Search results for: algebra and equations
1123 Hydrodynamic Study and Sizing of a Distillation Column by HYSYS Software
Authors: Derrouazin Mohammed Redhouane, Souakri Mohammed Lotfi, Henini Ghania
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This work consists, first of all, of mastering one of the powerful process simulation tools currently used in the industrial processes, which is the HYSYS sizing software, and second, of simulating a petroleum distillation column. This study is divided into two parts; where the first one consists of a dimensioning of the column with a fast approximating method using state equations, iterative calculations, and then a precise simulation method with the HYSYS software. The second part of this study is a hydrodynamic study in order to verify by obtained results the proper functioning of the plates.Keywords: industry process engineering, water distillation, environment, HYSYS simulation tool
Procedia PDF Downloads 1171122 Bubble Growth in a Two Phase Upward Flow in a Miniature Tube
Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev
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A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.Keywords: two phase flow, bubble growth, mini-channel, generation frequency
Procedia PDF Downloads 4281121 Lyapunov Functions for Extended Ross Model
Authors: Rahele Mosleh
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This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.Keywords: global stability, invariant solutions, Lyapunov function, stationary points
Procedia PDF Downloads 1561120 Exploring Counting Methods for the Vertices of Certain Polyhedra with Uncertainties
Authors: Sammani Danwawu Abdullahi
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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration
Procedia PDF Downloads 3451119 Stagnation Point Flow Over a Stretching Cylinder with Variable Thermal Conductivity and Slip Conditions
Authors: M. Y. Malik, Farzana Khan
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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity
Procedia PDF Downloads 4121118 A Graph SEIR Cellular Automata Based Model to Study the Spreading of a Transmittable Disease
Authors: Natasha Sharma, Kulbhushan Agnihotri
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Cellular Automata are discrete dynamical systems which are based on local character and spatial disparateness of the spreading process. These factors are generally neglected by traditional models based on differential equations for epidemic spread. The aim of this work is to introduce an SEIR model based on cellular automata on graphs to imitate epidemic spreading. Distinctively, it is an SEIR-type model where the population is divided into susceptible, exposed, infected and recovered individuals. The results obtained from simulations are in accordance with the spreading behavior of a real time epidemics.Keywords: cellular automata, epidemic spread, graph, susceptible
Procedia PDF Downloads 4491117 E-Bike FE Model Analysis: Connection Stiffness of Elements with Different DOFs
Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li
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Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.Keywords: coupling theory, stiffness matrix, e-bike, finite element model
Procedia PDF Downloads 3691116 A Mathematical Model for Hepatitis B Virus Infection and the Impact of Vaccination on Its Dynamics
Authors: T. G. Kassem, A. K. Adunchezor, J. P. Chollom
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This paper describes a mathematical model developed to predict the dynamics of Hepatitis B virus (HBV) infection and to evaluate the potential impact of vaccination and treatment on its dynamics. We used a compartmental model expressed by a set of differential equations based on the characteristic of HBV transmission. With these, we find the threshold quantity R0, then find the local asymptotic stability of disease free equilibrium and endemic equilibrium. Furthermore, we find the global stability of the disease free and endemic equilibrium.Keywords: hepatitis B virus, epidemiology, vaccination, mathematical model
Procedia PDF Downloads 3131115 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.Keywords: Riccati equation, analytical solution, proper solution, nonlinear
Procedia PDF Downloads 3481114 Examining Geometric Thinking Behaviours of Undergraduates in Online Geometry Course
Authors: Peter Akayuure
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Geometry is considered an important strand in mathematics due to its wide-ranging utilitarian value and because it serves as a building block for understanding other aspects of undergraduate mathematics, including algebra and calculus. Matters regarding students’ geometric thinking have therefore long been pursued by mathematics researchers and educators globally via different theoretical lenses, curriculum reform efforts, and innovative instructional practices. However, so far, studies remain inconclusive about the instructional platforms that effectively promote geometric thinking. At the University of Education, Winneba, an undergraduate geometry course was designed and delivered on UEW Learning Management System (LMS) using Moodle platform. This study utilizes van Hiele’s theoretical lens to examine the entry and exit’s geometric thinking behaviours of prospective teachers who took the undergraduate geometry course in the LMS platform. The study was a descriptive survey that involved an intact class of 280 first-year students enrolled to pursue a bachelor's in mathematics education at the university. The van Hiele’s Geometric thinking test was used to assess participants’ entry and exit behaviours, while semi-structured interviews were used to obtain data for triangulation. Data were analysed descriptively and displayed in tables and charts. An Independent t-test was used to test for significant differences in geometric thinking behaviours between those who entered the university with a diploma certificate and with senior high certificate. The results show that on entry, more than 70% of the prospective teachers operated within the visualization level of van Hiele’s geometric thinking. Less than 20% reached analysis and abstraction levels, and no participant reached deduction and rigor levels. On exit, participants’ geometric thinking levels increased markedly across levels, but the difference from entry was not significant and might have occurred by chance. The geometric thinking behaviours of those enrolled with diploma certificates did not differ significant from those enrolled directly from senior high school. The study recommends that the design principles and delivery of undergraduate geometry course via LMS should be structured and tackled using van Hiele’s geometric thinking levels to serve as means of bridging the existing learning gaps of undergraduate students.Keywords: geometric thinking, van Hiele’s, UEW learning management system, undergraduate geometry
Procedia PDF Downloads 1211113 Optimizing Cell Culture Performance in an Ambr15 Microbioreactor Using Dynamic Flux Balance and Computational Fluid Dynamic Modelling
Authors: William Kelly, Sorelle Veigne, Xianhua Li, Zuyi Huang, Shyamsundar Subramanian, Eugene Schaefer
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The ambr15™ bioreactor is a single-use microbioreactor for cell line development and process optimization. The ambr system offers fully automatic liquid handling with the possibility of fed-batch operation and automatic control of pH and oxygen delivery. With operating conditions for large scale biopharmaceutical production properly scaled down, micro bioreactors such as the ambr15™ can potentially be used to predict the effect of process changes such as modified media or different cell lines. In this study, gassing rates and dilution rates were varied for a semi-continuous cell culture system in the ambr15™ bioreactor. The corresponding changes to metabolite production and consumption, as well as cell growth rate and therapeutic protein production were measured. Conditions were identified in the ambr15™ bioreactor that produced metabolic shifts and specific metabolic and protein production rates also seen in the corresponding larger (5 liter) scale perfusion process. A Dynamic Flux Balance model was employed to understand and predict the metabolic changes observed. The DFB model-predicted trends observed experimentally, including lower specific glucose consumption when CO₂ was maintained at higher levels (i.e. 100 mm Hg) in the broth. A Computational Fluid Dynamic (CFD) model of the ambr15™ was also developed, to understand transfer of O₂ and CO₂ to the liquid. This CFD model predicted gas-liquid flow in the bioreactor using the ANSYS software. The two-phase flow equations were solved via an Eulerian method, with population balance equations tracking the size of the gas bubbles resulting from breakage and coalescence. Reasonable results were obtained in that the Carbon Dioxide mass transfer coefficient (kLa) and the air hold up increased with higher gas flow rate. Volume-averaged kLa values at 500 RPM increased as the gas flow rate was doubled and matched experimentally determined values. These results form a solid basis for optimizing the ambr15™, using both CFD and FBA modelling approaches together, for use in microscale simulations of larger scale cell culture processes.Keywords: cell culture, computational fluid dynamics, dynamic flux balance analysis, microbioreactor
Procedia PDF Downloads 2701112 Investigating the Impact of Enterprise Resource Planning System and Supply Chain Operations on Competitive Advantage and Corporate Performance (Case Study: Mamot Company)
Authors: Mohammad Mahdi Mozaffari, Mehdi Ajalli, Delaram Jafargholi
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The main purpose of this study is to investigate the impact of the system of ERP (Enterprise Resource Planning) and SCM (Supply Chain Management) on the competitive advantage and performance of Mamot Company. The methods for collecting information in this study are library studies and field research. A questionnaire was used to collect the data needed to determine the relationship between the variables of the research. This questionnaire contains 38 questions. The direction of the current research is applied. The statistical population of this study consists of managers and experts who are familiar with the SCM system and ERP. Number of statistical society is 210. The sampling method is simple in this research. The sample size is 136 people. Also, among the distributed questionnaires, Reliability of the Cronbach's Alpha Cronbach's Questionnaire is evaluated and its value is more than 70%. Therefore, it confirms reliability. And formal validity has been used to determine the validity of the questionnaire, and the validity of the questionnaire is confirmed by the fact that the score of the impact is greater than 1.5. In the present study, one variable analysis was used for central indicators, dispersion and deviation from symmetry, and a general picture of the society was obtained. Also, two variables were analyzed to test the hypotheses; measure the correlation coefficient between variables using structural equations, SPSS software was used. Finally, multivariate analysis was used with statistical techniques related to the SPLS structural equations to determine the effects of independent variables on the dependent variables of the research to determine the structural relationships between the variables. The results of the test of research hypotheses indicate that: 1. Supply chain management practices have a positive impact on the competitive advantage of the Mammoth industrial complex. 2. Supply chain management practices have a positive impact on the performance of the Mammoth industrial complex. 3. Planning system Organizational resources have a positive impact on the performance of the Mammoth industrial complex. 4. The system of enterprise resource planning has a positive impact on Mamot's competitive advantage. 5.The competitive advantage has a positive impact on the performance of the Mammoth industrial complex 6.The system of enterprise resource planning Mamot Industrial Complex Supply Chain Management has a positive impact. The above results indicate that the system of enterprise resource planning and supply chain management has an impact on the competitive advantage and corporate performance of Mamot Company.Keywords: enterprise resource planning, supply chain management, competitive advantage, Mamot company performance
Procedia PDF Downloads 811111 Study on the Central Differencing Scheme with the Staggered Version (STG) for Solving the Hyperbolic Partial Differential Equations
Authors: Narumol Chintaganun
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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.Keywords: central differencing scheme, STG, advection equation, burgers equation
Procedia PDF Downloads 5491110 Object-Oriented Programming for Modeling and Simulation of Systems in Physiology
Authors: J. Fernandez de Canete
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Object-oriented modeling is spreading in the current simulation of physiological systems through the use of the individual components of the model and its interconnections to define the underlying dynamic equations. In this paper, we describe the use of both the SIMSCAPE and MODELICA simulation environments in the object-oriented modeling of the closed-loop cardiovascular system. The performance of the controlled system was analyzed by simulation in light of the existing hypothesis and validation tests previously performed with physiological data. The described approach represents a valuable tool in the teaching of physiology for graduate medical students.Keywords: object-oriented modeling, SIMSCAPE simulation language, MODELICA simulation language, cardiovascular system
Procedia PDF Downloads 4951109 Online Estimation of Clutch Drag Torque in Wet Dual Clutch Transmission Based on Recursive Least Squares
Authors: Hongkui Li, Tongli Lu , Jianwu Zhang
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This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.Keywords: clutch drag torque, wet DCT, dynamic viscosity, recursive least squares
Procedia PDF Downloads 3131108 MHD Mixed Convection in a Vertical Porous Channel
Authors: Brahim Fersadou, Henda Kahalerras
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This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers respectively, as well as the Joule heating represented by Eckert number on the velocity and temperature fields, are examined. The main results show an augmentation of heat transfer rate with the decrease of Darcy number and the increase of Ri and Ha when Joule heating is neglected.Keywords: heat sources, magnetic field, mixed convection, porous channel
Procedia PDF Downloads 3651107 Generation of Numerical Data for the Facilitation of the Personalized Hyperthermic Treatment of Cancer with An Interstital Antenna Array Using the Method of Symmetrical Components
Authors: Prodromos E. Atlamazoglou
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The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.Keywords: hyperthermia, integral equations, insulated antennas, method of symmetrical components
Procedia PDF Downloads 2491106 Unsteady Stagnation-Point Flow towards a Shrinking Sheet with Radiation Effect
Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop
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In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.Keywords: heat transfer, radiation effect, shrinking sheet unsteady flow
Procedia PDF Downloads 3791105 Foundation Settlement Determination: A Simplified Approach
Authors: Adewoyin O. Olusegun, Emmanuel O. Joshua, Marvel L. Akinyemi
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The heterogeneous nature of the subsurface requires the use of factual information to deal with rather than assumptions or generalized equations. Therefore, there is need to determine the actual rate of settlement possible in the soil before structures are built on it. This information will help in determining the type of foundation design and the kind of reinforcement that will be necessary in constructions. This paper presents a simplified and a faster approach for determining foundation settlement in any type of soil using real field data acquired from seismic refraction techniques and cone penetration tests. This approach was also able to determine the depth of settlement of each strata of soil. The results obtained revealed the different settlement time and depth of settlement possible.Keywords: heterogeneous, settlement, foundation, seismic, technique
Procedia PDF Downloads 4351104 Molecular Dynamics Simulations on Richtmyer-Meshkov Instability of Li-H2 Interface at Ultra High-Speed Shock Loads
Authors: Weirong Wang, Shenghong Huang, Xisheng Luo, Zhenyu Li
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Material mixing process and related dynamic issues at extreme compressing conditions have gained more and more concerns in last ten years because of the engineering appealings in inertial confinement fusion (ICF) and hypervelocity aircraft developments. However, there lacks models and methods that can handle fully coupled turbulent material mixing and complex fluid evolution under conditions of high energy density regime up to now. In aspects of macro hydrodynamics, three numerical methods such as direct numerical simulation (DNS), large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equations (RANS) has obtained relative acceptable consensus under the conditions of low energy density regime. However, under the conditions of high energy density regime, they can not be applied directly due to occurrence of dissociation, ionization, dramatic change of equation of state, thermodynamic properties etc., which may make the governing equations invalid in some coupled situations. However, in view of micro/meso scale regime, the methods based on Molecular Dynamics (MD) as well as Monte Carlo (MC) model are proved to be promising and effective ways to investigate such issues. In this study, both classical MD and first-principle based electron force field MD (eFF-MD) methods are applied to investigate Richtmyer-Meshkov Instability of metal Lithium and gas Hydrogen (Li-H2) interface mixing at different shock loading speed ranging from 3 km/s to 30 km/s. It is found that: 1) Classical MD method based on predefined potential functions has some limits in application to extreme conditions, since it cannot simulate the ionization process and its potential functions are not suitable to all conditions, while the eFF-MD method can correctly simulate the ionization process due to its ‘ab initio’ feature; 2) Due to computational cost, the eFF-MD results are also influenced by simulation domain dimensions, boundary conditions and relaxation time choices, etc., in computations. Series of tests have been conducted to determine the optimized parameters. 3) Ionization induced by strong shock compression has important effects on Li-H2 interface evolutions of RMI, indicating a new micromechanism of RMI under conditions of high energy density regime.Keywords: first-principle, ionization, molecular dynamics, material mixture, Richtmyer-Meshkov instability
Procedia PDF Downloads 2201103 Some Aspects on Formation Initialization and Its Maintenance of Leo Satellites
Authors: Y. Johnson
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Study of multi-satellite formation flight systems has drawn wide attention recently due to so many potential advantages. The present work aims to model the relative motion dynamics in terms of change in classical orbital parameters between the two satellites-chief and deputy- under Earth’s oblateness effect. The required impulsive thrust control is calculated to minimize these orbital parameter changes. The formation configuration is initialized by selecting a set of orbital parameters for the chief and deputy satellites such that bounded motion is maintained for a long time in a J_2-invariant relative non-circular orbit between the satellites. The solution of J_2-modified Hill’s equations is also derived in this paper.Keywords: satellite, formation flight, j2 effect, control
Procedia PDF Downloads 2641102 Analysis of Chatterjea Type F-Contraction in F-Metric Space and Application
Authors: Awais Asif
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This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature.Keywords: Chatterjea type F-contraction, F-cauchy sequence, F-convergent, multi valued mappings
Procedia PDF Downloads 1281101 An Integrated Tailoring Method for Thermal Cycling Tests of Spacecraft Electronics
Authors: Xin-Yan Ji, Jing Wang, Chang Liu, Yan-Qiang Bi, Zhong-Xu Xu, Xi-Yuan Li
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Thermal tests of electronic units are critically important for the reliability validation and performance demonstration of the spacecraft hard-wares. The tailoring equation in MIL-STD-1540 is based on fatigue of solder date. In the present paper, a new test condition tailoring expression is proposed to fit different thermo-mechanical fatigue and different subsystems, by introducing an integrated evaluating method for the fatigue acceleration exponent. The validate test has been accomplished and the data has been analyzed and compared with that from the MIL-STD-1540 tailoring equations. The results are encouraging and reasonable.Keywords: thermal cycling test, thermal fatigue, tailoring equation, test condition planning
Procedia PDF Downloads 4441100 A 3D Eight Nodes Brick Finite Element Based on the Strain Approach
Authors: L. Belounar, K. Gerraiche, C. Rebiai, S. Benmebarek
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This paper presents the development of a new three dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending behavior. The developed element has the three essential external degrees of freedom (U, V and W) at each of the eight corner nodes. The displacements field of the developed element is based on assumed functions for the various strains satisfying the compatibility and the equilibrium equations. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element.Keywords: brick element, strain approach, plate bending, civil engineering
Procedia PDF Downloads 4781099 Turbulent Flow in Corrugated Pipes with Helical Grooves
Authors: P. Mendes, H. Stel, R. E. M. Morales
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This article presents a numerical and experimental study of turbulent flow in corrugated pipes with helically “d-type" grooves, for Reynolds numbers between 7500 and 100,000. The ANSYS-CFX software is used to solve the RANS equations with the BSL two equation turbulence model, through the element-based finite-volume method approach. Different groove widths and helix angles are considered. Numerical results are validated with experimental pressure drop measurements for the friction factor. A correlation for the friction factor is also proposed considering the geometric parameters and Reynolds numbers evaluated.Keywords: turbulent flow, corrugated pipe, helical, numerical, experimental, friction factor, correlation
Procedia PDF Downloads 4731098 Thermal Radiation and Chemical Reaction Effects on MHD Casson Fluid Past a Permeable Stretching Sheet in a Porous Medium
Authors: Y. Sunita Rani, Y. Hari Krishna, M. V. Ramana Murthy, K. Sudhaker Reddy
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This article studied effects of radiation and chemical reaction on MHD casson fluoid flow past a Permeable Stretching Sheet in a Porous Medium. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like Runge- Kutta – Fehlberg shooting technique method. The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically.Keywords: MHD, Casson fluid, porous medium, permeable stretching sheet
Procedia PDF Downloads 1161097 A Mixed Finite Element Formulation for Functionally Graded Micro-Beam Resting on Two-Parameter Elastic Foundation
Authors: Cagri Mollamahmutoglu, Aykut Levent, Ali Mercan
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Micro-beams are one of the most common components of Nano-Electromechanical Systems (NEMS) and Micro Electromechanical Systems (MEMS). For this reason, static bending, buckling, and free vibration analysis of micro-beams have been the subject of many studies. In addition, micro-beams restrained with elastic type foundations have been of particular interest. In the analysis of microstructures, closed-form solutions are proposed when available, but most of the time solutions are based on numerical methods due to the complex nature of the resulting differential equations. Thus, a robust and efficient solution method has great importance. In this study, a mixed finite element formulation is obtained for a functionally graded Timoshenko micro-beam resting on two-parameter elastic foundation. In the formulation modified couple stress theory is utilized for the micro-scale effects. The equation of motion and boundary conditions are derived according to Hamilton’s principle. A functional, derived through a scientific procedure based on Gateaux Differential, is proposed for the bending and buckling analysis which is equivalent to the governing equations and boundary conditions. Most important advantage of the formulation is that the mixed finite element formulation allows usage of C₀ type continuous shape functions. Thus shear-locking is avoided in a built-in manner. Also, element matrices are sparsely populated and can be easily calculated with closed-form integration. In this framework results concerning the effects of micro-scale length parameter, power-law parameter, aspect ratio and coefficients of partially or fully continuous elastic foundation over the static bending, buckling, and free vibration response of FG-micro-beam under various boundary conditions are presented and compared with existing literature. Performance characteristics of the presented formulation were evaluated concerning other numerical methods such as generalized differential quadrature method (GDQM). It is found that with less computational burden similar convergence characteristics were obtained. Moreover, formulation also includes a direct calculation of the micro-scale related contributions to the structural response as well.Keywords: micro-beam, functionally graded materials, two-paramater elastic foundation, mixed finite element method
Procedia PDF Downloads 1471096 Annular Axi-Symmetric Stagnation Flow of Electrically Conducting Fluid on a Moving Cylinder in the Presence of Axial Magnetic Field
Authors: Deva Kanta Phukan
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An attempt is made where an electrically conducting fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. A magnetic field is applied parallel to the axis of the cylindrical rod. The basic governing set of partial differential equations for conservation of mass and momentum are reduced to a set of non-linear ordinary differential equation by introducing similarity transformation, which are integrated numerically. A perturbation solution for the case of large magnetic parameter is derived for constant Reynolds number.Keywords: annular axi-symmetric stagnation flow, conducting fluid, magnetic field, moving cylinder
Procedia PDF Downloads 3891095 A Physical Theory of Information vs. a Mathematical Theory of Communication
Authors: Manouchehr Amiri
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This article introduces a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary data matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principles are investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Beckenstein, and mass-energy equivalence are derived.Keywords: physical theory of information, binary data matrix model, Shannon information theory, bit information principle
Procedia PDF Downloads 1561094 Study and Analysis of a Susceptible Infective Susceptible Mathematical Model with Density Dependent Migration
Authors: Jitendra Singh, Vivek Kumar
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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability
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