Search results for: mathematical model
7603 All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model
Authors: S. A. Sadegh Zadeh, C. Kambhampati
Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.
Keywords: All-or-none, computational modelling, mathematical model, transmembrane voltage, action potential.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1075
7602 Nonlinear Mathematical Model of the Rotor Motion in a Thin Hydrodynamic Gap
Authors: Jaroslav Krutil, František Pochylý, Simona Fialová
Abstract:The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.
Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1581
7601 Mathematical Modeling of Non-Isothermal Multi-Component Fluid Flow in Pipes Applying to Rapid Gas Decompression in Rich and Base Gases
Authors: Evgeniy Burlutskiy
Abstract:The paper presents a one-dimensional transient mathematical model of compressible non-isothermal multicomponent fluid mixture flow in a pipe. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved in the model. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales- Eakin (LGE) correlation. Numerical analysis of rapid gas decompression process in rich and base natural gases is made on the basis of the proposed mathematical model. The model is successfully validated on the experimental data . The proposed mathematical model shows a very good agreement with the experimental data  in a wide range of pressure values and predicts the decompression in rich and base gas mixtures much better than analytical and mathematical models, which are available from the open source literature.
Keywords: Mathematical model, Multi-Component gas mixture flow, Rapid Gas DecompressionProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1824
7600 Mathematical Models of Flow Shop and Job Shop Scheduling Problems
Authors: Miloš Šeda
In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.
Keywords: Flow shop, job shop, mixed integer model, representation scheme.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4512
7599 Model of Optimal Centroids Approach for Multivariate Data Classification
Authors: Pham Van Nha, Le Cam Binh
Abstract:Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.
Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 666
7598 Numerical Analysis on Rapid Decompression in Conventional Dry Gases using One- Dimensional Mathematical Modeling
Authors: Evgeniy Burlutskiy
Abstract:The paper presents a one-dimensional transient mathematical model of compressible thermal multi-component gas mixture flows in pipes. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales-Eakin (LGE) correlation. Numerical analysis on rapid decompression in conventional dry gases is performed by using the proposed mathematical model. The model is validated on measured values of the decompression wave speed in dry natural gas mixtures. All predictions show excellent agreement with the experimental data at high and low pressure. The presented model predicts the decompression in dry natural gas mixtures much better than GASDECOM and OLGA codes, which are the most frequently-used codes in oil and gas pipeline transport service.
Keywords: Mathematical model, Rapid Gas DecompressionProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2841
7597 Design of the Mathematical Model of the Respiratory System Using Electro-acoustic Analogy
Authors: M. Rozanek, K. Roubik
Abstract:The article deals with development, design and implementation of a mathematical model of the human respiratory system. The model is designed in order to simulate distribution of important intrapulmonary parameters along the bronchial tree such as pressure amplitude, tidal volume and effect of regional mechanical lung properties upon the efficiency of various ventilatory techniques. Therefore exact agreement of the model structure with the lung anatomical structure is required. The model is based on the lung morphology and electro-acoustic analogy is used to design the model.
Keywords: Model of the respiratory system, total lung impedance, intrapulmonary parameters.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1723
7596 Mathematical Modeling of Human Cardiovascular System: A Lumped Parameter Approach and Simulation
Authors: Ketan Naik, P. H. Bhathawala
Abstract:The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.
Keywords: Cardiovascular system, lumped parameter method, mathematical modeling, simulation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3038
7595 The Effects of a Thin Liquid Layer on the Hydrodynamic Machine Rotor
Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán
Abstract:A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.
Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1440
7594 On the Mathematical Model of Vascular Endothelial Growth Connected with a Tumor Proliferation
Authors: N. Khatiashvili, Ch. Pirumova, V. Akhobadze
Abstract:In the paper the mathematical model of tumor growth is considered. New capillary network formation, which supply cancer cells with the nutrients, is taken into the account. A formula estimating a tumor growth in connection with the number of capillaries is obtained.
Keywords: Differential Equations, Mathematical Models, Vascular Endothelial, TumorProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1081
7593 Mathematical Modeling of Surface Roughness in Surface Grinding Operation
Authors: M.A. Kamely, S.M. Kamil, C.W. Chong
Abstract:A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.
Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3117
7592 Simulating the Dynamics of Distribution of Hazardous Substances Emitted by Motor Engines in a Residential Quarter
Authors: S. Grishin
Abstract:This article is dedicated to development of mathematical models for determining the dynamics of concentration of hazardous substances in urban turbulent atmosphere. Development of the mathematical models implied taking into account the time-space variability of the fields of meteorological items and such turbulent atmosphere data as vortex nature, nonlinear nature, dissipativity and diffusivity. Knowing the turbulent airflow velocity is not assumed when developing the model. However, a simplified model implies that the turbulent and molecular diffusion ratio is a piecewise constant function that changes depending on vertical distance from the earth surface. Thereby an important assumption of vertical stratification of urban air due to atmospheric accumulation of hazardous substances emitted by motor vehicles is introduced into the mathematical model. The suggested simplified non-linear mathematical model of determining the sought exhaust concentration at a priori unknown turbulent flow velocity through non-degenerate transformation is reduced to the model which is subsequently solved analytically.
Keywords: Urban ecology, time-dependent mathematical model, exhaust concentration, turbulent and molecular diffusion, airflow velocity.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1293
7591 Evaluation of Low-Reducible Sinter in Blast Furnace Technology by Mathematical Model Developed at Centre ENET, VSB – Technical University of Ostrava
Authors: S. Jursová, P. Pustějovská, S. Brožová, J. Bilík
The paper deals with possibilities of interpretation of iron ore reducibility tests. It presents a mathematical model developed at Centre ENET, VŠB – Technical University of Ostrava, Czech Republic for an evaluation of metallurgical material of blast furnace feedstock such as iron ore, sinter or pellets. According to the data from the test, the model predicts its usage in blast furnace technology and its effects on production parameters of shaft aggregate. At the beginning, the paper sums up the general concept and experience in mathematical modelling of iron ore reduction. It presents basic equation for the calculation and the main parts of the developed model. In the experimental part, there is an example of usage of the mathematical model. The paper describes the usage of data for some predictive calculation. There are presented material, method of carried test of iron ore reducibility. Then there are graphically interpreted effects of used material on carbon consumption, rate of direct reduction and the whole reduction process.
Keywords: Blast furnace technology, iron ore reduction, mathematical model, prediction of iron ore reduction.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1793
7590 A Sustainable Design Model by Integrated Evaluation of Closed-loop Design and Supply Chain Using a Mathematical Model
Authors: Yuan-Jye Tseng, Yi-Shiuan Chen
Abstract:The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.
Keywords: Closed-loop design, closed-loop supply chain, design evaluation, mathematical model, supply chain management, sustainable design model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1144
7589 Numerical Analysis of Oil-Water Transport in Horizontal Pipes Using 1D Transient Mathematical Model of Thermal Two-Phase Flows
Authors: Evgeniy Burlutskiy
Abstract:The paper presents a one-dimensional transient mathematical model of thermal oil-water two-phase emulsion flows in pipes. The set of the mass, momentum and enthalpy conservation equations for the continuous fluid and droplet phases are solved. Two friction correlations for the continuous fluid phase to wall friction are accounted for in the model and tested. The aerodynamic drag force between the continuous fluid phase and droplets is modeled, too. The density and viscosity of both phases are assumed to be constant due to adiabatic experimental conditions. The proposed mathematical model is validated on the experimental measurements of oil-water emulsion flows in horizontal pipe [1,2]. Numerical analysis on single- and two-phase oil-water flows in a pipe is presented in the paper. The continuous oil flow having water droplets is simulated. Predictions, which are performed by using the presented model, show excellent agreement with the experimental data if the water fraction is equal or less than 10%. Disagreement between simulations and measurements is increased if the water fraction is larger than 10%.
Keywords: Mathematical model, Oil-Water, Pipe flows.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2190
7588 A New Fuzzy Mathematical Model in Recycling Collection Networks: A Possibilistic Approach
Authors: B. Vahdani, R. Tavakkoli-Moghaddam, A. Baboli, S. M. Mousavi
Focusing on the environmental issues, including the reduction of scrap and consumer residuals, along with the benefiting from the economic value during the life cycle of goods/products leads the companies to have an important competitive approach. The aim of this paper is to present a new mixed nonlinear facility locationallocation model in recycling collection networks by considering multi-echelon, multi-suppliers, multi-collection centers and multifacilities in the recycling network. To make an appropriate decision in reality, demands, returns, capacities, costs and distances, are regarded uncertain in our model. For this purpose, a fuzzy mathematical programming-based possibilistic approach is introduced as a solution methodology from the recent literature to solve the proposed mixed-nonlinear programming model (MNLP). The computational experiments are provided to illustrate the applicability of the designed model in a supply chain environment and to help the decision makers to facilitate their analysis.
Keywords: Location-allocation model, recycling collection networks, fuzzy mathematical programming.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1964
7587 Mathematical Models for Overall Gas Transfer Coefficient Using Different Theories and Evaluating Their Measurement Accuracy
Authors: Shashank.B. Thakre, Lalit.B. Bhuyar, Samir.J. Deshmukh
Abstract:Oxygen transfer, the process by which oxygen is transferred from the gaseous to liquid phase, is a vital part of the waste water treatment process. Because of low solubility of oxygen and consequent low rate of oxygen transfer, sufficient oxygen to meet the requirement of aerobic waste does not enter through normal surface air water interface. Many theories have come up in explaining the mechanism of gas transfer and absorption of non-reacting gases in a liquid, of out of which, Two film theory is important. An exiting mathematical model determines approximate value of Overall Gas Transfer coefficient. The Overall Gas Transfer coefficient, in case of Penetration theory, is 1.13 time more than that obtained in case of Two film theory. The difference is due to the difference in assumptions in the two theories. The paper aims at development of mathematical model which determines the value of Overall Gas Transfer coefficient with greater accuracy than the existing model.
Keywords: Theories, Dissolved oxygen, Mathematical model, Gas Transfer coefficient, Accuracy.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1436
7586 A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem
Authors: Mohsen Ziaee
Abstract:In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.
Keywords: Scheduling, flexible job shop, makespan, mixed integer linear programming.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1418
7585 Optimal Network of Secondary Warehouses for Production-Distribution Inventory Model
Authors: G. M. Arun Prasath, N. Arthi
Abstract:This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.
Keywords: Fuzzy inventory model, warehouse location model, triangular fuzzy number, secondary warehouse, LINGO software.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1023
7584 Mathematical Modeling of Elastically Creeping State of Arbitrarily Orientated Cavities in the Transversally Isotropic Massif
Authors: N. Azhikhanov, T. Turimbetov, Zh. Masanov, N. Zhunisov
It can be determined in preference between representative mechanical and mathematical model of elasticcreeping deformation of transversally isotropic array with doubly periodic system of tilted slots, and offer of the finite elements calculation scheme, and inspection of the states of two diagonal arbitrary profile cavities of deep inception, and in setting up the tense and dislocation fields distribution nature in computing processes.
Keywords: Mathematical model, tunnel, transversally isotropic, finite elements.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1426
7583 Formulation of Extended-Release Gliclazide Tablet Using a Mathematical Model for Estimation of Hypromellose
Authors: Farzad Khajavi, Farzaneh Jalilfar, Faranak Jafari, Leila Shokrani
Formulation of gliclazide in the form of extended-release tablet in 30 and 60 mg dosage forms was performed using hypromellose (HPMC K4M) as a retarding agent. Drug-release profiles were investigated in comparison with references Diamicron MR 30 and 60 mg tablets. The effect of size of powder particles, the amount of hypromellose in formulation, hardness of tablets, and also the effect of halving the tablets were investigated on drug release profile. A mathematical model which describes hypromellose behavior in initial times of drug release was proposed for the estimation of hypromellose content in modified-release gliclazide 60 mg tablet. This model is based on erosion of hypromellose in dissolution media. The model is applicable to describe release profiles of insoluble drugs. Therefore, by using dissolved amount of drug in initial times of dissolution and the model, the amount of hypromellose in formulation can be predictable. The model was used to predict the HPMC K4M content in modified-release gliclazide 30 mg and extended-release quetiapine 200 mg tablets.
Keywords: Hypromellose, gliclazide, drug release, modified-release tablet, mathematical model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1554
7582 Influence of IMV on Space Station
Authors: Fu Shiming, Pei Yifei
To study the impact of the inter-module ventilation (IMV) on the space station, the Computational Fluid Dynamic (CFD) model under the influence of IMV, the mathematical model, boundary conditions and calculation method are established and determined to analyze the influence of IMV on cabin air flow characteristics and velocity distribution firstly; and then an integrated overall thermal mathematical model of the space station is used to consider the impact of IMV on thermal management. The results show that: the IMV has a significant influence on the cabin air flow, the flowrate of IMV within a certain range can effectively improve the air velocity distribution in cabin, if too much may lead to its deterioration; IMV can affect the heat deployment of the different modules in space station, thus affecting its thermal management, the use of IMV can effectively maintain the temperature levels of the different modules and help the space station to dissipate the waste heat.
Keywords: CFD, Environment control and life support, Space station, Thermal management, Thermal mathematical model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1887
7581 A Fuzzy Mathematical Model for Order Acceptance and Scheduling Problem
Authors: E. Koyuncu
The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.
Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 915
7580 Drilling of Glass Sheets by Abrasive Jet Machining
Authors: A. El-Domiaty, H. M. Abd El-Hafez, M. A. Shaker
Abstract:Drilling of glass sheets with different thicknesses have been carried out by Abrasive Jet Machining process (AJM) in order to determine its machinability under different controlling parameters of the AJM process. The present study has been introduced a mathematical model and the obtained results have been compared with that obtained from other models published earlier [1-6]. The experimental results of the present work are used to discuss the validity of the proposed model as well as the other models.
Keywords: Abrasive Jet Machining, Erosion rate, Glass, Mathematical model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3831
7579 Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases
Authors: Rujira Kongnuy, Puntani Pongsumpun, I-Ming Tang
Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.
Keywords: Dengue disease, local stability, mathematical model, pregnancy.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1815
7578 Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
Authors: Gilbert Makanda, Roelf Sypkens
Abstract:A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.
Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 679
7577 Development of Admire Longitudinal Quasi-Linear Model by using State Transformation Approach
Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He
This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.
Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1376
7576 Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions
Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon
Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.
Keywords: Eukaryotic cell, mathematical modeling, osmosis, volume alterations.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1919
7575 Numerical Analysis of Rapid Gas Decompression in Pure Nitrogen using 1D and 3D Transient Mathematical Models of Gas Flow in Pipes
Authors: Evgeniy Burlutskiy
Abstract:The paper presents a numerical investigation on the rapid gas decompression in pure nitrogen which is made by using the one-dimensional (1D) and three-dimensional (3D) mathematical models of transient compressible non-isothermal fluid flow in pipes. A 1D transient mathematical model of compressible thermal multicomponent fluid mixture flow in pipes is presented. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved in the model. Thermo-physical properties of multicomponent gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. This model is successfully validated on the experimental data  and shows a good agreement with measurements. A 3D transient mathematical model of compressible thermal single-component gas flow in pipes, which is built by using the CFD Fluent code (ANSYS), is presented in the paper. The set of unsteady Reynolds-averaged conservation equations for gas phase is solved. Thermo-physical properties of single-component gas are calculated by solving the Real Gas Equation of State (EOS) model. The simplest case of gas decompression in pure nitrogen is simulated using both 1D and 3D models. The ability of both models to simulate the process of rapid decompression with a high order of agreement with each other is tested. Both, 1D and 3D numerical results show a good agreement between each other. The numerical investigation shows that 3D CFD model is very helpful in order to validate 1D simulation results if the experimental data is absent or limited.
Keywords: Mathematical model, Rapid Gas DecompressionProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2105
7574 Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans
Authors: P. Pongsumpun
Abstract:Leptospirosis occurs worldwide (except the poles of the earth), urban and rural areas, developed and developing countries, especially in Thailand. It can be transmitted to the human by rats through direct and indirect ways. Human can be infected by either touching the infected rats or contacting with water, soil containing urine from the infected rats through skin, eyes and nose. The data of the people who are infected with this disease indicates that most of the patients are adults. The transmission of this disease is studied through mathematical model. The population is separated into human and rat. The human is divided into two classes, namely juvenile and adult. The model equation is constructed for each class. The standard dynamical modeling method is then used for analyzing the behaviours of solutions. In addition, the conditions of the parameters for the disease free and endemic states are obtained. Numerical solutions are shown to support the theoretical predictions. The results of this study guide the way to decrease the disease outbreak.
Keywords: Adult human, juvenile human, leptospirosis, mathematical model.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2392