Search results for: Fractional neutral differential equation

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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Authors: Bin Mu, Site Li, Shijin Yuan

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Under the circumstance of environment deterioration, people are increasingly concerned about the quality of the environment, especially air quality. As a result, it is of great value to give accurate and timely forecast of AQI (air quality index). In order to simplify influencing factors of air quality in a city, and forecast the city’s AQI tomorrow, this study used MATLAB software and adopted the method of constructing a mathematic model of PCA-GABP to provide a solution. To be specific, this study firstly made principal component analysis (PCA) of influencing factors of AQI tomorrow including aspects of weather, industry waste gas and IAQI data today. Then, we used the back propagation neural network model (BP), which is optimized by genetic algorithm (GA), to give forecast of AQI tomorrow. In order to verify validity and accuracy of PCA-GABP model’s forecast capability. The study uses two statistical indices to evaluate AQI forecast results (normalized mean square error and fractional bias). Eventually, this study reduces mean square error by optimizing individual gene structure in genetic algorithm and adjusting the parameters of back propagation model. To conclude, the performance of the model to forecast AQI is comparatively convincing and the model is expected to take positive effect in AQI forecast in the future.

Keywords: AQI forecast, principal component analysis, genetic algorithm, back propagation neural network model.

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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: Bilal Barakeh

Abstract:

In this paper we discuss the effect of unbounded particle interaction operator on particle growth and we study how this can address the choice of appropriate time steps of the numerical simulation. We provide also rigorous mathematical proofs showing that large particles become dominating with increasing time while small particles contribute negligibly. Second, we discuss the efficiency of the algorithm by performing numerical simulations tests and by comparing the simulated solutions with some known analytic solutions to the Smoluchowski equation.

Keywords: Stochastic processes, coagulation of particles, numerical scheme.

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Authors: Peng Zhang, Lihui Zheng, Xiangchun Wang, Xiaopan Kou

Abstract:

Quantitative research on the main control factors of lost circulation has few considerations and single data source. Using Unmanned Intervention Algorithm to find the main control factors of lost circulation adopts all measurable parameters. The degree of lost circulation is characterized by the loss rate as the objective function. Geological, engineering and fluid data are used as layers, and 27 factors such as wellhead coordinates and Weight on Bit (WOB) used as dimensions. Data classification is implemented to determine function independent variables. The mathematical equation of loss rate and 27 influencing factors is established by multiple regression method, and the undetermined coefficient method is used to solve the undetermined coefficient of the equation. Only three factors in t-test are greater than the test value 40, and the F-test value is 96.557%, indicating that the correlation of the model is good. The funnel viscosity, final shear force and drilling time were selected as the main control factors by elimination method, contribution rate method and functional method. The calculated values of the two wells used for verification differ from the actual values by -3.036 m3/h and -2.374 m3/h, with errors of 7.21% and 6.35%. The influence of engineering factors on the loss rate is greater than that of funnel viscosity and final shear force, and the influence of the three factors is less than that of geological factors. The best combination of funnel viscosity, final shear force and drilling time is obtained through quantitative calculation. The minimum loss rate of lost circulation wells in Shunbei area is 10 m3/h. It can be seen that man-made main control factors can only slow down the leakage, but cannot fundamentally eliminate it. This is more in line with the characteristics of karst caves and fractures in Shunbei fault solution oil and gas reservoir.

Keywords: Drilling fluid, loss rate, main controlling factors, Unmanned Intervention Algorithm.

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Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria

Abstract:

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.

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Authors: Alexander B. Bichkov, Valery V. Smirnov

Abstract:

Total cross section of helium atom photo-ionization by weak short pulse is calculated using the variant of trajectory method, developed in our earlier work. The method enables simple estimation of total ionization probability (or cross section) without integration of differential one.

Keywords: Evaluation of Photo-Ionization, Helium, Trajectory Method

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Authors: S. S. Gautam, S. Samanta

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The aim of the paper work is to investigate and predict the static performance of journal bearing in turbulent flow condition considering micropolar lubrication. The Reynolds equation has been modified considering turbulent micropolar lubrication and is solved for steady state operations. The Constantinescu-s turbulence model is adopted using the coefficients. The analysis has been done for a parallel and inertia less flow. Load capacity and friction factor have been evaluated for various operating parameters.

Keywords: hydrodynamic bearing, micropolar lubrication, coupling number, characteristic length, perturbation analysis

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Authors: Mete Kazaz, Birol Gülnar

Abstract:

Television news has gained a new dimension in terms of ideological approaches as a result of such factors as globalization, cross monopolization, presence of international companies etc. and certain strategies have been developed at the production, presentation and distribution stages of news. In this study, television news about a process called “settlement process” was investigated. In this framework, news about the settlement process on TV channels of TRT 1, ATV, FOX TV, NTV, HABERTÜRK, TRT HABER and STV was investigated using the content analysis method in terms of the strategies the ideology construction, attitude towards the party in power, attitude towards parties in opposition and attitude towards BDP (Peace and Democracy Part) and Imrali (the island where Abdullah Ocalan, head of PKK, is kept). First, the aforementioned TV channels were selected randomly from 3 groups in order to be able to reveal the representational capacity of commercial, news and public channels. The study covers 557 news items broadcast in the main news bulletins between the dates of 15 March 2013 and 15 March 2013. While there was a positive attitude towards the government in a sizable portion of the news about the settlement process (63.6%), the attitude of 25.3% of the news was impartial towards the government and 11.3% had a negative attitude. On the other hand, there was a negative attitude towards the Opposition in a considerable portion of the news about the settlement process (56.1%). The attitude of 35.9% of the news towards the Opposition was impartial whereas 8.0% had a positive attitude. While 34.9% of the news about the settlement process used the legitimization strategy from among the ideology construction strategies, 22.8% used the unification strategy, 15.7% the reification strategy, 15.6% fractional and 11% concealment/mystification strategy.

Keywords: Attitude, Ideological Framing, Television News.

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Authors: Nirmala P. Ratchagar, S. Senthamilselvi

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The heat and mass transfer characteristics of contaminants in groundwater subjected to a biodegradation reaction is analyzed by taking into account the thermal diffusion (Soret) effects. This phenomenon is modulated mathematically by a system of partial differential equations which govern the motion of fluid (groundwater) and solid (contaminants) particles. The numerical results are presented graphically for different values of the parameters entering into the problem on the velocity profiles of fluid, contaminants, temperature and concentration profile.

Keywords: Heat and mass transfer, Soret number, porous media.

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Authors: Bhawna Tandon, Shiv Narayan, Jagdish Kumar

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This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is performed using a maximum of N-1 steps where N being the dimension of the system.

Keywords: Explicit Algorithm, Feedback Linearization, Nonlinear control, Magnetic Levitation System.

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Authors: Qazi Nasir, K. K. Lau, Bhajan Lal

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In this study the enthalpies of dissociation for pure methane and pure carbon dioxide was calculated using a hydrate equilibrium data obtained in this study. The enthalpy of dissociation was determined using Clausius-Clapeyron equation. The results were compared with the values reported in literature obtained using various techniques.

Keywords: Enthalpies of dissociation, methane, carbon dioxide, gas hydrate, natural gas.

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Authors: Z. Haddad, C. Abid, O. Rahli, O. Margeat, W. Dachraoui, A. Mataoui

Abstract:

The present study aims to measure the volumetric mass density of NiPd-heptane nanofluids synthesized using a one step method known as thermal decomposition of metal-surfactant complexes. The particle concentration is up to 7.55g/l and the temperature range of the experiment is from 20°C to 50°C. The measured values were compared with the mixture theory and good agreement between the theoretical equation and measurement were obtained. Moreover, the available nanofluids volumetric mass density data in the literature is reviewed.

Keywords: NiPd nanoparticles, nanofluids, volumetric mass density, stability.

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Authors: Changjin Xu

Abstract:

In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.

Keywords: Two-neuron system, delay, stability, Hopf bifurcation.

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Authors: Arafa A. Alholaisi, Jamal H. Madani, M. A. Alvi

Abstract:

The radial form of nuclear matter distribution, charge and the shape of nuclei are essential properties of nuclei, and hence, are of great attention for several areas of research in nuclear physics. More than last three decades have witnessed a range of experimental means employing leptonic probes (such as muons, electrons etc.) for exploring nuclear charge distributions, whereas the hadronic probes (for example alpha particles, protons, etc.) have been used to investigate the nuclear matter distributions. In this paper, p-^9,11Li elastic scattering differential cross sections in the energy range  to  MeV have been studied by means of Coulomb modified Glauber scattering formalism. By applying the semi-phenomenological Bhagwat-Gambhir-Patil [BGP] nuclear density for loosely bound neutron rich ¹¹Li nucleus, the estimated matter radius is found to be 3.446 fm which is quite large as compared to so known experimental value 3.12 fm. The results of microscopic optical model based calculation by applying Bethe-Brueckner–Hartree–Fock formalism (BHF) have also been compared. It should be noted that in most of phenomenological density model used to reproduce the p-¹¹Li differential elastic scattering cross sections data, the calculated matter radius lies between 2.964 and 3.55 fm. The calculated results with phenomenological BGP model density and with nucleon density calculated in the relativistic mean-field (RMF) reproduces p-⁹Li and p-¹¹Li experimental data quite nicely as compared to Gaussian- Gaussian or Gaussian-Oscillator densities at all energies under consideration. In the approach described here, no free/adjustable parameter has been employed to reproduce the elastic scattering data as against the well-known optical model based studies that involve at least four to six adjustable parameters to match the experimental data. Calculated reaction cross sections σ_R for p-¹¹Li at these energies are quite large as compared to estimated values reported by earlier works though so far no experimental studies have been performed to measure it.

Keywords: Bhagwat-Gambhir-Patil density, coulomb modified Glauber model, halo nucleus, optical limit approximation.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

Abstract:

We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Kwa-Sur Tam

Abstract:

This paper reviews various approaches that have been used for the modeling and simulation of large-scale engineering systems and determines their appropriateness in the development of a RICS modeling and simulation tool. Bond graphs, linear graphs, block diagrams, differential and difference equations, modeling languages, cellular automata and agents are reviewed. This tool should be based on linear graph representation and supports symbolic programming, functional programming, the development of noncausal models and the incorporation of decentralized approaches.

Keywords: Interdisciplinary, dynamic, functional programming, object-oriented.

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Authors: Sie-Tiong Ha, Teck-Leong Lee, Yip-Foo Win, Siew-Ling Lee, Guan-Yeow Yeap

Abstract:

A homologous series of aromatic esters, 4-nalkanoyloxybenzylidene- 4--bromoanilines, nABBA, consisting of two 1,4-disubstituted phenyl cores and a Schiff base central linkage was synthesized. All the members can be differed by the number of carbon atoms at terminal alkanoyloxy chain (CnH2n-1COO-, n = 2, 6, 18). The molecular structure of nABBA was confirmed with infrared spectroscopy, nuclear magnetic resonance (NMR) spectroscopy and electron-ionization mass (EI-MS) spectrometry. Mesomorphic properties were studied using differential scanning calorimetry and polarizing optical microscopy.

Keywords: Liquid Crystals, Schiff base, Smectic, Mesomorphic

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: A. Zerarka, A. Soukeur, N. Khelil

Abstract:

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.

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Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Swarniv Chandra, Basudev Ghosh, S. N. Paul

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Using one dimensional Quantum hydrodynamic (QHD) model Korteweg de Vries (KdV) solitary excitations of electron-acoustic waves (EAWs) have been examined in twoelectron- populated relativistically degenerate super dense plasma. It is found that relativistic degeneracy parameter influences the conditions of formation and properties of solitary structures.

Keywords: Relativistic Degeneracy, Electron-Acoustic Waves, Quantum Plasma, KdV Equation.

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Authors: Farouk Cherif

Abstract:

This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.

Keywords: Chaotic neural network, Hamiltonian systems, Pseudo almost periodic.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: Ali Poureslami, Hossein Borhanifar, Seyed Ali Alavian

Abstract:

In this paper, we implement a modern serial backplane platform for telecommunication inter-rack systems. For combination high reliability and low cost protocol property, we applied high level data link control (HDLC) protocol with low voltage differential signaling (LVDS) bus for card to card communicated over backplane. HDLC protocol is a high performance with several operation modes and is famous in telecommunication systems. LVDS bus is a high reliability with high immunity against electromagnetic interference (EMI) and noise.

Keywords: Backplane, BLVDS, HDLC, EMI, I2C, LCT, OSC, SFP, SNMP.

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Authors: Safae El Alaoui, Mohamed Ouzahra

Abstract:

In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.

Keywords: Exponential stabilization, unbounded operator, Desch-Schappacher, Miyadera-Voigt operator.

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Authors: Y. C. Liou, J. M. Miao, T. L. Liu, M. H. Ho

Abstract:

The purpose of this study was to explore the complex flow structure a novel active-type micromixer that based on concept of Wankle-type rotor. The characteristics of this micromixer are two folds; a rapid mixing of reagents in a limited space due to the generation of multiple vortices and a graduate increment in dynamic pressure as the mixed reagents is delivered to the output ports. Present micro-mixer is consisted of a rotor with shape of triangle column, a blending chamber and several inlet and outlet ports. The geometry of blending chamber is designed to make the rotor can be freely internal rotated with a constant eccentricity ratio. When the shape of the blending chamber and the rotor are fixed, the effects of rotating speed of rotor and the relative locations of ports on the mixing efficiency are numerical studied. The governing equations are unsteady, two-dimensional incompressible Navier-Stokes equation and the working fluid is the water. The species concentration equation is also solved to reveal the mass transfer process of reagents in various regions then to evaluate the mixing efficiency. The dynamic mesh technique was implemented to model the dynamic volume shrinkage and expansion of three individual sub-regions of blending chamber when the rotor conducted a complete rotating cycle. Six types of ports configuration on the mixing efficiency are considered in a range of Reynolds number from 10 to 300. The rapid mixing process was accomplished with the multiple vortex structures within a tiny space due to the equilibrium of shear force, viscous force and inertial force. Results showed that the highest mixing efficiency could be attained in the following conditions: two inlet and two outlet ports configuration, that is an included angle of 60 degrees between two inlets and an included angle of 120 degrees between inlet and outlet ports when Re=10.

Keywords: active micro-mixer, CFD, mixing efficiency, ports configuration, Reynolds number, Wankle-type rotor

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Authors: Hsuan-Ku Liu

Abstract:

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

Keywords: Fuzzy derivative, lateral type of H-derivative, fuzzy differential equations, fuzzy boundary value problems, boundary value problems.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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