Search results for: reaction diffusion equation

Authors: M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation.

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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Authors: Mohammad Amin Safi, Mahmud Ashrafizaadeh, Amir Ali Ashrafizaadeh

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A highly optimized implementation of binary mixture diffusion with no initial bulk velocity on graphics processors is presented. The lattice Boltzmann model is employed for simulating the binary diffusion of oxygen and nitrogen into each other with different initial concentration distributions. Simulations have been performed using the latest proposed lattice Boltzmann model that satisfies both the indifferentiability principle and the H-theorem for multi-component gas mixtures. Contemporary numerical optimization techniques such as memory alignment and increasing the multiprocessor occupancy are exploited along with some novel optimization strategies to enhance the computational performance on graphics processors using the C for CUDA programming language. Speedup of more than two orders of magnitude over single-core processors is achieved on a variety of Graphical Processing Unit (GPU) devices ranging from conventional graphics cards to advanced, high-end GPUs, while the numerical results are in excellent agreement with the available analytical and numerical data in the literature.

Keywords: Lattice Boltzmann model, Graphical processing unit, Binary mixture diffusion, 2D flow simulations, Optimized algorithm.

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Authors: Velid Demir, Mesut Akgün

Abstract:

The lanthanum and zinc oxide were synthesized and then loaded with 6 wt% over γ-Al2O3 using the wet impregnation method. The samples were calcined at 900 °C to ensure a coherent structure with high catalytic performance. Characterization of the catalysts was verified by X-ray diffraction (XRD) and Fourier-transform infrared spectroscopy (FTIR). The effect of catalysts on biodiesel content from jatropha oil was studied under supercritical conditions. The results showed that ZnO/γ-Al2O3 was the superior catalyst for jatropha oil with 98.05% biodiesel under reaction conditions of 7 min reaction time, 1:40 oil to methanol molar ratio, 6 wt% of catalyst loading, 90 bar of reaction pressure, and 300 °C of reaction temperature, compared to 95.50% with La2O3/γ-Al2O3 at the same parameters. For this study, ZnO/γ-Al2O3 was the most suitable catalyst due to performance and cost considerations.

Keywords: Biodiesel, heterogeneous catalyst, Jatropha oil, supercritical methanol, transesterification.

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.

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Authors: Azita Tajaddini, Ramleh Shamsi

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In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.

Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.

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Authors: Asadollah Aghajani, Yaghoub Jalilian

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Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.

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Authors: Flora Elvistia Firdaus

Abstract:

Polyurethane foam (PUF) were prepared by reacting polyols synthesized from soy-oil into mixture of 2,4- Toluene diisocyanate (TDI) with 4,4--Methylene Diamine Isocyanate (MDI) with ratio of 70:30. The polyols obtained via esterification reaction were categorize into different temperature of reaction and by used of varied concentration of phosphoric acid catalyst. The purpose of catalysts is to shifting selectivity to a desired and value added of product. The effect of stoichiometric balance (molar ratio of epoxide/ethylene glycol) to the concentration of the catalyst on the final properties was evaluated.

Keywords: temperature, phosphate, soy polyurethane

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.

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Authors: Iuliia Zarubiieva, Joyun Tseng, Vishwesh Kulkarni

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Recent researches has focused on nucleic acids as a substrate for designing biomolecular circuits for in situ monitoring and control. A common approach is to express them by a set of idealised abstract chemical reaction networks (ACRNs). Here, we present new results on how abstract chemical reactions, viz., catalysis, annihilation and degradation, can be used to implement circuit that accurately computes logarithm function using the method of Arithmetic-Geometric Mean (AGM), which has not been previously used in conjunction with ACRNs.

Keywords: Abstract chemical reaction network, DNA strand displacement, natural logarithm.

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Authors: Manisha Kankarej

Abstract:

The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, Integrability condition & Nijenhuis tensor.

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Authors: R. Mangiaracina, A. Perego, F. Campari

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Despite the fact that B2c eCommerce has become important in numerous economies, its adoption varies from country to country. This paper aims to identify the factors affecting (enabling or inhibiting) B2c eCommerce and to determine their quantitative impact on the diffusion of online sales across countries. A dynamic panel model analyzing the relationship between 13 factors (Macroeconomic, Demographic, Socio-Cultural, Infrastructural and Offer related) stemming from a complete literature analysis and the B2c eCommerce value in 45 countries over 9 years has been developed. Having a positive correlation coefficient, GDP, mobile penetration, Internet user penetration and credit card penetration resulted as enabling drivers of the B2c eCommerce value across countries, whereas, having a negative correlation coefficient,equal distribution of income and the development of traditional retailing network act as inhibiting factors.

Keywords: B2c eCommerce diffusion, influencing factors, dynamic panel model

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

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In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation

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Authors: Chandrashekar, R. T. Radhika, B. M. Venkatesha, S. Ananda, Shivalingegowda, T. S. Shashikumar, H. Ramachandra

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The kinetics of the oxidation of amitriptyline (AT) by sodium N-bromotoluene sulphonamide (C₆H₅SO₂NBrNa) has been studied in an acidic buffer medium of pH 1.2 at 303 K. The oxidation reaction of AT was followed spectrophotometrically at maximum wavelength, 410 nm. The reaction rate shows a first order dependence each on concentration of AT and concentration of sodium N-bromotoluene sulphonamide. The reaction also shows an inverse fractional order dependence at low or high concentration of HCl. The dielectric constant of the solvent shows negative effect on the rate of reaction. The addition of halide ions and the reduction product of BAT have no significant effect on the rate. The rate is unchanged with the variation in the ionic strength (NaClO₄) of the medium. Addition of reaction mixtures to be aqueous acrylamide solution did not initiate polymerization, indicating the absence of free radical species. The stoichiometry of the reaction was found to be 1:1 and oxidation product of AT is identified. The Michaelis-Menton type of kinetics has been proposed. The CH₃C₆H₅SO₂NHBr has been assumed to be the reactive oxidizing species. Thermodynamical parameters were computed by studying the reactions at different temperatures. A mechanism consistent with observed kinetics is presented.

Keywords: Amitriptyline, bromamine-T, kinetics, oxidation.

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Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali

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In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.

Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.

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Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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Authors: Subariah Ibrahim, Mohd Aizaini Maarof

Abstract:

A generalization of the concepts of Feistel Networks (FN), known as Extended Feistel Network (EFN) is examined. EFN splits the input blocks into n > 2 sub-blocks. Like conventional FN, EFN consists of a series of rounds whereby at least one sub-block is subjected to an F function. The function plays a key role in the diffusion process due to its completeness property. It is also important to note that in EFN the F-function is the most computationally expensive operation in a round. The aim of this paper is to determine a suitable type of EFN for a scalable cipher. This is done by analyzing the threshold number of rounds for different types of EFN to achieve the completeness property as well as the number of F-function required in the network. The work focuses on EFN-Type I, Type II and Type III only. In the analysis it is found that EFN-Type II and Type III diffuses at the same rate and both are faster than Type-I EFN. Since EFN-Type-II uses less F functions as compared to EFN-Type III, therefore Type II is the most suitable EFN for use in a scalable cipher.

Keywords: Cryptography, Extended Feistel Network, Diffusion Analysis.

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Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu

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In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

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In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: Kelong Zheng, Jinsong Hu,

Abstract:

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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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: Virendra J. Majarikar, Harikrishnan N. Unni

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This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m³ and 0 mol/m³, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process.

Keywords: COMSOL, electrokinetic, electroosmotic, microfluidics, zeta potential.

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Authors: H. Dehghan, E. Mahdavi, M. M. Heyhat

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In pressure vessels contain hydrogen, the role of hydrogen will be important because of hydrogen cracking problem. It is difficult to predict what is happened in metallurgical field spite of a lot of studies have been searched. The main role in controlling the mass diffusion as driving force is related to stress. In this study, finite element analysis is implemented to estimate material-s behavior associated with hydrogen embrittlement. For this purpose, one model of a pressure vessel is introduced that it has definite boundary and initial conditions. In fact, finite element is employed to solve the sequentially coupled mass diffusion with stress near a crack front in a pressure vessel. Modeling simulation intergrarnular fracture of AISI 4135 steel due to hydrogen is investigated. So, distribution of hydrogen and stress are obtained and they indicate that their maximum amounts occur near the crack front. This phenomenon is happened exactly the region between elastic and plastic field. Therefore, hydrogen is highly mobile and can diffuse through crystal lattice so that this zone is potential to trap high volume of hydrogen. Consequently, crack growth and fast fracture will be happened.

Keywords: Stress Intensity Factor, Mass Diffusion, FEM, Pressure Vessel

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Authors: Sayantan Khanra, Rojers P. Joseph

Abstract:

This study attempts to analyze the impact of demography and service quality on the adoption and diffusion of e-Government services in the context of India. The objective of this paper is to study the users' perception about e-Government services and investigate the key variables that are most salient to the Indian populace. At the completion of this study, a research model that would help to understand the relationship involving the demographic variables and service quality dimensions, and the willingness to adopt e-Government services is expected to be developed. Dedicated authorities, particularly those in developing economies, may use that model or its augmented versions to design and update e-Government services and promote their use among citizens. After all, enhanced public participation is required to improve efficiency, engagement and transparency in the implementation of the aforementioned services.

Keywords: Adoption and diffusion of e-Government services, demographic variables, hierarchical regression analysis, service quality dimensions.

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Authors: L. Parisi

Abstract:

In this research work, neural networks were applied to classify two types of hip joint implants based on the relative hip joint implant side speed and three components of each ground reaction force. The condition of walking gait at normal velocity was used and carried out with each of the two hip joint implants assessed. Ground reaction forces’ kinetic temporal changes were considered in the first approach followed but discarded in the second one. Ground reaction force components were obtained from eighteen patients under such gait condition, half of which had a hip implant type I-II, whilst the other half had the hip implant, defined as type III by Orthoload®. After pre-processing raw gait kinetic data and selecting the time frames needed for the analysis, the ground reaction force components were used to train a MLP neural network, which learnt to distinguish the two hip joint implants in the abovementioned condition. Further to training, unknown hip implant side and ground reaction force components were presented to the neural networks, which assigned those features into the right class with a reasonably high accuracy for the hip implant type I-II and the type III. The results suggest that neural networks could be successfully applied in the performance assessment of hip joint implants.

Keywords: Kinemic gait data, Neural networks, Hip joint implant, Hip arthroplasty, Rehabilitation Engineering.

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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: L. Torchane

Abstract:

In this work, our goal is to optimize the nitriding treatment at a low-temperature of the steel 32CrMoV13 using gas mixtures of ammonia, nitrogen and hydrogen to improve the mechanical properties of the surface (good wear resistance, friction and corrosion), and of the diffusion layer of the nitrogen (good resistance to fatigue and good tenacity with heart). By limiting our work to the pure iron and to the alloys iron-chromium and iron-chromium-carbon, we have studied the various parameters which manage the nitriding: flow rate and composition of the gaseous phase, the interaction chromium-nitrogen and chromium-carbon by the help of experiments of nitriding realized in the laboratory by thermogravimetry. The acquired knowledge has been applied by the mastery of the growth of the γ' combination layer on the α diffusion layer in the case of the industrial steel 32CrMoV13.

Keywords: Diffusion of nitrogen, Gaseous nitriding, Layer growth kinetic.

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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

Abstract:

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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