workpiece for grinding. Then positioning errors of the workpiece including the translation positioning error and the rotation positioning error were analyzed respectively, and the main locating datum was obtained. According to the analysis results, the grinding tool path was planned and generated to grind the complex surface, and good form accuracy was obtained. The grinding mathematical model is simple, feasible and can be widely applied.

Hemomath the mathematics of blood

CERN Document Server

Fasano, Antonio

2017-01-01

This book illustrates applications of mathematics to various processes (physiological or artificial) involving flowing blood, including hemorheology, microcirculation, coagulation, kidney filtration and dialysis, offering a historical overview of each topic. Mathematical models are used to simulate processes normally occurring in flowing blood and to predict the effects of dysfunctions (e.g. bleeding disorders, renal failure), as well as the effects of therapies with an eye to improving treatments. Most of the models have a completely new approach that makes patient-specific simulations possible. The book is mainly intended for mathematicians interested in medical applications, but it is also useful for clinicians such as hematologists, nephrologists, cardio-surgeons, and bioengineers. Some parts require no specific knowledge of mathematics. The book is a valuable addition to mathematics, medical, biology, and bioengineering libraries.

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

Genetic demographic networks: Mathematical model and applications.

Science.gov (United States)

Kimmel, Marek; Wojdyła, Tomasz

2016-10-01

Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise

A Mathematical Model for Dynamic Simulation of Anaerobic Digestion of Complex Substrates

DEFF Research Database (Denmark)

Angelidaki, Irini; Ellegaard, L.; Ahring, Birgitte Kiær

1993-01-01

of pH and temperature characteristics in order to accurately simulate free ammonia concentration. Free ammonia and acetate constitute the primary modulating factors in the model. The model has been applied for the simulation of digestion of cattle manure in continuously stirred tank reactors (CSTRs...

Teaching mathematical modelling through project work

DEFF Research Database (Denmark)

Blomhøj, Morten; Kjeldsen, Tinne Hoff

2006-01-01

are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...

Mathematical Model of Piston Ring Sealing in Combustion Engine

Directory of Open Access Journals (Sweden)

Koszałka Grzegorz

2015-01-01

Full Text Available This paper presents a mathematical model of piston-rings-cylinder sealing (TPC of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The paper contains descriptions of: assumptions used for developing the model, the model itself, its numerical solution as well as its computer application for carrying out simulation tests.

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

Characteristics of economic and mathematical simulation of development of working mines

Energy Technology Data Exchange (ETDEWEB)

Gorodnichiy, V G

1979-01-01

Economic and mathematical simulation is promoted by a standard procedure of computations to optimize development of production for the future as the principal method of solution of a problem. However traditional approaches to design of models need refinement which take into account the dynamic nature of a coal mine. First, the characteristics of the elements in subsystems change; second, as time passes the very structure of the system is transformed. Consequently, these processes should be reflected in the simulation in a corresponding manner. In practical terms this is expressed in the formation of files of forecast information used in computations according to a model and also in development of procedures of transformation of the model structure with a change of the structure of the subject mine with time. Let us note that the invariability of the state of the principal elements of the technological scheme of a mine with time is the necessary condition of acceptability of a model of the evolution type which is most common. For working mines the freedom of selecting solutions is considerably less than the analogous one in design.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

Science.gov (United States)

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

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…

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

Milan, Houška; Martina, Beránková

2005-01-01

The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.

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…

MATHEMATICAL MODEL OF UNSTEADY HEAT TRANSFER OF PASSENGER CAR WITH HEATING SYSTEM

Directory of Open Access Journals (Sweden)

E. V. Biloshytskyi

2018-02-01

Full Text Available Purpose. The existing mathematical models of unsteady heat processes in a passenger car do not fully reflect the thermal processes, occurring in the car wits a heating system. In addition, unsteady heat processes are often studied in steady regime, when the heat fluxes and the parameters of the thermal circuit are constant and do not depend on time. In connection with the emergence of more effective technical solutions to the life support system there is a need for creating a new mathematical apparatus, which would allow taking into account these features and their influence on the course of unsteady heat processes throughout the travel time. The purpose of this work is to create a mathematical model of the heat regime of a passenger car with a heating system that takes into account the unsteady heat processes. Methodology. To achieve this task the author composed a system of differential equations, describing unsteady heat processes during the heating of a passenger car. For the solution of the composed system of equations, the author used the method of elementary balances. Findings. The paper presents the developed numerical algorithm and computer program for simulation of transitional heat processes in a locomotive traction passenger car, which allows taking into account the various constructive solutions of the life support system of passenger cars and to simulate unsteady heat processes at any stage of the trip. Originality. For the first time the author developed a mathematical model of heat processes in a car with a heating system, that unlike existing models, allows to investigate the unsteady heat engineering performance in the cabin of the car under different operating conditions and compare the work of various life support systems from the point of view their constructive solutions. Practical value. The work presented the developed mathematical model of the unsteady heat regime of the passenger car with a heating system to estimate

Mathematical modeling of olive mill waste composting process.

Science.gov (United States)

Vasiliadou, Ioanna A; Muktadirul Bari Chowdhury, Abu Khayer Md; Akratos, Christos S; Tekerlekopoulou, Athanasia G; Pavlou, Stavros; Vayenas, Dimitrios V

2015-09-01

The present study aimed at developing an integrated mathematical model for the composting process of olive mill waste. The multi-component model was developed to simulate the composting of three-phase olive mill solid waste with olive leaves and different materials as bulking agents. The modeling system included heat transfer, organic substrate degradation, oxygen consumption, carbon dioxide production, water content change, and biological processes. First-order kinetics were used to describe the hydrolysis of insoluble organic matter, followed by formation of biomass. Microbial biomass growth was modeled with a double-substrate limitation by hydrolyzed available organic substrate and oxygen using Monod kinetics. The inhibitory factors of temperature and moisture content were included in the system. The production and consumption of nitrogen and phosphorous were also included in the model. In order to evaluate the kinetic parameters, and to validate the model, six pilot-scale composting experiments in controlled laboratory conditions were used. Low values of hydrolysis rates were observed (0.002841/d) coinciding with the high cellulose and lignin content of the composting materials used. Model simulations were in good agreement with the experimental results. Sensitivity analysis was performed and the modeling efficiency was determined to further evaluate the model predictions. Results revealed that oxygen simulations were more sensitive on the input parameters of the model compared to those of water, temperature and insoluble organic matter. Finally, the Nash and Sutcliff index (E), showed that the experimental data of insoluble organic matter (E>0.909) and temperature (E>0.678) were better simulated than those of water. Copyright © 2015 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

An inverse problem for a mathematical model of aquaponic agriculture

Science.gov (United States)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

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.

Mathematical modeling of a mixed flow spray dryer

International Nuclear Information System (INIS)

Kasiri, N.; Delkhan, F.

2001-01-01

In this paper a mathematical model has been developed to simulate the behavior of spray dryers with an up-flowing spray. The model is based on mass, energy and momentum balance on a single droplet , and mass and energy balances on the drying gas. The system of nonlinear differential equations thus obtained is solved to predict the changes in temperature, humidity, diameter, velocity components and the density of the droplets as well as the temperature and the humidity changes of the drying gas. The predicted results were then compared with an industrially available set of results. A good degree of proximity between the two is reported

The invaluable benefits of modeling and simulation in our lives

Energy Technology Data Exchange (ETDEWEB)

Lorencez, C., E-mail: carlos.lorencez@opg.com [Ontario Power Generation, Nuclear Safety Div., Pickering, Ontario (Canada)

2015-07-01

'Full text:' In general terms, we associate the words 'modeling and simulation' with semi-ideal mathematical models reproducing complex Engineering problems. However, the use of modeling and simulation is much more extensive than that: it is applied on a daily basis in almost every front of Science, from sociology and biology to climate change, medicine, robotics, war strategies, etc. It is also being applied by our frontal lobe when we make decisions. The results of these exercises on modeling and simulation have had invaluable benefits on our well being, and we are just at the beginning. (author)

The invaluable benefits of modeling and simulation in our lives

International Nuclear Information System (INIS)

Lorencez, C.

2015-01-01

'Full text:' In general terms, we associate the words 'modeling and simulation' with semi-ideal mathematical models reproducing complex Engineering problems. However, the use of modeling and simulation is much more extensive than that: it is applied on a daily basis in almost every front of Science, from sociology and biology to climate change, medicine, robotics, war strategies, etc. It is also being applied by our frontal lobe when we make decisions. The results of these exercises on modeling and simulation have had invaluable benefits on our well being, and we are just at the beginning. (author)

Mathematical model of an indirect action fuel flow controller for aircraft jet engines

Science.gov (United States)

Tudosie, Alexandru-Nicolae

2017-06-01

The paper deals with a fuel mass flow rate controller with indirect action for aircraft jet engines. The author has identified fuel controller's main parts and its operation mode, then, based on these observations, one has determined motion equations of each main part, which have built system's non-linear mathematical model. In order to realize a better study this model was linearised (using the finite differences method) and then adimensionalized. Based on this new form of the mathematical model, after applying Laplace transformation, the embedded system (controller+engine) was described by the block diagram with transfer functions. Some Simulink-Matlab simulations were performed, concerning system's time behavior for step input, which lead to some useful conclusions and extension possibilities.

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

Science.gov (United States)

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

2014-01-01

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

A Mathematical Model for the Exhaust Gas Temperature Profile of a Diesel Engine

Science.gov (United States)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2015-09-01

This work presents a heat transfer model for the exhaust gas of a diesel power generator to determine the gas temperature profile in the exhaust pipe. The numerical methodology to solve the mathematical model was developed using a finite difference method approach for energy equation resolution and determination of temperature profiles considering turbulent fluid flow and variable fluid properties. The simulation was carried out for engine operation under loads from 0 kW to 40 kW. The model was compared with results obtained using the multidimensional Ansys CFX software, which was applied to solve the governor equations of turbulent fluid flow. The results for the temperature profiles in the exhaust pipe show a good proximity between the mathematical model developed and the multidimensional software.

Simulation model for electron irradiated IGZO thin film transistors

Science.gov (United States)

Dayananda, G. K.; Shantharama Rai, C.; Jayarama, A.; Kim, Hyun Jae

2018-02-01

An efficient drain current simulation model for the electron irradiation effect on the electrical parameters of amorphous In-Ga-Zn-O (IGZO) thin-film transistors is developed. The model is developed based on the specifications such as gate capacitance, channel length, channel width, flat band voltage etc. Electrical parameters of un-irradiated IGZO samples were simulated and compared with the experimental parameters and 1 kGy electron irradiated parameters. The effect of electron irradiation on the IGZO sample was analysed by developing a mathematical model.

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

Science.gov (United States)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Mathematical Modelling as a Professional Task

Science.gov (United States)

Frejd, Peter; Bergsten, Christer

2016-01-01

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

Mathematical modeling of wastewater decolorization in a trickle-bed bioreactor.

Science.gov (United States)

Skybová, T; Přibyl, M; Pocedič, J; Hasal, P

2012-02-20

This work focuses on mathematical modeling of removal of organic dyes from textile industry waste waters by a white-rot fungus Irpex lacteus in a trickle-bed bioreactor. We developed a mathematical model of biomass and decolorization process dynamics. The model comprises mass balances of glucose and the dye in a fungal biofilm and a liquid film. The biofilm is modeled using a spatially two-dimensional domain. The liquid film is considered as homogeneous in the direction normal to the biofilm surface. The biomass growth, decay and the erosion of the biofilm are taken into account. Using experimental data, we identified values of key model parameters: the dye degradation rate constant, biofilm corrugation factor and liquid velocity. Considering the dye degradation rate constant 1×10⁻⁵ kg m⁻³ s⁻¹, we found optimal values of the corrugation factor 0.853 and 0.59 and values of the liquid velocity 5.23×10⁻³ m s⁻¹ and 6.2×10⁻³ m s⁻¹ at initial dye concentrations 0.09433 kg m⁻³ and 0.05284 kg m⁻³, respectively. A good agreement between the simulated and experimental data using estimated values of the model parameters was achieved. The model can be used to simulate the performance of laboratory scale trickle-bed bioreactor operated in a batch regime or to estimate values of principal parameters of the bioreactor system. Copyright © 2011 Elsevier B.V. All rights reserved.

Mathematical Modeling of Hybrid Electrical Engineering Systems

Directory of Open Access Journals (Sweden)

A. A. Lobaty

2016-01-01

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

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

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

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

Perrenet, J.C.; Zwaneveld, B.

2012-01-01

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

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.

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Directory of Open Access Journals (Sweden)

Xu Shixin

2014-01-01

Full Text Available Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP equations that are solved by Finite Element Method (FEM. Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods

Directory of Open Access Journals (Sweden)

Chiara Biscarini

2013-01-01

Full Text Available The numerical simulation of fast-moving fronts originating from dam or levee breaches is a challenging task for small scale engineering projects. In this work, the use of fully three-dimensional Navier-Stokes (NS equations and lattice Boltzmann method (LBM is proposed for testing the validity of, respectively, macroscopic and mesoscopic mathematical models. Macroscopic simulations are performed employing an open-source computational fluid dynamics (CFD code that solves the NS combined with the volume of fluid (VOF multiphase method to represent free-surface flows. The mesoscopic model is a front-tracking experimental variant of the LBM. In the proposed LBM the air-gas interface is represented as a surface with zero thickness that handles the passage of the density field from the light to the dense phase and vice versa. A single set of LBM equations represents the liquid phase, while the free surface is characterized by an additional variable, the liquid volume fraction. Case studies show advantages and disadvantages of the proposed LBM and NS with specific regard to the computational efficiency and accuracy in dealing with the simulation of flows through complex geometries. In particular, the validation of the model application is developed by simulating the flow propagating through a synthetic urban setting and comparing results with analytical and experimental laboratory measurements.

Modeling and simulation of different and representative engineering problems using Network Simulation Method.

Science.gov (United States)

Sánchez-Pérez, J F; Marín, F; Morales, J L; Cánovas, M; Alhama, F

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model.

Mathematical modelling a case studies approach

CERN Document Server

Illner, Reinhard; McCollum, Samantha; Roode, Thea van

2004-01-01

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...

Clock error models for simulation and estimation

International Nuclear Information System (INIS)

Meditch, J.S.

1981-10-01

Mathematical models for the simulation and estimation of errors in precision oscillators used as time references in satellite navigation systems are developed. The results, based on all currently known oscillator error sources, are directly implementable on a digital computer. The simulation formulation is sufficiently flexible to allow for the inclusion or exclusion of individual error sources as desired. The estimation algorithms, following from Kalman filter theory, provide directly for the error analysis of clock errors in both filtering and prediction

Solving a bi-objective mathematical programming model for bloodmobiles location routing problem

Directory of Open Access Journals (Sweden)

Masoud Rabbani

2017-01-01

Full Text Available Perishability of platelets, uncertainty of donors’ arrival and conflicting views in platelet supply chain have made platelet supply chain planning a problematic issue. In this paper, mobile blood collection system for platelet production is investigated. Two mathematical models are presented to cover the bloodmobile collection planning problem. The first model is a multi-objective fuzzy mathematical programming in which the bloodmobiles locations are considered with the aim of maximizing potential amount of blood collection and minimizing the operational cost. The second model is a vehicle routing problem with time windows which studies the shuttles routing problem. To tackle the first model, it is reformulated as a crisp multi objective linear programming model and then solved through a fuzzy multi objective programming approach. Several sensitivity analysis are conducted on important parameters to demonstrate the applicability of the proposed model. The proposed model is then solved by using a tailored Simulated Annealing (SA algorithm. The numerical results demonstrate promising efficiency of the proposed solution method.

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

Directory of Open Access Journals (Sweden)

Jennifer M. Suh

2017-06-01

Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.

Mathematical model of water transport in Bacon and alkaline matrix-type hydrogen-oxygen fuel cells

Science.gov (United States)

Prokopius, P. R.; Easter, R. W.

1972-01-01

Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.

Applied Computational Mathematics in Social Sciences

CERN Document Server

Damaceanu, Romulus-Catalin

2010-01-01

Applied Computational Mathematics in Social Sciences adopts a modern scientific approach that combines knowledge from mathematical modeling with various aspects of social science. Special algorithms can be created to simulate an artificial society and a detailed analysis can subsequently be used to project social realities. This Ebook specifically deals with computations using the NetLogo platform, and is intended for researchers interested in advanced human geography and mathematical modeling studies.

The High Level Mathematical Models in Calculating Aircraft Gas Turbine Engine Parameters

Directory of Open Access Journals (Sweden)

Yu. A. Ezrokhi

2017-01-01

Full Text Available The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine

Modelling and Simulation of Volume Controlled Mechanical Ventilation System

Directory of Open Access Journals (Sweden)

Yan Shi

2014-01-01

Full Text Available Volume controlled mechanical ventilation system is a typical time-delay system, which is applied to ventilate patients who cannot breathe adequately on their own. To illustrate the influences of key parameters of the ventilator on the dynamics of the ventilated respiratory system, this paper firstly derived a new mathematical model of the ventilation system; secondly, simulation and experimental results are compared to verify the mathematical model; lastly, the influences of key parameters of ventilator on the dynamics of the ventilated respiratory system are carried out. This study can be helpful in the VCV ventilation treatment and respiratory diagnostics.

A Mathematical Model of Economic Population Dynamics in a Country That Has Optimal Zakat Management

Science.gov (United States)

Subhan, M.

2018-04-01

Zakat is the main tools against two issues in Islamic economy: economic justice and helping the poor. However, no government of Islamic countries can solve the economic disparity today. A mathematical model could give some understanding about this phenomenon. The goal of this research is to obtain a mathematical model that can describe the dynamic of economic group population. The research is theoretical based on relevance references. From the analytical and numerical simulation, we conclude that well-manage zakat and full comitment of the wealthy can achieve wealth equilibrium that represents minimum poverty.

Mathematical modelling of steam generator and design of temperature regulator

Energy Technology Data Exchange (ETDEWEB)

Bogdanovic, S.S. [EE Institute Nikola Tesla, Belgrade (Yugoslavia)

1999-07-01

The paper considers mathematical modelling of once-through power station boiler and numerical algorithm for simulation of the model. Fast and numerically stable algorithm based on the linearisation of model equations and on the simultaneous solving of differential and algebraic equations is proposed. The paper also presents the design of steam temperature regulator by using the method of projective controls. Dynamic behaviour of the system closed with optimal linear quadratic regulator is taken as the reference system. The desired proprieties of the reference system are retained and solutions for superheated steam temperature regulator are determined. (author)

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

Mathematical biophysics

CERN Document Server

Rubin, Andrew

2014-01-01

This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...

Mathematical Simulation of Contaminant Flow in Closed Reservoir

Science.gov (United States)

Agranat, V. M.; Goudov, A. M.; Perminov, V. A.

2016-01-01

A mathematical model of the propagation in flooded mine lightweight contaminant due to allocation of groundwater is considered. Mathematical model was based on an analysis of experimental data and using concept and methods from reactive media mechanics. The boundary-value problem is solved numerically using the finite volume method. The distribution of fields of velocities and concentration of impurity particles in a flooded mine have been obtained at different times. These results can be used to analyze mining water treatment process due to environment and evaluate its further possible improvements.

Mathematical simulation of sediment and contaminant transport in surface waters. Annual report, October 1977--September 1978

International Nuclear Information System (INIS)

Onishi, Y.; Arnold, E.M.; Serne, R.J.; Cowan, C.E.; Thompson, F.L.; Mayer, D.W.

1979-01-01

Various pathways exist for exposure of humans and biota to radioactive materials released from nuclear facilities. Hydrologic transport (liquid pathway) is one element in the evaluation of the total radiation dose to man. Mathematical models supported by well-planned field data collection programs can be useful tools in assessing the hydrologic transport and ultimate fate of radionuclides. Radionuclides with high distribution coefficients or radionuclides in surface waters with high suspended sediment concentrations are, to a great extent, adsorbed by river and marine sediments. Thus, otherwise dilute contaminants are concentrated. Contaminated sediments may be deposited on the river and ocean beds creating a significant pathway to man. Contaminated bed sediment in turn may become a long-term source of pollution through desorption and resuspension. In order to assess migration and accumulation of radionuclides in surface waters, mathematical models must correctly simulate essential mechanisms of radionuclide transport. The objectives of this study were: (1) to conduct a critical review of (a) radionuclide transport models as well as sediment transport and representative water quality models in rivers, estuaries, oceans, lakes, and reservoirs, and (b) adsorption and desorption mechanisms of radionuclides with sediments in surface waters; (2) to synthesize a mathematical model capable of predicting short- and long-term transport and accumulation of radionuclides in marine environments

Mathematical basis for the process of model simulation of drilling operations

Energy Technology Data Exchange (ETDEWEB)

Lipovetskiy, G M; Lebedinskiy, G L

1979-01-01

The authors describe the application of a method for the model simulation of drilling operations and for the solution of problems concerned with the planning and management of such operations. A description is offered for an approach to the simulator process when the drilling operations are part of a large system. An algorithm is provided for calculating complex events.

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

2018-01-01

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Students’ mathematical learning in modelling activities

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....

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

Science.gov (United States)

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

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

Directory of Open Access Journals (Sweden)

Diego Abreu-López

2017-04-01

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

Cell damage from radiation-induced bystander effects for different cell densities simulated by a mathematical model via cellular automata

Energy Technology Data Exchange (ETDEWEB)

Meireles, Sincler P. de; Santos, Adriano M.; Grynberg, Suely Epsztein, E-mail: spm@cdtn.b, E-mail: amsantos@cdtn.b, E-mail: seg@cdtn.b [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil); Nunes, Maria Eugenia S., E-mail: mariaeugenia@iceb.ufop.b [Universidade Federal de Ouro Preto (UFOP), MG (Brazil)

2011-07-01

During recent years, there has been a shift from an approach focused entirely on DNA as the main target of ionizing radiation to a vision that considers complex signaling pathways in cells and among cells within tissues. Several newly recognized responses were classified as the so-called non-target responses in which the biological effects are not directly related to the amount of energy deposited in the DNA of cells that were traversed by radiation. In 1992 the bystander effect was described referring to a series of responses such as death, chromosomal instability or other abnormalities that occur in non-irradiated cells that came into contact with irradiated cells or medium from irradiated cells. In this work, we have developed a mathematical model via cellular automata, to quantify cell death induced by the bystander effect. The model is based on experiments with irradiated cells conditioned medium which suggests that irradiated cells secrete molecules in the medium that are capable of damaging other cells. The computational model consists of two-dimensional cellular automata which is able to simulate the transmission of bystander signals via extrinsic route and via Gap junctions. The model has been validated by experimental results in the literature. The time evolution of the effect and the dose-response curves were obtained in good accordance to them. Simulations were conducted for different values of bystander and irradiated cell densities with constant dose. From this work, we have obtained a relationship between cell density and effect. (author)

Cell damage from radiation-induced bystander effects for different cell densities simulated by a mathematical model via cellular automata

International Nuclear Information System (INIS)

Meireles, Sincler P. de; Santos, Adriano M.; Grynberg, Suely Epsztein; Nunes, Maria Eugenia S.

2011-01-01

During recent years, there has been a shift from an approach focused entirely on DNA as the main target of ionizing radiation to a vision that considers complex signaling pathways in cells and among cells within tissues. Several newly recognized responses were classified as the so-called non-target responses in which the biological effects are not directly related to the amount of energy deposited in the DNA of cells that were traversed by radiation. In 1992 the bystander effect was described referring to a series of responses such as death, chromosomal instability or other abnormalities that occur in non-irradiated cells that came into contact with irradiated cells or medium from irradiated cells. In this work, we have developed a mathematical model via cellular automata, to quantify cell death induced by the bystander effect. The model is based on experiments with irradiated cells conditioned medium which suggests that irradiated cells secrete molecules in the medium that are capable of damaging other cells. The computational model consists of two-dimensional cellular automata which is able to simulate the transmission of bystander signals via extrinsic route and via Gap junctions. The model has been validated by experimental results in the literature. The time evolution of the effect and the dose-response curves were obtained in good accordance to them. Simulations were conducted for different values of bystander and irradiated cell densities with constant dose. From this work, we have obtained a relationship between cell density and effect. (author)

A Mathematical model to predict the US Airlines operation costs and airports charges per route per passenger

NARCIS (Netherlands)

Carmona Benitez, R.B.; Lodewijiks, G.

2010-01-01

A mathematical model to estimate the average airlines operational costs and airports charges per route is important for airlines companies trying to open new routes and for data generation for other purpose such as transport modeling, simulation modeling, investment analyses for airlines and

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

Science.gov (United States)

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Mathematic models for a ray tracing method and its applications in wireless optical communications.

Science.gov (United States)

Zhang, Minglun; Zhang, Yangan; Yuan, Xueguang; Zhang, Jinnan

2010-08-16

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

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

Science.gov (United States)

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

2012-09-01

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

Mathematical and numerical analysis of PN models for photons transport problems

International Nuclear Information System (INIS)

Valentin, Xavier

2015-01-01

Computational costs for direct numerical simulations of photon transport problems are very high in terms of CPU time and memory. One way to tackle this issue is to develop reduced models that a cheaper to solve numerically. There exists number of these models: moments models, discrete ordinates models (S N ), diffusion-like models... In this thesis, we focus on P N models in which the transport operator is approached by mean of a truncated development on the spherical harmonics basis. These models are arbitrary accurate in the angular dimension and are rotationally invariants (in multiple space dimensions). The latter point is fundamental when one wants to simulate inertial confinement fusion (ICF) experiments where the spherical symmetry plays an important part in the accuracy of the numerical solutions. We study the mathematical structure of the PN models and construct a new numerical method in the special case of a one dimensional space dimension with spherical symmetry photon transport problems. We first focus on a linear transport problem in the vacuum. Even in this simple case, it appears in the P N equations geometrical source terms that are stiff in the neighborhood of r = 0 and thus hard to discretize. Existing numerical methods are not satisfactory for multiple reasons: (1) inaccuracy in the neighborhood of r = 0 ('flux-dip'), (2) do not capture steady states (well-balanced scheme), (3) no stability proof. Following recent works, we develop a new well-balanced scheme for which we show the L 2 stability. We then extend the scheme for photon transport problems within a no moving media, the linear Boltzmann equation, and interest ourselves on its behavior in the diffusion limit (asymptotic-preserving property). In a second part, we consider radiation hydrodynamics problems. Since modelization of these problems is still under discussion in the literature, we compare a set of existing models by mean of mathematical analysis and establish a hierarchy

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Current problems in applied mathematics and mathematical physics

Science.gov (United States)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Modeling and simulation of different and representative engineering problems using Network Simulation Method

Science.gov (United States)

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model. PMID:29518121

Preservice Teachers' Video Simulations and Subsequent Noticing: A Practice-Based Method to Prepare Mathematics Teachers

Science.gov (United States)

Amador, Julie M.

2017-01-01

The purpose of this study was to implement a Video Simulation Task in a mathematics methods teacher education course to engage preservice teachers in considering both the teaching and learning aspects of mathematics lesson delivery. Participants anticipated student and teacher thinking and created simulations, in which they acted out scenes on a…

Mathematical model of accelerator output characteristics and their calculation on a computer

International Nuclear Information System (INIS)

Mishulina, O.A.; Ul'yanina, M.N.; Kornilova, T.V.

1975-01-01

A mathematical model is described of output characteristics of a linear accelerator. The model is a system of differential equations. Presence of phase limitations is a specific feature of setting the problem which makes it possible to ensure higher simulation accuracy and determine a capture coefficient. An algorithm is elaborated of computing output characteristics based upon the mathematical model suggested. A capture coefficient, coordinate expectation characterizing an average phase value of the beam particles, coordinate expectation characterizing an average value of the reverse relative velocity of the beam particles as well as dispersion of these coordinates are output characteristics of the accelerator. Calculation methods of the accelerator output characteristics are described in detail. The computations have been performed on the BESM-6 computer, the characteristics computing time being 2 min 20 sec. Relative error of parameter computation averages 10 -2

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

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

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Nita Delima

2017-03-01

Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices

CERN Document Server

Merten, K; Bulirsch, R

1990-01-01

Numerical simulation and modelling of electric circuits and semiconductor devices are of primal interest in today's high technology industries. At the Oberwolfach Conference more than forty scientists from around the world, in­ cluding applied mathematicians and electrical engineers from industry and universities, presented new results in this area of growing importance. The contributions to this conference are presented in these proceedings. They include contributions on special topics of current interest in circuit and device simulation, as well as contributions that present an overview of the field. In the semiconductor area special lectures were given on mixed finite element methods and iterative procedures for the solution of large linear systems. For three dimensional models new discretization procedures including software packages were presented. Con­ nections between semiconductor equations and the Boltzmann equation were shown as well as relations to the quantum transport equation. Other issues dis...

Mathematical modeling courses for Media technology students

DEFF Research Database (Denmark)

Timcenko, Olga

2009-01-01

This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...

Teaching Mathematical Modelling for Earth Sciences via Case Studies

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).

Mathematical modeling of large floating roof reservoir temperature arena

Directory of Open Access Journals (Sweden)

Liu Yang

2018-03-01

Full Text Available The current study is a simplification of related components of large floating roof tank and modeling for three dimensional temperature field of large floating roof tank. The heat transfer involves its transfer between the hot fluid in the oil tank, between the hot fluid and the tank wall and between the tank wall and the external environment. The mathematical model of heat transfer and flow of oil in the tank simulates the temperature field of oil in tank. Oil temperature field of large floating roof tank is obtained by numerical simulation, map the curve of central temperature dynamics with time and analyze axial and radial temperature of storage tank. It determines the distribution of low temperature storage tank location based on the thickness of the reservoir temperature. Finally, it compared the calculated results and the field test data; eventually validated the calculated results based on the experimental results.

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

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

2007-08-01

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

Two-dimensional mathematical model for simulation of the drying process of thick layers of natural materials in a conveyor-belt dryer

Directory of Open Access Journals (Sweden)

Salemović Duško R.

2017-01-01

Full Text Available This paper presents the mathematical model and numerical analysis of the convective drying process of thick slices of colloidal capillary-porous materials slowly moving through conveyor-belt dryer. A flow of hot moist air was used as drying agent. The drying process has been analyzed in the form of a 2-D mathematical model, in two directions: along the conveyor and perpendicular on it. The mathematical model consists of two non-linear differential equations and one equation with a transcendent character and it is based on the mathematical model developed for drying process in a form of a 1-D thin layer. The appropriate boundary conditions were introduced. The presented model is suitable for the automated control of conveyor-belt dryers. The obtained results with analysis could be useful in predicting the drying kinetics of potato slices and similar natural products.

DEVELOPING INDUSTRIAL ROBOT SIMULATION MODEL TUR10-K USING “UNIVERSAL MECHANISM” SOFTWARE COMPLEX

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Vadim Vladimirovich Chirkov

2018-02-01

Full Text Available Manipulation robots are complex spatial mechanical systems having five or six degrees of freedom, and sometimes more. For this reason, modeling manipulative robots movement, even in the kinematic formulation, is a complex mathematical task. If one moves from kinematic modeling of motion to dynamic modeling then there must be taken into account the inertial properties of the modeling object. In this case, analytical constructing of such a complex object mathematical model as a manipulation robot becomes practically impossible. Therefore, special computer-aided design systems, called CAE-systems, are used for modeling complex mechanical systems. The purpose of the paper is simulation model construction of a complex mechanical system, such as the industrial robot TUR10-K, to obtain its dynamic characteristics. Developing such models makes it possible to reduce the complexity of designing complex systems process and to obtain the necessary characteristics. Purpose. Developing the simulation model of the industrial robot TUR10-K and obtaining dynamic characteristics of the mechanism. Methodology: the article is used a computer simulation method. Results: There is obtained the simulation model of the robot and its dynamic characteristics. Practical implications: the results can be used in the mechanical systems design and various simulation models.

Mathematical modeling of water radiolysis in the Syrian MNSR reactor

International Nuclear Information System (INIS)

Soukieh, M.

2009-11-01

Because it is difficult to measure the concentration of the radiolytic species in reactors under operating conduction, they must be estimated by computer simulation techniques. This study discusses the mathematical modeling of water radiolysis modeling of the MNSR nuclear reactor cooling water. The mathematical model comprising of 13 differential equations describe 55 chemical reactions of radiolytic species e - a q H + , OH - , H, H 2 , OH, HO 2 , O 2 , HO - 2 , O - , O - 2 , O - 3 . The mathematical model have been tested and it shows a good agreement of the computed values in this work with the results cited in references [1,18] in case of only γray irradiation of pure water with dose rate of 1.18x10 19 eV/L s. The neutron fluxes and dose rates at the interface of cladding-water for the different fuel rings in the MNSR core are determined using MCNP-4C code. In addition, the time dependent of the radiolytic specie concentrations were estimated for max. and min. dose rates and at temperature of 20 degree centigrade in the MNSR. The radiolytic specie concentrations reach the steady sate after about 200-400 s. The radiolytic specie concentrations order of H 2 , O 2 , H 2 O 2 were about ppb. Also this study shows the possibility of suppressed the water radiolysis reactions by adding hydrogen to the MNSR reactor cooling water. (author)

Traffic flow dynamics data, models and simulation

CERN Document Server

Treiber, Martin

2013-01-01

This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on ...

Mathematical methods for cancer evolution

CERN Document Server

Suzuki, Takashi

2017-01-01

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematica...

A mathematical model of brain glucose homeostasis

Directory of Open Access Journals (Sweden)

Kimura Hidenori

2009-11-01

Full Text Available Abstract Background The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation. Methods In order to demonstrate the relationship between brain glucose homeostasis and blood hyperglycemia in diabetes, a brain-oriented mathematical model was developed by considering the brain as the controlled object while the remaining body as the actuator. After approximating the body compartmentally, the concentration dynamics of glucose, as well as those of insulin and glucagon, are described in each compartment. The brain-endocrine crosstalk, which regulates blood glucose level for brain glucose homeostasis together with the peripheral interactions among glucose, insulin and glucagon, is modeled as a proportional feedback control of brain glucose. Correlated to the brain, long-term effects of psychological stress and effects of blood-brain-barrier (BBB adaptation to dysglycemia on the generation of hyperglycemia are also taken into account in the model. Results It is shown that simulation profiles obtained from the model are qualitatively or partially quantitatively consistent with clinical data, concerning the GIG regulatory system responses to bolus glucose, stepwise and continuous glucose infusion. Simulations also revealed that both stress and BBB adaptation contribute to the generation of hyperglycemia. Conclusion Simulations of the model of a healthy person under long-term severe stress demonstrated that feedback control of brain glucose concentration results in elevation of blood glucose level. In this paper, we try to suggest that hyperglycemia in diabetes may be a normal outcome of brain glucose homeostasis.

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

2012-01-01

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

Development of a mathematical model for sugar cane borer population, Diatrea sacharalis (Fabr., 1794) and simulation of the Sterile Insect Technique (SIT)

International Nuclear Information System (INIS)

Sgrillo, R.B.

1979-08-01

The determination of the theoretical possibility of applying the Sterile Insect Technique (SIT) to control sugar cane borer, Diatraea saccharalis (Fabricius, 1794), population in the State of Sao Paulo was aimed at. This has been achieved with the development of a mathematical model of the insect population dynamics after simulation of the SIT. The model was constructed based on a field survey made in 1976 in four sugar cane regions of the State. With the surveys, data relative to insect population density of larvae and pupae was obtained. Data regarding fluctuation of adults and of some predators population were obtained using light traps. Through mathematical analysis of the data from the surveys it was noted that diapause occurred in large larvae. The percentage of larvae in diapause showed correlation with photoperiod and temperature. It was established that the number of degree days necessary for the insect to complement a generation is 954. A method was proposed to utilize the thermic constant concept equally for diapause conditions. A laboratory experiment showed that male adults irradiated at 50 krad gamma radiation ( 60 Co) produced a non-viable generation. Monthly mortality in each stage was estimated. From these data, sub-models were developed, correlating mortality with climatic and biological variables. The sub-models when grouped formed a model that permitted the simulation of the SIT. It was concluded that release of sterile insects in a number equal to those existing in the field, during the first three generations, would be an efficient method to control insect populations. Theoretically, a profit would be obtained if the cost for application of the method was up to Cr$ 1,355 per hectare. Release of sterile insects in a number nine times larger than those existing in the field during the first generation, would be equally efficient and a profit would be obtained if the cost for application of the method was Cr$ 975 per hectare. (Author) [pt

Mathematical models of tumour and normal tissue response

International Nuclear Information System (INIS)

Jones, B.; Dale, R.G.; Charing Cross Group of Hospitals, London

1999-01-01

The historical application of mathematics in the natural sciences and in radiotherapy is compared. The various forms of mathematical models and their limitations are discussed. The Linear Quadratic (LQ) model can be modified to include (i) radiobiological parameter changes that occur during fractionated radiotherapy, (ii) situations such as focal forms of radiotherapy, (iii) normal tissue responses, and (iv) to allow for the process of optimization. The inclusion of a variable cell loss factor in the LQ model repopulation term produces a more flexible clonogenic doubling time, which can simulate the phenomenon of 'accelerated repopulation'. Differential calculus can be applied to the LQ model after elimination of the fraction number integers. The optimum dose per fraction (maximum cell kill relative to a given normal tissue fractionation sensitivity) is then estimated from the clonogen doubling times and the radiosensitivity parameters (or α/β ratios). Economic treatment optimization is described. Tumour volume studies during or following teletherapy are used to optimize brachytherapy. The radiation responses of both individual tumours and tumour populations (by random sampling 'Monte-Carlo' techniques from statistical ranges of radiobiological and physical parameters) can be estimated. Computerized preclinical trials can be used to guide choice of dose fractionation scheduling in clinical trials. The potential impact of gene and other biological therapies on the results of radical radiotherapy are testable. New and experimentally testable hypotheses are generated from limited clinical data by exploratory modelling exercises. (orig.)

Analog quantum simulation of generalized Dicke models in trapped ions

Science.gov (United States)

Aedo, Ibai; Lamata, Lucas

2018-04-01

We propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behavior arises, and the ultrastrong coupling (USC) regime, where a rotating-wave approximation cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes and the two-qubit anisotropic Dicke model in the USC regime and the deep-strong coupling regime. The agreement between the mathematical models and the ion system convinces us that these quantum simulations can be implemented in the laboratory with current or near-future technology. This formalism establishes an avenue for the quantum simulation of many-spin Dicke models in trapped ions.

Generalized math model for simulation of high-altitude balloon systems

Science.gov (United States)

Nigro, N. J.; Elkouh, A. F.; Hinton, D. E.; Yang, J. K.

1985-01-01

Balloon systems have proved to be a cost-effective means for conducting research experiments (e.g., infrared astronomy) in the earth's atmosphere. The purpose of this paper is to present a generalized mathematical model that can be used to simulate the motion of these systems once they have attained float altitude. The resulting form of the model is such that the pendulation and spin motions of the system are uncoupled and can be analyzed independently. The model is evaluated by comparing the simulation results with data obtained from an actual balloon system flown by NASA.

Modeling and simulation of thermally actuated bilayer plates

Science.gov (United States)

Bartels, Sören; Bonito, Andrea; Muliana, Anastasia H.; Nochetto, Ricardo H.

2018-02-01

We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be discretized with standard plate elements. We devise a fully practical iterative scheme and apply it to the simulation of folding of several practically useful compliant structures comprising of thin elastic layers.

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.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Mathematical modeling of acid-base physiology.

Science.gov (United States)

Occhipinti, Rossana; Boron, Walter F

2015-01-01

pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.

Normal Brain-Skull Development with Hybrid Deformable VR Models Simulation.

Science.gov (United States)

Jin, Jing; De Ribaupierre, Sandrine; Eagleson, Roy

2016-01-01

This paper describes a simulation framework for a clinical application involving skull-brain co-development in infants, leading to a platform for craniosynostosis modeling. Craniosynostosis occurs when one or more sutures are fused early in life, resulting in an abnormal skull shape. Surgery is required to reopen the suture and reduce intracranial pressure, but is difficult without any predictive model to assist surgical planning. We aim to study normal brain-skull growth by computer simulation, which requires a head model and appropriate mathematical methods for brain and skull growth respectively. On the basis of our previous model, we further specified suture model into fibrous and cartilaginous sutures and develop algorithm for skull extension. We evaluate the resulting simulation by comparison with datasets of cases and normal growth.

Modeling and numerical simulations of the influenced Sznajd model

Science.gov (United States)

Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep

2017-08-01

This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

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

Mathematical modeling improves EC50 estimations from classical dose-response curves.

Science.gov (United States)

Nyman, Elin; Lindgren, Isa; Lövfors, William; Lundengård, Karin; Cervin, Ida; Sjöström, Theresia Arbring; Altimiras, Jordi; Cedersund, Gunnar

2015-03-01

The β-adrenergic response is impaired in failing hearts. When studying β-adrenergic function in vitro, the half-maximal effective concentration (EC50 ) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50 . Instead, we have applied a mathematical modeling approach to interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nm) is higher than the classically interpreted EC50 (46-191 nm). Mathematical modeling thus makes it possible to re-interpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible. The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at http://jjj.bio.vu.nl/database/nyman. © 2015 FEBS.

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

Science.gov (United States)

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

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

Science.gov (United States)

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided. PMID:26309390

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...

Simulation modelling for new gas turbine fuel controller creation.

Science.gov (United States)

Vendland, L. E.; Pribylov, V. G.; Borisov, Yu A.; Arzamastsev, M. A.; Kosoy, A. A.

2017-11-01

State of the art gas turbine fuel flow control systems are based on throttle principle. Major disadvantage of such systems is that they require high pressure fuel intake. Different approach to fuel flow control is to use regulating compressor. And for this approach because of controller and gas turbine interaction a specific regulating compressor is required. Difficulties emerge as early as the requirement definition stage. To define requirements for new object, his properties must be known. Simulation modelling helps to overcome these difficulties. At the requirement definition stage the most simplified mathematical model is used. Mathematical models will get more complex and detailed as we advance in planned work. If future adjusting of regulating compressor physical model to work with virtual gas turbine and physical control system is planned.

Computer Simulation of Noise Effects of the Neighborhood of Stimulus Threshold for a Mathematical Model of Homeostatic Regulation of Sleep-Wake Cycles

Directory of Open Access Journals (Sweden)

Wuyin Jin

2017-01-01

Full Text Available The noise effects on a homeostatic regulation of sleep-wake cycles’ neuronal mathematical model determined by the hypocretin/orexin and the local glutamate interneurons spatiotemporal behaviors are studied within the neighborhood of stimulus threshold in this work; the neuronal noise added to the stimulus, the conductance, and the activation variable of the modulation function are investigated, respectively, based on a circadian input skewed in sine function. The computer simulation results suggested that the increased amplitude of external current input will lead to the fact that awakening time is advanced but the sleepy time remains the same; for the bigger conductance and modulation noise, the regulatory mechanism of the model sometimes will be collapsed and the coupled two neurons of the model show very irregular activities; the falling asleep or wake transform appears at nondeterminate time.

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Mathematical modeling of the working cycle of oil injected rotary twin screw compressor

Energy Technology Data Exchange (ETDEWEB)

Seshaiah, N. [Cryogenics and Gas dynamics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Sector-2, NIT Campus, Rourkela 769008, Orissa (India)]. E-mail: seshuet@yahoo.com; Ghosh, Subrata Kr. [Cryogenics and Gas dynamics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Sector-2, NIT Campus, Rourkela 769008, Orissa (India); Sahoo, R.K. [Cryogenics and Gas dynamics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Sector-2, NIT Campus, Rourkela 769008, Orissa (India); Sarangi, Sunil Kr. [Cryogenics and Gas dynamics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Sector-2, NIT Campus, Rourkela 769008, Orissa (India)

2007-01-15

Oil injected twin-screw air and gas compressors are widely used for medium pressure applications in many industries. Low cost air compressors can be adopted for compression of helium and special gases, leading to significant cost saving. Mathematical analysis of oil injected twin-screw compressor is carried out on the basis of the laws of perfect gas and standard thermodynamic relations. Heat transfer coefficient required for computer simulation is experimentally obtained and used in performance prediction, when the working medium being air or helium. A mathematical model has been developed for calculating the compressor performance and for validating the results with experimental data. The flow coefficients required for numerical simulation to calculate leakage flow rates are obtained from efficiency verses clearance curves. Effect of some of the compressor operating and design parameters on power and volumetric efficiencies have been analyzed and presented.

Mathematical modeling of the working cycle of oil injected rotary twin screw compressor

International Nuclear Information System (INIS)

Seshaiah, N.; Ghosh, Subrata Kr.; Sahoo, R.K.; Sarangi, Sunil Kr.

2007-01-01

Oil injected twin-screw air and gas compressors are widely used for medium pressure applications in many industries. Low cost air compressors can be adopted for compression of helium and special gases, leading to significant cost saving. Mathematical analysis of oil injected twin-screw compressor is carried out on the basis of the laws of perfect gas and standard thermodynamic relations. Heat transfer coefficient required for computer simulation is experimentally obtained and used in performance prediction, when the working medium being air or helium. A mathematical model has been developed for calculating the compressor performance and for validating the results with experimental data. The flow coefficients required for numerical simulation to calculate leakage flow rates are obtained from efficiency verses clearance curves. Effect of some of the compressor operating and design parameters on power and volumetric efficiencies have been analyzed and presented

Continuum mathematical modelling of pathological growth of blood vessels

Science.gov (United States)

Stadnik, N. E.; Dats, E. P.

2018-04-01

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

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

Physical and mathematical models for diffusion of thermal pollutants in water

International Nuclear Information System (INIS)

Pires, E.C.; Giorgetti, M.F.; Carajilescov, P.

1983-01-01

Mathematical models, such as the Fickian model and the model at PAILY and SAYRE, have been used in the analysis of thermal pollution. In the present work, experimental simulations of thermal dispersion were made using an artificial channel with injection of hat water and measurements of the temperature field were taken. The results were compared with the results given by the mentioned models, applying the image sources method. Due to the limitations of the model of PAILY and SAYRE, it was generalized for thermal sources posicioned at any place in the channel. The model of PAILY and SAYRE proved to be more satisfactory than the Fickian model and the image sources method was considered adequate. (Author) [pt

Comparison of Different Mathematical Models of Cavitation

Directory of Open Access Journals (Sweden)

Dorota HOMA

2014-12-01

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

Mathematical modeling of photoinitiated coating degradation: Effects of coating glass transition temperature and light stabilizers

DEFF Research Database (Denmark)

Kiil, Søren; G.de With, R.A.T.M.Van Benthem

2013-01-01

A mathematical model, describing coating degradation mechanisms of thermoset coatings exposed to ultraviolet radiation and humidity at constant temperature, was extended to simulate the behavior of a coating with a low glass transition temperature. The effects of adding light stabilizers (a UV...

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

Science.gov (United States)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Mathematical modelling of two-phase flows

International Nuclear Information System (INIS)

Komen, E.M.J.; Stoop, P.M.

1992-11-01

A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

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

2012-04-01

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

Math modeling and computer mechanization for real time simulation of rotary-wing aircraft

Science.gov (United States)

Howe, R. M.

1979-01-01

Mathematical modeling and computer mechanization for real time simulation of rotary wing aircraft is discussed. Error analysis in the digital simulation of dynamic systems, such as rotary wing aircraft is described. The method for digital simulation of nonlinearities with discontinuities, such as exist in typical flight control systems and rotor blade hinges, is discussed.

Mathematical 3D modelling and sensitivity analysis of multipolar radiofrequency ablation in the spine.

Science.gov (United States)

Matschek, Janine; Bullinger, Eric; von Haeseler, Friedrich; Skalej, Martin; Findeisen, Rolf

2017-02-01

Radiofrequency ablation is a valuable tool in the treatment of many diseases, especially cancer. However, controlled heating up to apoptosis of the desired target tissue in complex situations, e.g. in the spine, is challenging and requires experienced interventionalists. For such challenging situations a mathematical model of radiofrequency ablation allows to understand, improve and optimise the outcome of the medical therapy. The main contribution of this work is the derivation of a tailored, yet expandable mathematical model, for the simulation, analysis, planning and control of radiofrequency ablation in complex situations. The dynamic model consists of partial differential equations that describe the potential and temperature distribution during intervention. To account for multipolar operation, time-dependent boundary conditions are introduced. Spatially distributed parameters, like tissue conductivity and blood perfusion, allow to describe the complex 3D environment representing diverse involved tissue types in the spine. To identify the key parameters affecting the prediction quality of the model, the influence of the parameters on the temperature distribution is investigated via a sensitivity analysis. Simulations underpin the quality of the derived model and the analysis approach. The proposed modelling and analysis schemes set the basis for intervention planning, state- and parameter estimation, and control. Copyright © 2016. Published by Elsevier Inc.

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...

MathModelica - An Extensible Modeling and Simulation Environment with Integrated Graphics and Literate Programming

OpenAIRE

Fritzson, Peter; Gunnarsson, Johan; Jirstrand, Mats

2002-01-01

MathModelica is an integrated interactive development environment for advanced system modeling and simulation. The environment integrates Modelica-based modeling and simulation with graphic design, advanced scripting facilities, integration of program code, test cases, graphics, documentation, mathematical type setting, and symbolic formula manipulation provided via Mathematica. The user interface consists of a graphical Model Editor and Notebooks. The Model Editor is a graphical user interfa...

Mathematical analysis and algorithms for efficiently and accurately implementing stochastic simulations of short-term synaptic depression and facilitation

Directory of Open Access Journals (Sweden)

Mark D McDonnell

2013-05-01

Full Text Available The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of action-potential arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic action potential, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.

Modeling and simulation of cars in frontal collision

Science.gov (United States)

Deac, S. C.; Perescu, A.; Simoiu, D.; Nyaguly, E.; Crâştiu, I.; Bereteu, L.

2018-01-01

Protection of cars, mainly drivers and passengers in a collision are very important issues worldwide. Statistics given by “World Health Organization” are alarming rate of increase in the number of road accidents, most claiming with serious injury, human and material loss. For these reasons has been a continuous development of protection systems, especially car causing three quarters of all accidents. Mathematical modeling and simulation of a car behavior during a frontal collision leads to new solutions in the development of protective systems. This paper presents several structural models of a vehicle during a frontal collision and its behavior is analyzed by numerical simulation using Simulink.

Mathematical models and accuracy of radioisotope gauges

International Nuclear Information System (INIS)

Urbanski, P.

1989-01-01

Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

Seshaiyer, Padmanabhan

2017-01-01

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

Dynamic modeling and simulation of a real world billiard

International Nuclear Information System (INIS)

Hartl, Alexandre E.; Miller, Bruce N.; Mazzoleni, Andre P.

2011-01-01

Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model's predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence. -- Highlights: → We create a model of a gravitational billiard that includes rotation and dissipation. → Predictions of the model are compared with the experiments of Felt and Olafsen. → The simulations correctly predict the essential features of the experiments.

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

Science.gov (United States)

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

2018-03-01

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

Geometry optimization of a fibrous scaffold based on mathematical modelling and CFD simulation of a dynamic cell culture

DEFF Research Database (Denmark)

Tajsoleiman, Tannaz; J. Abdekhodaie, Mohammad; Gernaey, Krist

2016-01-01

simulation of cartilage cell culture under a perfusion flow, which allows not only to characterize the supply of nutrients and metabolic products inside a fibrous scaffold, but also to assess the overall culture condition and predict the cell growth rate. Afterwards, the simulation results supported finding...... an optimized design of the scaffold within a new mathematical optimization algorithm that is proposed. The main concept of this optimization routine isto maintain a large effective surface while simultaneously keeping the shear stress levelin an operating range that is expected to be supporting growth....... Therewith, it should bepossible to gradually reach improved culture efficiency as defined in the objective function....

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

The Spectrum of Mathematical Models.

Science.gov (United States)

Karplus, Walter J.

1983-01-01

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

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

Mathematical models in nuclear safety and radiation protection of nuclear energy

International Nuclear Information System (INIS)

1993-01-01

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

MATHEMATICAL MODELING OF UNSTEADY HEAT EXCHANGE IN A PASSENGER CAR

Directory of Open Access Journals (Sweden)

I. Yu. Khomenko

2013-07-01

Full Text Available Purpose.Existing mathematicalmodelsofunsteadyheatexchangeinapassengercardonotsatisfytheneedofthedifferentconstructivedecisionsofthelifesupportsystemefficiencyestimation. They also don’t allow comparing new and old life support system constructions influence on the inner environment conditions. Moreoverquite frequently unsteady heat exchange processes were studied at the initial car motion stage. Due to the new competitive engineering decisionsof the lifesupportsystemthe need of a new mathematical instrument that would satisfy the mentioned features and their influence on the unsteadyheatexchangeprocesses during the whole time of the road appeared. The purpose of this work is creation of the mathematicalmodel ofunsteadyheatexchangeinapassengercarthatcan satisfythe above-listed requirements. Methodology. Fortheassigned task realizationsystemofdifferentialequationsthatcharacterizesunsteadyheatexchangeprocessesinapassengercarwascomposed; forthesystemof equationssolution elementary balance method was used. Findings. Computational algorithm was developed andcomputer program for modeling transitional heat processes in the car was designed. It allows comparing different life support system constructions influence on the inner environment conditionsand unsteady heat exchange processes can be studied at every car motion stage. Originality.Mathematicalmodelofunsteadyheatexchangeinapassengercarwasimproved. That is why it can be used for the heat engineering studying of the inner car state under various conditions and for the operation of the different life support systems of passenger cars comparison. Mathematicalmodelingofunsteadyheatexchangeinapassengercarwas made by the elementary balance method. Practical value. Created mathematical model gives the possibility to simulate temperature changes in passenger car on unsteady thermal conditions with enough accuracy and to introduce and remove additional elements to the designed model. Thus different

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

Science.gov (United States)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Volcano Modelling and Simulation gateway (VMSg): A new web-based framework for collaborative research in physical modelling and simulation of volcanic phenomena

Science.gov (United States)

Esposti Ongaro, T.; Barsotti, S.; de'Michieli Vitturi, M.; Favalli, M.; Longo, A.; Nannipieri, L.; Neri, A.; Papale, P.; Saccorotti, G.

2009-12-01

Physical and numerical modelling is becoming of increasing importance in volcanology and volcanic hazard assessment. However, new interdisciplinary problems arise when dealing with complex mathematical formulations, numerical algorithms and their implementations on modern computer architectures. Therefore new frameworks are needed for sharing knowledge, software codes, and datasets among scientists. Here we present the Volcano Modelling and Simulation gateway (VMSg, accessible at http://vmsg.pi.ingv.it), a new electronic infrastructure for promoting knowledge growth and transfer in the field of volcanological modelling and numerical simulation. The new web portal, developed in the framework of former and ongoing national and European projects, is based on a dynamic Content Manager System (CMS) and was developed to host and present numerical models of the main volcanic processes and relationships including magma properties, magma chamber dynamics, conduit flow, plume dynamics, pyroclastic flows, lava flows, etc. Model applications, numerical code documentation, simulation datasets as well as model validation and calibration test-cases are also part of the gateway material.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

Science.gov (United States)

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

Mathematical Modelling of a Hybrid Micro-Cogeneration Group Based on a Four Stroke Diesel Engine

Directory of Open Access Journals (Sweden)

Apostol Valentin

2014-06-01

Full Text Available The paper presents a part of the work conducted in the first stage of a Research Grant called ”Hybrid micro-cogeneration group of high efficiency equipped with an electronically assisted ORC” acronym GRUCOHYB. The hybrid micro-cogeneration group is equipped with a four stroke Diesel engine having a maximum power of 40 kW. A mathematical model of the internal combustion engine is presented. The mathematical model is developed based on the Laws of Thermodynamics and takes into account the real, irreversible processes. Based on the mathematical model a computation program was developed. The results obtained were compared with those provided by the Diesel engine manufacturer. Results show a very high correlation between the manufacturer’s data and the simulation results for an engine running at 100% load. Future developments could involve using an exergetic analysis to show the ability of the ORC to generate electricity from recovered heat

Mathematical model of the Savannah River Site waste tank farm

International Nuclear Information System (INIS)

Smith, F.G. III.

1991-01-01

A mathematical model has been developed to simulate operation of the waste tank farm and the associated evaporator systems at the Savannah River Site. The model solves material balance equations to predict the volumes of liquid waste, salt, and sludge for all of the tanks within each of the evaporator systems. Additional logic is included to model the behavior of waste tanks not directly associated with the evaporators. Input parameters include the Material Management Plan forecast of canyon operations, specification of other waste sources for the evaporator systems, evaporator operating characteristics, and salt and sludge removal schedules. The model determines how the evaporators will operate, when waste transfers can be made, and waste accumulation rates. Output from the model includes waste tank contents, summaries of systems operations, and reports of space gain and the remaining capacity to store waste materials within the tank farm. Model simulations can be made to predict waste tank capacities on a daily basis for up to 20 years. The model is coded as a set of three computer programs designed to run on either IBM compatible or Apple Macintosh II personal computers

A Simple Mathematical Model of the Anaerobic Digestion of Wasted Fruits and Vegetables in Mesophilic Conditions

Directory of Open Access Journals (Sweden)

Elena Chorukova

2015-04-01

Full Text Available Anaerobic digestion is an effective biotechnological process for treatment of different agricultural, municipal and industrial wastes. Use of mathematical models is a powerful tool for investigations and optimisation of the anaerobic digestion. In this paper a simple mathematical model of the anaerobic digestion of wasted fruits and vegetables was developed and verified experimentally and by computer simulations using Simulink. A three-step mass-balance model was considered including the gas phase. The parameter identification was based on a set of 150 days of dynamical experiments in a laboratory bioreactor. Two step identification procedure to estimate 4 model parameters is presented. The results of 15 days of experiment in a pilot-scale bioreactor were then used to validate the model.

Sensor-Augmented Pump-Based Customized Mathematical Model for Type 1 Diabetes.

Science.gov (United States)

Grosman, Benyamin; Wu, Di; Miller, Diana; Lintereur, Louis; Roy, Anirban; Parikh, Neha; Kaufman, Francine R

2018-03-01

Simulations using mathematical models are important for studying, developing, and improving therapies for people with type 1 diabetes. The Medtronic CareLink ® database was used to create virtual patients with a variety of inter-insulin sensitivities, meal absorption rates, pharmacokinetics, age, and gender. In addition, intra-insulin sensitivities of the virtual patients change over a 24-h cycle. A total of 2087 virtual patients were developed. The time percentage between 70 and 180 mg/dL of the CareLink uploads and the simulated virtual patients was 72.4% (18.6) and 74.1% (16.9), respectively. The time percentage 18 years) and 90 adult (>28 years) virtual patients, respectively. The Medtronic CareLink database was utilized to generate a large number of virtual patients with a variety of insulin sensitivities, pharmacokinetics, and meal absorption rates. This new simulation model can be potentially used to evaluate and prognosticate the outcomes of studies of artificial pancreas algorithms and systems.

Enhanced model for integrated simulation of an entrained bed gasifier implemented as Aspen Hysys extension

Energy Technology Data Exchange (ETDEWEB)

Perez-Fortes, M; Bojarski, A; Ferrer-Nadal, S; Kopanos, G; Mitta, N; Pinilla, C A; Nougues, J M; Velo, E; Puigjaner, L [Universitat Politecnica de Catalunya, Barcelona (Spain). Dept. of Chemical Engineering-CEPIMA

2007-07-01

In this work an enhanced mathematical model of an entrained bed gasifier has been developed for improved synthesis gas production. The gasification model considers five stages: pyrolysis, volatiles combustion, char combustion, gasification and a final gas equilibrium zone. Mathematical simulations are carried out to help finding out feasible operating conditions of the process to achieve improved process performance. Visual Basic (VB) is tested as tool for modelling, by using the Aspen Hysys Extension (AHE) interface standards. This standard provides a suitable environment for this purpose, since it allows the creation of completely custom modules which are easy to plug and use thus facilitating the handling of complex models ready to interact with commercial simulation platforms. In this work, integration of different models is accomplished in Aspen Hysys (AH), which provides the basic connectivity within models components, and the thermodynamic framework needed. The integrated modules simulation environment platform uses data from ELCOGAS for validation purposes with excellent preliminary results. 9 refs., 2 figs.

Mathematical and numerical modeling of early atherosclerotic lesions***

Directory of Open Access Journals (Sweden)

Raoult Annie

2010-12-01

Full Text Available This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting, we couple a simple lesion growth model relying on the biomolecular process that takes place in the intima with blood flow dynamics and mass transfer. We perform numerical simulations on a two-dimensional geometry taken from [6,7] that mimicks a carotid artery deformed by a perivascular cast and we compare the numerical results with experimental data.

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary

Regulatory T cell effects in antitumor laser immunotherapy: a mathematical model and analysis

Science.gov (United States)

Dawkins, Bryan A.; Laverty, Sean M.

2016-03-01

Regulatory T cells (Tregs) have tremendous influence on treatment outcomes in patients receiving immunotherapy for cancerous tumors. We present a mathematical model incorporating the primary cellular and molecular components of antitumor laser immunotherapy. We explicitly model developmental classes of dendritic cells (DCs), cytotoxic T cells (CTLs), primary and metastatic tumor cells, and tumor antigen. Regulatory T cells have been shown to kill antigen presenting cells, to influence dendritic cell maturation and migration, to kill activated killer CTLs in the tumor microenvironment, and to influence CTL proliferation. Since Tregs affect explicitly modeled cells, but we do not explicitly model dynamics of Treg themselves, we use model parameters to analyze effects of Treg immunosuppressive activity. We will outline a systematic method for assigning clinical outcomes to model simulations and use this condition to associate simulated patient treatment outcome with Treg activity.

Use of mathematical modeling in nuclear measurements projects

International Nuclear Information System (INIS)

Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

2011-01-01

Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-06-01

This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.

2013-01-01

methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more