Search results for: extended Arrhenius equation.

Authors: Tomoaki Hashimoto

Abstract:

Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: Optimal control, stochastic systems, quantum systems, stabilization.

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Authors: ByungHoon Kang, Jeawook Shin, Ju-man Song, Hyun-Taek Choi, PooGyeon Park

Abstract:

In this study, we consider a special situation that only a pair of hydrophone on a moving underwater vehicle is available to localize a fixed acoustic source of far distance. The trigonometry can be used in this situation by using two different DOA of different locations. Notice that the distance between the two locations should be measured. Therefore, we assume that the vehicle is sailing straightly and the moving distance for each unit time is measured continuously. However, the accuracy of the localization using the trigonometry is highly dependent to the accuracy of DOAs and measured moving distances. Therefore, we proposed another method based on the extended Kalman filter that gives more robust and accurate localization result.

Keywords: Localization, acoustic, underwater, extended Kalman filter.

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Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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Authors: Hsuan-Ku Liu, Ming Long Liu

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In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Amit Kumar, Ramendeep Grawal, Peeyush Sharma, Dinesh Puri, Anil Bhandari

Abstract:

The main perspective of the present study aims at overcoming solubility problems by using the technique of solid dispersion. Repaglinide is a BCS Class II drug, having low aqueous solubility and therefore, low bioavailability. Solid dispersions of repaglinide with different carriers Polyvinyl Pyrrolidone (PVP) and Ethyl Cellulose (EC) in different ratios were prepared by suspending method and Dissolving methods. In vitro release studies revealed that the F7 formulation showed extended drug release. So, the dissolution profile of solid dispersion containing EC and PVP K30 (1: 3) was selected as the best formulation because of its extended drug release among all formulations. In conclusion, solid dispersions of Repaglinide in PVP have shown to be a promising approach to improve the bioavailability of Repaglinide.

Keywords: Ethyl Cellulose, Glibenclamide, Polyvinyl Pyrrolidone, Repaglinide, Solid Dispersion.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

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In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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Authors: Fred Lacy

Abstract:

Electrical resistivity is a fundamental parameter of metals or electrical conductors. Since resistivity is a function of temperature, in order to completely understand the behavior of metals, a temperature dependent theoretical model is needed. A model based on physics principles has recently been developed to obtain an equation that relates electrical resistivity to temperature. This equation is dependent upon a parameter associated with the electron travel time before being scattered, and a parameter that relates the energy of the atoms and their separation distance. Analysis of the energy parameter reveals that the equation is optimized if the proportionality term in the equation is not constant but varies over the temperature range. Additional analysis reveals that the theoretical equation can be used to determine the mean free path of conduction electrons, the number of defects in the atomic lattice, and the ‘equivalent’ charge associated with the metallic bonding of the atoms. All of this analysis provides validation for the theoretical model and provides insight into the behavior of metals where performance is affected by temperatures (e.g., integrated circuits and temperature sensors).

Keywords: Callendar–van Dusen, conductivity, mean free path, resistance temperature detector, temperature sensor.

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Authors: Peter N. Khakina, Mohammed I. Ali, Enchun Zhu, Huazhang Zhou, Baydaa H. Moula

Abstract:

Rise/span ratio has been mentioned as one of the reasons which contribute to the lower buckling load as compared to the Classical theory buckling load but this ratio has not been quantified in the equation. The purpose of this study was to determine a more realistic buckling load by quantifying the effect of the rise/span ratio because experiments have shown that the Classical theory overestimates the load. The buckling load equation was derived based on the theorem of work done and strain energy. Thereafter, finite element modeling and simulation using ABAQUS was done to determine the variables that determine the constant in the derived equation. The rise/span was found to be the determining factor of the constant in the buckling load equation. The derived buckling load correlates closely to the load obtained from experiments.

Keywords: Buckling, Finite element, Rise/span ratio, Sphericalcap

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Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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Authors: Ning Dong, Bo Yu

Abstract:

We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algorithm.

Keywords: Fast algorithm, Cyclic reduction, Overdampedquadratic matrix equation, Structure-preserving doubling algorithm

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

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Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.

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Authors: Hui-Min Lai, Chin-Pin Chen, Yung-Fu Chang

Abstract:

The expectation-confirmation model (ECM) is one of the most widely used models for evaluating information system continuance, and this model has been extended to other study backgrounds, or expanded with other theoretical perspectives. However, combining ECM with other theories or investigating the background problem may produce some disparities, thus generating inaccurate conclusions. Habit is considered to be an important factor that influences the user’s continuance behavior. This paper thus critically examines seven pairs of relationships from the original ECM and the habit variable. A meta-analysis was used to tackle the development of ECM research over the last 10 years from a range of journals and conference papers published in 2005–2014. Forty-six journal articles and 19 conference papers were selected for analysis. The results confirm our prediction that a high effect size for the seven pairs of relationships was obtained (ranging from r=0.386 to r=0.588). Furthermore, a meta-analytic structural equation modeling was performed to simultaneously test all relationships. The results show that habit had a significant positive effect on continuance intention at p<=0.05 and that the six other pairs of relationships were significant at p<0.10. Based on the findings, we refined our original research model and an alternative model was proposed for understanding and predicting information system continuance. Some theoretical implications are also discussed.

Keywords: Expectation-confirmation theory, expectation- confirmation model, meta-analysis, meta-analytic structural equation modeling.

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Authors: I. Sarras, G. Gerakios, A. Diamantis, A. I. Dounis, G. P. Syrcos

Abstract:

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.

Keywords: Extended Kalman filter, GPS, Pseudorange

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Authors: MA. Ansari

Abstract:

In cancer progress, the optical properties of tissues like absorption and scattering coefficient change, so by these changes, we can trace the progress of cancer, even it can be applied for pre-detection of cancer. In this paper, we investigate the effects of changes of optical properties on light penetrated into tissues. The diffusion equation is widely used to simulate light propagation into biological tissues. In this study, the boundary integral method (BIM) is used to solve the diffusion equation. We illustrate that the changes of optical properties can modified the reflectance or penetrating light.

Keywords: Diffusion equation, boundary element method, refractive index

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Soon-Mo Jung

Abstract:

The functional equation f(3x) = 4f(3x-3)+f(3x- 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X, where X is a real Banach space.

Keywords: Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

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Authors: Imad Chaddad, Andrei A. Kolyshkin

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory.

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Authors: Robersy Sánchez, Ricardo Grau

Abstract:

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represent one or more hypothetical bases with unspecific pairing. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvements of a primitive DNA repair system could make possible the transition from the ancient to the modern genetic code. Our results suggest that the Watson-Crick base pairing and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as the transition from the former to the later. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences.

Keywords: Genetic code vector space, primeval genetic code, power spectrum.

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Authors: Jaipong Kasemsuwan

Abstract:

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation

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Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

Abstract:

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

Abstract:

A dynamic stall-corrected Blade Element-Momentum algorithm based on a hybrid polar is validated through the comparison with Sandia experimental measurements on a 5-m diameter wind turbine of Troposkien shape. Different dynamic stall models are evaluated. The numerical predictions obtained using the extended aerodynamic coefficients provided by both Sheldal and Klimas and Raciti Castelli et al. are compared to experimental data, determining the potential of the hybrid database for the numerical prediction of vertical-axis wind turbine performances.

Keywords: Darrieus wind turbine, Blade Element-Momentum Theory, extended airfoil database, hybrid database, Sandia 5-m wind turbine.

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Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim

Abstract:

Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.

Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation

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Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.

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