Search results for: incompressible navier-stokes equations

Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

Procedia PDF Downloads 129

Authors: Krzysztof Pomorski

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In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

Procedia PDF Downloads 145

Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

Procedia PDF Downloads 154

Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

Procedia PDF Downloads 308

Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

Procedia PDF Downloads 443

Authors: Niloufar Ghoreishi, Ali Nekouzadeh

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The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: flight stability, phugoid mode, short period mode, climb phase, damping coefficient

Procedia PDF Downloads 170

Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

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This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

Procedia PDF Downloads 198

Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

Procedia PDF Downloads 413

Authors: Emmanuel Ophel Gilbert, Williams Speret

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The control for fluid flow behaviours of viscous fluids and heat transfer occurrences within heated mini-channel is considered. Heat transfer and flow characteristics of different viscous liquids, such as engine oil, automatic transmission fluid, one-half ethylene glycol, and deionized water were numerically analyzed. Some mathematical applications such as Fourier series and Laplace Z-Transforms were employed to ascertain the behaviour-wave like structure of these each viscous fluids. The steady, laminar flow and heat transfer equations are reckoned by the aid of numerical simulation technique. Further, this numerical simulation technique is endorsed by using the accessible practical values in comparison with the anticipated local thermal resistances. However, the roughness of this mini-channel that is one of the physical limitations was also predicted in this study. This affects the frictional factor. When an additive such as tetracycline was introduced in the fluid, the heat input was lowered, and this caused pro rata effect on the minor and major frictional losses, mostly at a very minute Reynolds number circa 60-80. At this ascertained lower value of Reynolds numbers, there exists decrease in the viscosity and minute frictional losses as a result of the temperature of these viscous liquids been increased. It is inferred that the three equations and models are identified which supported the numerical simulation via interpolation and integration of the variables extended to the walls of the mini-channel, yields the utmost reliance for engineering and technology calculations for turbulence impacting jets in the near imminent age. Out of reasoning with a true equation that could support this control for the fluid flow, Navier-stokes equations were found to tangential to this finding. Though, other physical factors with respect to these Navier-stokes equations are required to be checkmated to avoid uncertain turbulence of the fluid flow. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme via numerical simulation method that takes into account certain terms in the full Navier-Stokes equations. However, this resulted in dropping out in the approximation of certain assumptions. Concrete questions raised in the main body of the work are sightseen further in the appendices.

Keywords: frictional losses, heat transfer, laminar flow, mini-channel, number simulation, Reynolds number, turbulence, viscous fluids

Procedia PDF Downloads 176

Authors: Yasaman Azarmjoo

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Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

Procedia PDF Downloads 93

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

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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: Davide Forcellini, James Marshal Kelly

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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

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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

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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 402

Authors: Mohammad R. Jalali

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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: Hassan Parandvar, Mehrdad Farid

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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

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

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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

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

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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: A. Maghari, V. M. Maleki

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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

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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 180

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

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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: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional g-Brownian motion, Taylor's series of fractional order, uncertain volatility

Procedia PDF Downloads 163

Authors: M. Meenasaranya, S. Saravanan

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Nonlinear stability analysis is carried out to determine the effect of surface temperature modulation in an infinite horizontal porous layer heated from below. The layer is saturated by an electrically conducting, viscous, incompressible and Newtonian fluid. The Brinkman model is used for momentum equation, and the Boussinesq approximation is invoked. The system is assumed to be bounded by rigid boundaries. The energy theory is implemented to find the global exponential stability region of the considered system. The results are analysed for arbitrary values of modulation frequency and amplitude. The existence of subcritical instability region is confirmed by comparing the obtained result with the known linear result. The vertical magnetic field is found to stabilize the system.

Keywords: Brinkman model, energy method, magnetic field, surface temperature modulation

Procedia PDF Downloads 395

Authors: Altayeb Abdalla Ahmed

Abstract:

Skeletal phenotype is a product of a balanced interaction between genetics and environmental factors throughout different life stages. Therefore, interlimb proportions are variable between populations. Although interlimb proportion indices have been used in anthropology in assessing the influence of various environmental factors on limbs, an extensive literature review revealed that there is a paucity of published research assessing interlimb part correlations and possibility of reconstruction. Hence, this study aims to assess the relationships between upper and lower limb parts and develop regression formulae to reconstruct the parts from one another. The left upper arm length, ulnar length, wrist breadth, hand length, hand breadth, tibial length, bimalleolar breadth, foot length, and foot breadth of 376 right-handed subjects, comprising 187 males and 189 females (aged 25-35 years), were measured. Initially, the data were analyzed using basic univariate analysis and independent t-tests; then sex-specific simple and multiple linear regression models were used to estimate upper limb parts from lower limb parts and vice-versa. The results of this study indicated significant sexual dimorphism for all variables. The results indicated a significant correlation between the upper and lower limbs parts (p < 0.01). Linear and multiple (stepwise) regression equations were developed to reconstruct the limb parts in the presence of a single or multiple dimension(s) from the other limb. Multiple stepwise regression equations generated better reconstructions than simple equations. These results are significant in forensics as it can aid in identification of multiple isolated limb parts particularly during mass disasters and criminal dismemberment. Although a DNA analysis is the most reliable tool for identification, its usage has multiple limitations in undeveloped countries, e.g., cost, facility availability, and trained personnel. Furthermore, it has important implication in plastic and orthopedic reconstructive surgeries. This study is the only reported study assessing the correlation and prediction capabilities between many of the upper and lower dimensions. The present study demonstrates a significant correlation between the interlimb parts in both sexes, which indicates a possibility to reconstruction using regression equations.

Keywords: anthropometry, correlation, limb, Sudanese

Procedia PDF Downloads 295

Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

Abstract:

Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations

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