Search results for: mathematical equations

Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

Abstract:

The field of tissue engineering is an active area of research. Bone tissue engineering helps to resolve the clinical problems of critical size and non-healing defects by the creation of man-made bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature, with which we will not only be able to predict the oxygen, glucose and cell density dynamics, more accurately, but will also sort the issues arising due to anisotropy. We will fix these problems with the help of modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes, by adaptive grid refinement strategy and by transient analysis.

Keywords: scaffolds, porosity, diffusion, transient analysis

Procedia PDF Downloads 541

Authors: Tamara Díaz-Chang, Elizabeth-H Arredondo

Abstract:

This article presents the results of mixed approach research, where the ocular movements of students are examined while they solve questionnaires related to some abstract mathematical concepts. The objective of this research is to determine possible correlations between the parameters of ocular activity and the level of difficulty of the tasks. The difficulty level categories were established based on two types of criteria: a subjective one, through an evaluation, carried out by the subjects, and a behavioral one, related to obtaining the correct solution. Correlations of these criteria with ocular activity parameters, which were considered indicators of mental effort, were identified. The analysis of the data obtained allowed us to observe discrepancies in the categorization of difficulty levels based on subjective and behavioral criteria. There was a negative correlation of the eye movement parameters with the students' opinions on the level of difficulty of the questions, while a strong positive and significant correlation was noted between most of the parameters of ocular activity and the level of difficulty, determined by the percentage of correct answers. The results obtained by the analysis of the data suggest that eye movement parameters can be taken as indicators of the difficulty level of the tasks related to the study of some abstract mathematical concepts at the university.

Keywords: abstract mathematical concepts, cognitive neuroscience, eye-tracking, university education

Procedia PDF Downloads 120

Authors: Maruful H. Mazumder, Raymond I. Gilbert

Abstract:

The design specifications for calculating development and lapped splice lengths of reinforcement in concrete are derived from a conventional empirical modelling approach that correlates experimental test data using a single mathematical equation. This paper describes part of a recently completed experimental research program to assess the effects of different structural parameters on the development length requirements of modern high strength steel reinforcing bars, including the case of lapped splices in large-scale reinforced concrete members. The normalized average bond stresses for the different variations of anchorage lengths are assessed according to the general form of a typical empirical analytical model of bond and anchorage. Improved analytical modelling equations are developed in the paper that better correlate the normalized bond strength parameters with the structural parameters of an empirical model of bond and anchorage.

Keywords: bond stress, development length, lapped splice length, reinforced concrete

Procedia PDF Downloads 438

Authors: Davide Forcellini, James Marshal Kelly

Abstract:

Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

Procedia PDF Downloads 435

Authors: I. Kruashvili, I. Inashvili, K. Bziava, M. Lomishvili

Abstract:

Seepage capillary anomalies in the active layer of soil, related to the soil water movement, often cause variation of soil hydrophysical properties and become one of the main objectives of the hydroecology. It is necessary to mention that all existing equations for computing the seepage flow particularly from soil channels, through dams, bulkheads, and foundations of hydraulic engineering structures are preferable based on the linear seepage law. Regarding the existing beliefs, anomalous seepage is based on postulates according to which the fluid in free volume is characterized by resistance against shear deformation and is presented in the form of initial gradient. According to the above-mentioned information, we have determined: Equation to calculate seepage coefficient when the velocity of transition flow is equal to seepage flow velocity; by means of power function, equations for the calculation of average and maximum velocities of seepage flow have been derived; taking into consideration the fluid continuity condition, average velocity for calculation of average velocity in capillary tube has been received.

Keywords: seepage, soil, velocity, water

Procedia PDF Downloads 462

Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: operational matrix of differentiation, similarity transformation, shifted second kind chebyshev wavelets, stefan problem

Procedia PDF Downloads 403

Authors: Mohammad R. Jalali

Abstract:

Movement of liquid with a free surface in a container is known as slosh. For instance, slosh occurs when water in a closed tank is set in motion by a free surface displacement, or when liquid natural gas in a container is vibrated by an external driving force, such as an earthquake or movement induced by transport. Slosh is also derived from resonant switching of a natural basin. During sloshing, different types of motion are produced by energy exchange between the liquid and its container. In present study, a numerical model is developed to simulate the nonlinear even harmonic oscillations of free surface sloshing of an initial disturbance to the free surface of a liquid in a closed square basin. The response of the liquid free surface is affected by amplitude and motion frequencies of its container; therefore, sloshing involves complex fluid-structure interactions. In the present study, nonlinear interaction of free surface sloshing of an initial Gaussian hump with its uneven container is predicted numerically. For this purpose, Green-Naghdi (GN) equations are applied as governing equation of fluid field to produce nonlinear second-order and higher-order wave interactions. These equations reduce the dimensions from three to two, yielding equations that can be solved efficiently. The GN approach assumes a particular flow kinematic structure in the vertical direction for shallow and deep-water problems. The fluid velocity profile is finite sum of coefficients depending on space and time multiplied by a weighting function. It should be noted that in GN theory, the flow is rotational. In this study, GN numerical simulations of initial Gaussian hump are compared with Fourier series semi-analytical solutions of the linearized shallow water equations. The comparison reveals that satisfactory agreement exists between the numerical simulation and the analytical solution of the overall free surface sloshing patterns. The resonant free surface motions driven by an initial Gaussian disturbance are obtained by Fast Fourier Transform (FFT) of the free surface elevation time history components. Numerically predicted velocity vectors and magnitude contours for the free surface patterns indicate that interaction of Gaussian hump with its container has localized effect. The result of this sloshing is applicable to the design of stable liquefied oil containers in tankers and offshore platforms.

Keywords: fluid-structure interactions, free surface sloshing, Gaussian hump, Green-Naghdi equations, numerical predictions

Procedia PDF Downloads 398

Authors: Nurudeen O. Lasisi, Sirajo Abdulrahman, Abdulkareem A. Ibrahim

Abstract:

Newcastle disease is an infection of domestic poultry and other bird species with the virulent Newcastle disease virus (NDV). In this paper, we study the dynamics of the modeling of the Newcastle disease virus (NDV) using a novel quarantine-adjusted incidence. The comparison of Vaccination, linear incident rate and novel quarantine-adjusted incident rate in the models are discussed. The dynamics of the models yield disease-free and endemic equilibrium states.The effective reproduction numbers of the models are computed in order to measure the relative impact of an individual bird or combined intervention for effective disease control. We showed the local and global stability of endemic equilibrium states of the models and we found that the stability of endemic equilibrium states of models are globally asymptotically stable if the effective reproduction numbers of the models equations are greater than a unit.

Keywords: effective reproduction number, Endemic state, Mathematical model, Newcastle disease virus, novel quarantine-adjusted incidence, stability analysis

Procedia PDF Downloads 121

Authors: Hassan Parandvar, Mehrdad Farid

Abstract:

In this paper, a finite element modeling is presented for large amplitude vibration of functionally graded material (FGM) plates subjected to combined random pressure and thermal load. The material properties of the plates are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The material properties depend on the temperature whose distribution along the thickness can be expressed explicitly. The von Karman large deflection strain displacement and extended Hamilton's principle are used to obtain the governing system of equations of motion in structural node degrees of freedom (DOF) using finite element method. Three-node triangular Mindlin plate element with shear correction factor is used. The nonlinear equations of motion in structural degrees of freedom are reduced by using modal reduction method. The reduced equations of motion are solved numerically by 4th order Runge-Kutta scheme. In this study, the random pressure is generated using Monte Carlo method. The modeling is verified and the nonlinear dynamic response of FGM plates is studied for various values of volume fraction and sound pressure level under different thermal loads. Snap-through type behavior of FGM plates is studied too.

Keywords: nonlinear vibration, finite element method, functionally graded material (FGM) plates, snap-through, random vibration, thermal effect

Procedia PDF Downloads 262

Authors: D. Mehdizadeh, M. Rahimian, M. Eskandari-Ghadi

Abstract:

This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.

Keywords: transversely isotropic, rigid disc, elasticity, dual integral equations, tri-material full-space

Procedia PDF Downloads 440

Authors: Indrajit Ghosh, Jaydip Roy

Abstract:

Literacy rate is an important indicator for measurement of human development. But this is not a good one to capture the qualitative dimension of educational attainment of an individual or a society. The overall educational level of an area is an important issue beyond the literacy rate. The overall educational level can be thought of as an outcome of the educational levels of individuals. But there is no well-defined algorithm and mathematical model available to measure the overall educational level of an area. A heuristic approach based on accumulated experience of experts is effective one. It is evident that fuzzy logic offers a natural and convenient framework in modeling various concepts in social science domain. This work suggests the implementation of fuzzy logic to develop a mathematical model for measurement of educational attainment of an area in terms of Education Index. The contribution of the study is two folds: conceptualization of “Education Profile” and proposing a new mathematical model to measure educational attainment in terms of “Education Index”.

Keywords: education index, education profile, fuzzy logic, literacy

Procedia PDF Downloads 316

Authors: Khaled Benyounes

Abstract:

Determination of the rock mechanical properties such as unconfined compressive strength UCS, Young’s modulus E, and tensile strength by the Brazilian test Rtb is considered to be the most important component in drilling and mining engineering project. Research related to establishing correlation between strength and physical parameters of rocks has always been of interest to mining and reservoir engineering. For this, many rock blocks of limestone were collected from the quarry located in Meftah(Algeria), the cores were crafted in the laboratory using a core drill. This work examines the relationships between mechanical properties and some physical properties of limestone. Many empirical equations are established between UCS and physical properties of limestone (such as dry bulk density, velocity of P-waves, dynamic Young’s modulus, alteration index, and total porosity). Others correlations UCS-tensile strength, dynamic Young’s modulus-static Young’s modulus have been find. Based on the Mohr-Coulomb failure criterion, we were able to establish mathematical relationships that will allow estimating the cohesion and internal friction angle from UCS and indirect tensile strength. Results from this study can be useful for mining industry for resolve range of geomechanical problems such as slope stability.

Keywords: limestone, mechanical strength, Young’s modulus, porosity

Procedia PDF Downloads 454

Authors: S. P. Sharma, Som Nath Saha

Abstract:

This paper presents the performance, based on exergy analysis of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater based on energy balance equations has been presented and the results obtained have been compared with that of a conventional flat-plate solar air heater. The double flow corrugated absorber solar air heater performs thermally better than the flat plate double flow and conventional flat-plate solar air heater under same operating conditions. However, the corrugated absorber leads to higher pressure drop thereby increasing pumping power. The results revealed that the energy and exergy efficiencies of double flow corrugated absorber solar air heater is much higher than conventional solar air heater with the concept involving of increase in heat transfer surface area and turbulence in air flow. The results indicate that the energy efficiency increases, however, exergy efficiency decreases with increase in mass flow rate.

Keywords: corrugated absorber, double flow, exergy efficiency, solar air heater

Procedia PDF Downloads 374

Authors: Faisal Salah, Z. A. Aziz, K. K. Viswanathan

Abstract:

In this article, the effects of g-jitter induced and combined with heat and mass transfer by mixed convection of MHD Maxwell fluid in microgravity situation is investigated for a simple system. This system consists of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. By using modified Darcy’s law, the equations governing the flow are modelled. These equations are solved analytically for the induced velocity, temperature and concentration distributions. Many interesting available results in the relevant literature (i.e. Newtonian fluid) is obtained as the special case of the present general analysis. Finally, the graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for different values of the material constants.

Keywords: g-jitter, heat and mass transfer, mixed convection, Maxwell fluid, porous medium

Procedia PDF Downloads 492

Authors: Prerana Sharma

Abstract:

Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.

Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering

Procedia PDF Downloads 638

Authors: Josephine Shamash, Stuart Smith

Abstract:

We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

Procedia PDF Downloads 129

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

Procedia PDF Downloads 160

Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

Abstract:

Analytical expressions of the current and angular errors, as well as the frequency characteristics of an induction converter describing the relation with its structural parameters, the core and winding characteristics are obtained. Based on estimation of the dependences obtained, a mathematical problem of parametric optimization is formulated which can successfully be used for investigation and diagnosing an induction converter.

Keywords: induction converters, magnetic circuit material, current and angular errors, frequency response, mathematical formulation, structural parameters

Procedia PDF Downloads 345

Authors: Jose Francisco Ferreira Ribeiro, Alexandre Bevilacqua Leoneti, Andre Lucirton Costa

Abstract:

This paper presents a mathematical model in binary variables 0/1 to make the assignment of surgical procedures to the operating rooms in a hospital. The proposed mathematical model is based on the generalized assignment problem, which maximizes the sum of preferences for the use of the operating rooms by doctors, respecting the time available in each room. The corresponding program was written in Visual Basic of Microsoft Excel, and tested to schedule surgeries at St. Lydia Hospital in Ribeirao Preto, Brazil.

Keywords: generalized assignment problem, logistics, optimization, scheduling

Procedia PDF Downloads 292

Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

Abstract:

A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

Procedia PDF Downloads 433

Authors: Khaled Al-Mansour, Nawaf Esmael, Abdulaziz Al-Zaid, Mohammed Al Ateeqi, Ali Al-Yousfi, Sayed Al-Zalzalah

Abstract:

In this project we will create the new schedule of nurse according to the preference of them. We did our project in Mubarak Al Kabeer Hospital (in Kuwait). The project aims to optimize the schedule of nurses in Mubarak Al Kabeer Hospital. The schedule of the nurses was studied and understood well to do any modification for their schedule to make the nurses feel as much comfort as they are. First constraints were found to know what things we can change and what things we can’t, the hard constraints are the hospital and ministry policies where we can’t change anything about, and the soft constraints are things that make nurses more comfortable. Data were collected and nurses were interviewed to know what is more better for them. All these constraints and date have been formulated to mathematical equations. This report will first contain an introduction to the topic which includes details of the problem definition. It will also contain information regarding the optimization of a nurse schedule and its contents and importance; furthermore, the report will contain information about the data needed to solve the problem and how it was collected. The problem requires formulation and that is also to be shown. The methodology will be explained which will state what has already been done. We used the lingo software to find the best schedule for the nurse. The schedule has been made according to what the nurses prefer, and also took consideration of the hospital policy when we make the schedule.

Keywords: nurse schedule problem, Kuwait, hospital policy, optimization of schedules

Procedia PDF Downloads 268

Authors: A. Maghari, V. M. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1 + (2,3)-> 1 + (2,3) as well as recombination 1 + (2,3) -> 2 + (3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the three-dimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: statistical mechanics, nonlocal separable potential, three-body interaction, faddeev equations

Procedia PDF Downloads 401

Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: dynamic analysis, high frequency, integration method, overshoot, weak instability

Procedia PDF Downloads 223

Authors: Alia Alghosoun, Ashraf Osman, Mohammed Seaid

Abstract:

A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: dam-break flows, deformable beds, finite element method, finite volume method, hybrid techniques, linear elasticity, shallow water equations

Procedia PDF Downloads 181

Authors: Dairo Jose Hernandez Paez

Abstract:

The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

Procedia PDF Downloads 104

Authors: Leonardo Herrera, Shield B. Lin, Stephen J. Montgomery-Smith, Ziraguen O. Williams

Abstract:

A one-directional dynamic model of a Stewart Platform was developed to assist NASA in analyzing the dynamic response in spacecraft docking operations. A simplified mechanical drawing was created, capturing the physical structure's main features. A simplified schematic diagram was developed into a lumped mass model from the mechanical drawing. Three differential equations were derived according to the schematic diagram. A Simulink diagram was created using MATLAB to represent the three equations. System parameters, including spring constants and masses, are derived in detail from the physical system. The model can be used for further analysis via computer simulation in predicting dynamic response in its main docking direction, i.e., up-and-down motion.

Keywords: stewart platform, docking operation, spacecraft, spring constant

Procedia PDF Downloads 199

Authors: Jyh Sheen, Yong-Lin Wang

Abstract:

This research dedicates to find a different measurement procedure of microwave dielectric properties of ceramic materials with high dielectric constants. For the composite of ceramic dispersed in the polymer matrix, the dielectric constants of the composites with different concentrations can be obtained by various mixture equations. The other development of mixture rule is to calculate the permittivity of ceramic from measurements on composite. To do this, the analysis method and theoretical accuracy on six basic mixture laws derived from three basic particle shapes of ceramic fillers have been reported for dielectric constants of ceramic less than 40 at microwave frequency. Similar researches have been done for other well-known mixture rules. They have shown that both the physical curve matching with experimental results and low potential theory error are important to promote the calculation accuracy. Recently, a modified of mixture equation for high dielectric constant ceramics at microwave frequency has also been presented for strontium titanate (SrTiO3) which was selected from five more well known mixing rules and has shown a good accuracy for high dielectric constant measurements. However, it is still not clear the accuracy of this modified equation for other high dielectric constant materials. Therefore, the five more well known mixing rules are selected again to understand their application to other high dielectric constant ceramics. The other high dielectric constant ceramic, TiO2 with dielectric constant 100, was then chosen for this research. Their theoretical error equations are derived. In addition to the theoretical research, experimental measurements are always required. Titanium dioxide is an interesting ceramic for microwave applications. In this research, its powder is adopted as the filler material and polyethylene powder is like the matrix material. The dielectric constants of those ceramic-polyethylene composites with various compositions were measured at 10 GHz. The theoretical curves of the five published mixture equations are shown together with the measured results to understand the curve matching condition of each rule. Finally, based on the experimental observation and theoretical analysis, one of the five rules was selected and modified to a new powder mixture equation. This modified rule has show very good curve matching with the measurement data and low theoretical error. We can then calculate the dielectric constant of pure filler medium (titanium dioxide) by those mixing equations from the measured dielectric constants of composites. The accuracy on the estimating dielectric constant of pure ceramic by various mixture rules will be compared. This modified mixture rule has also shown good measurement accuracy on the dielectric constant of titanium dioxide ceramic. This study can be applied to the microwave dielectric properties measurements of other high dielectric constant ceramic materials in the future.

Keywords: microwave measurement, dielectric constant, mixture rules, composites

Procedia PDF Downloads 367

Authors: Gholamreza Koochaki

Abstract:

This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

Procedia PDF Downloads 392

Authors: Nurudeen Oluwasola Lasisi, Abdulkareem Afolabi Ibrahim

Abstract:

Newcastle disease is an infection of domestic poultry and other bird species with virulent Newcastle disease virus (NDV). In this paper, we study the dynamics of modeling the Newcastle disease virus (NDV) using a novel quarantine-adjusted incidence. We do a comparison of Vaccination, linear incident rate, and novel quarantine adjusted incident rate in the models. The dynamics of the models yield disease free and endemic equilibrium states. The effective reproduction numbers of the models are computed in order to measure the relative impact for the individual bird or combined intervention for effective disease control. We showed the local and global stability of endemic equilibrium states of the models, and we found that stability of endemic equilibrium states of models are globally asymptotically stable if the effective reproduction numbers of the models equations are greater than a unit.

Keywords: effective reproduction number, endemic state, mathematical model, Newcastle disease virus, novel quarantine-adjusted incidence, stability analysis

Procedia PDF Downloads 243

Authors: C. Mekala, Indumathi M. Nambi

Abstract:

Nitrogen pollution in groundwater arising from wastewater and fertilizer application through vadose zone is a major problem and it causes a prime risk to groundwater based drinking water supplies. Nitrogenous compounds namely ammonium, nitrate and nitrite fate and transport in soil subsurface were studied experimentally. The major process like sorption, leaching, biotransformation involving microbial growth kinetics, and biological clogging due to biomass growth were assessed and modeled with advection-dispersion reaction equations for ammonium, nitrate and acetate in a saturated, heterogeneous soil medium. The transport process was coupled with freundlich sorption and monod inhibition kinetics for immobile bacteria and permeability reduction due to biomass growth will be verified and validated with the numerical model. This proposed mathematical model will be very helpful in the development of a management model for a sustainable and safe wastewater reuse strategies such as irrigation and groundwater recharge.

Keywords: nitrogen species transport, transformation, biological clogging, biokinetic parameters, contaminant transport model, saturated soil

Procedia PDF Downloads 400