Search results for: equilibrium equations

Authors: Yasuhito Tanaka

Abstract:

In this paper we will constructively prove the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium in a competitive economy implies Sperner-s lemma. We follow the Bishop style constructive mathematics.

Keywords: Sequentially locally non-constant excess demand functions, Equilibrium in a competitive economy, Constructive mathematics

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Authors: Gabriela R. Fernandes, Danilo H. Konda, Luiz C. F. Sanches

Abstract:

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner?s hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

Keywords: Boundary elements, Building floor structures, Platebending.

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Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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Authors: Gholamreza Hojjati, Kourosh Parand

Abstract:

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

Abstract:

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.

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Authors: M. Karami Khorramabadi, P. Khazaeinejad

Abstract:

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: Alessandro A. Zizzari, Francesca Calabrese, Giovanni Indiveri, Andrea Coraddu, Diego Villa

Abstract:

The aim of this paper is to present a comparative study on two different methods for the evaluation of the equilibrium point of a ship, core issue for designing an On Board Stability System (OBSS) module that, starting from geometry information of a ship hull, described by a discrete model in a standard format, and the distribution of all weights onboard calculates the ship floating conditions (in draught, heel and trim).

Keywords: Algorithms, Computer applications, Equilibrium, Marine applications, Stability System.

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Authors: Asfaw Gezae Daful

Abstract:

In the present study, two distinctly different approaches are followed for modeling of reactive distillation column, the equilibrium stage model and the nonequilibrium stage model. These models are simulated with a computer code developed in the present study using MATLAB programming. In the equilibrium stage models, the vapor and liquid phases are assumed to be in equilibrium and allowance is made for finite reaction rates, where as in the nonequilibrium stage models simultaneous mass transfer and reaction rates are considered. These simulated model results are validated from the experimental data reported in the literature. The simulated results of equilibrium and nonequilibrium models are compared for concentration, temperature and reaction rate profiles in a reactive distillation column for Methyl Tert Butyle Ether (MTBE) production. Both the models show similar trend for the concentration, temperature and reaction rate profiles but the nonequilibrium model predictions are higher and closer to the experimental values reported in the literature.

Keywords: Reactive Distillation, Equilibrium model, Nonequilibrium model, Methyl Tert-Butyl Ether

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Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: Peiangpob Monnuanprang

Abstract:

In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

Keywords: Euler equations, transformation, hyperbolic, elliptic

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Authors: R. Haoui

Abstract:

Hypersonic flows around spatial vehicles during their reentry phase in planetary atmospheres are characterized by intense aerothermodynamics phenomena. The aim of this work is to analyze high temperature flows around an axisymmetric blunt body taking into account chemical and vibrational non-equilibrium for air mixture species and the no slip condition at the wall. For this purpose, the Navier-Stokes equations system is resolved by the finite volume methodology to determine the flow parameters around the axisymmetric blunt body especially at the stagnation point and in the boundary layer along the wall of the blunt body. The code allows the capture of shock wave before a blunt body placed in hypersonic free stream. The numerical technique uses the Flux Vector Splitting method of Van Leer. CFL coefficient and mesh size level are selected to ensure the numerical convergence.

Keywords: Hypersonic flow, viscous flow, chemical kinetic, dissociation, finite volumes, frozen and non-equilibrium flow.

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Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat

Abstract:

Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.

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Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

Abstract:

We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

Abstract:

In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Spin systems, equivalent counterparts, integrable reductions, self-consistent potentials.

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Authors: Ehsan Vaziri Goodarzi, Mahmood Houshmand, Omid Fatahi Valilai, Vahidreza Ghezavati, Shahrooz Bamdad

Abstract:

One important paradigm of industry 4.0 is Cloud Manufacturing (CM). In CM everything is considered as a service, therefore, the CM platform should consider all service provider's capabilities and tries to integrate services in an equilibrium state. This research develops a framework for implementing manufacturing cloud service composition in the equilibrium state. The developed framework using well-known tools called axiomatic design (AD) and game theory. The research has investigated the factors for forming equilibrium for measures of the manufacturing cloud service composition. Functional requirements (FRs) represent the measures of manufacturing cloud service composition in the equilibrium state. These FRs satisfied by related Design Parameters (DPs). The FRs and DPs are defined by considering the game theory, QoS, consumer needs, parallel and cooperative services. Ultimately, four FRs and DPs represent the framework. To insure the validity of the framework, the authors have used the first AD’s independent axiom.

Keywords: Axiomatic design, manufacturing cloud service composition, cloud manufacturing, Industry 4.0.

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Authors: K. Sudprasert, M. Precharattana, N. Nuttavut, D. Triampo, B. Pattanasiri, Y. Lenbury, W. Triampo

Abstract:

The study of non-equilibrium systems has attracted increasing interest in recent years, mainly due to the lack of theoretical frameworks, unlike their equilibrium counterparts. Studying the steady state and/or simple systems is thus one of the main interests. Hence in this work we have focused our attention on the driven lattice gas model (DLG model) consisting of interacting particles subject to an external field E. The dynamics of the system are given by hopping of particles to nearby empty sites with rates biased for jumps in the direction of E. Having used small two dimensional systems of DLG model, the stochastic properties at nonequilibrium steady state were analytically studied. To understand the non-equilibrium phenomena, we have applied the analytic approach via master equation to calculate probability function and analyze violation of detailed balance in term of the fluctuation-dissipation theorem. Monte Carlo simulations have been performed to validate the analytic results.

Keywords: Non-equilibrium, lattice gas, stochastic process

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: Belkacem Meziane

Abstract:

The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.

Keywords: chaos, Lorenz-Haken equations, laser dynamics, nonlinearities

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Sanjay K.Srivastava, Bhanu Gupta

Abstract:

In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: Fuzzy differential equations, Impulsive differential equations, Strict stability, Lyapunov function, Razumikhin technique.

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Authors: Gunawan Nugroho, Ahmed M. S. Ali, Zainal A. Abdul Karim

Abstract:

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion.

Keywords: Navier-Stokes Equations, potential function, turbulent flows.

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Authors: Ping Du, Masaki Sagehashi, Akihiko Terada, Masaaki Hosomi

Abstract:

Prediction of benzene transport in soil and volatilization from soil to the atmosphere is important for the preservation of human health and management of contaminated soils. The adequacy of a simple numerical model, assuming two-phase diffusion and equilibrium of liquid/solid adsorption, was investigated by experimental data of benzene concentration in a flux chamber (with headspace) where Andosol and sand were filled. Adsorption experiment for liquid phase was performed to determine an adsorption coefficient. Furthermore, adequacy of vapor phase adsorption was also studied through two runs of experiment using sand with different water content. The results show that the model adequately predicted benzene transport and volatilization from Andosol and sand with water content of 14.0%. In addition, the experiment additionally revealed that vapor phase adsorption should be considered in diffusion model for sand with very low water content.

Keywords: Benzene; Transport Model, Adsorption, Soil Contaminant.

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Authors: Yongxin Yuan, Kezheng Zuo

Abstract:

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Debashish Panda, Kannan A.

Abstract:

Equilibrium and rate based models have been applied in the simulation of methyl tertiary-butyl ether (MTBE) synthesis through reactive distillation. Temperature and composition profiles were compared for both the models and found that both the profiles trends, though qualitatively similar are significantly different quantitatively. In the rate based method (RBM), multicomponent mass transfer coefficients have been incorporated to describe interphase mass transfer. MTBE mole fraction in the bottom stream is found to be 0.9914 in the Equilibrium Model (EQM) and only 0.9904 for RBM when the same column configuration was preserved. The individual tray efficiencies were incorporated in the EQM and simulations were carried out. Dynamic simulation have been also carried out for the two column configurations and compared.

Keywords: Aspen Plus, equilibrium stage model, methyl tertiary-butyl ether, rate based model.

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Authors: Shyh-Ming Chern

Abstract:

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and reasonable accuracy, are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, they often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance at and above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: Equation of state, EoS, supercritical water, SCW.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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