Search results for: periodic solutions.

Authors: B. Tomczyk, R. Mania

Abstract:

Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

Abstract:

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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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: Liu Ning, Zhong Chongquan, Teng Hongfei

Abstract:

EPA (Ethernet for Plant Automation) resolves the nondeterministic problem of standard Ethernet and accomplishes real-time communication by means of micro-segment topology and deterministic scheduling mechanism. This paper studies the real-time performance of EPA periodic data transmission from theoretical and experimental perspective. By analyzing information transmission characteristics and EPA deterministic scheduling mechanism, 5 indicators including delivery time, time synchronization accuracy, data-sending time offset accuracy, utilization percentage of configured timeslice and non-RTE bandwidth that can be used to specify the real-time performance of EPA periodic data transmission are presented and investigated. On this basis, the test principles and test methods of the indicators are respectively studied and some formulas for real-time performance of EPA system are derived. Furthermore, an experiment platform is developed to test the indicators of EPA periodic data transmission in a micro-segment. According to the analysis and the experiment, the methods to improve the real-time performance of EPA periodic data transmission including optimizing network structure, studying self-adaptive adjustment method of timeslice and providing data-sending time offset accuracy for configuration are proposed.

Keywords: EPA system, Industrial Ethernet, Periodic data, Real-time performance

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Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

One of the most attractive and important field of chaos theory is control of chaos. In this paper, we try to present a simple framework for chaotic motion control using the feedback linearization method. Using this approach, we derive a strategy, which can be easily applied to the other chaotic systems. This task presents two novel results: the desired periodic orbit need not be a solution of the original dynamics and the other is the robustness of response against parameter variations. The illustrated simulations show the ability of these. In addition, by a comparison between a conventional state feedback and our proposed method it is demonstrated that the introduced technique is more efficient.

Keywords: chaos, feedback linearization, robust control, periodic motion.

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

Diffraction grating is periodic module used in many engineering fields, its geometrical conception gives interesting properties of diffraction and interferences, a uniform and periodic diffraction grating consists of a number of identical apertures that are equally spaced, in this case, the amplitude of intensity distribution in the far field region is generally modulated by diffraction pattern of single aperture. In this paper, we study the case of aperiodic diffraction grating with identical rectangular apertures where theirs coordinates are modeled by square root function, we elaborate a computer simulation comparatively to the periodic array with same length and we discuss the numerical results.

Keywords: Diffraction grating, interferences, amplitude modulation, laser.

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Authors: Hsiang-Fu Yu, Yu-Chan Hsu, Chun Fang, Hao-Yun Yang

Abstract:

Periodic broadcast is a cost-effective solution for large-scale distribution of popular videos because this approach guarantees constant worst service latency, regardless of the number of video requests. An essential periodic broadcast method is the client-centric approach (CCA), which allows clients to use smaller receiving bandwidth to download broadcast data. An enhanced version, namely CCA++, was proposed to yield a shorter waiting time. This work further improves CCA++ in reducing client buffer requirements. The new scheme decreases the buffer requirements by as much as 52% when compared to CCA++. This study also provides an analytical evaluation to demonstrate the performance advantage, as compared with particular schemes.

Keywords: Periodic broadcast, client-centric approach, buffer space, multimedia communications.

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Authors: Arash Karimipour, M. Afrand, M. M. Bazofti

Abstract:

The periodic mixed convection of a water-copper nanofluid inside a rectangular cavity with aspect ratio of 3 is investigated numerically. The temperature of the bottom wall of the cavity is assumed greater than the temperature of the top lid which oscillates horizontally with the velocity defined as u = u0 sin (ω t). The effects of Richardson number, Ri, and volume fraction of nanoparticles on the flow and thermal behavior of the nanofluid are investigated. Velocity and temperature profiles, streamlines and isotherms are presented. It is observed that when Ri < 1, heat transfer rate is much greater than when Ri > 1. The higher value of Ri corresponds to a lower value of the amplitude of the oscillation of Num in the steady periodic state. Moreover, increasing the volume fraction of the nanoparticles increases the heat transfer rate.

Keywords: Nanofluid, Top lid oscillation, Mixed convection, Volume fraction

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Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma

Abstract:

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.

Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.

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Authors: Kejun Zhuang

Abstract:

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.

Keywords: Chaotic system, Hopf bifurcation, normal form theory.

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Authors: Atul Krishna Banik

Abstract:

Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.

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Authors: Kejun Zhuang, Hailong Zhu

Abstract:

The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.

Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop

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Authors: Jonathan Bohn, Jorge Rebaza, Kaitlin Speer

Abstract:

The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well as some heteroclinic orbits are computed.

Keywords: Predator-prey models, threshold harvesting, dynamicalsystems

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: Anand Dass, Hiroaki Murakami

Abstract:

The paper outlines the drivers behind the movement from products to solutions in the Hi-Tech Business-to-Business markets. The paper lists out the challenges in enabling the transformation from products to solutions and also attempts to explore strategic and operational recommendations based on the authors- factual experiences with Japanese Hi-tech manufacturing organizations. Organizations in the Hi-Tech Business-to-Business markets are increasingly being compelled to move to a solutions model from the conventional products model. Despite the added complexity of solutions, successful technology commercialization can be achieved by making prudent choices in defining a relevant solutions model, by backing the solution model through appropriate organizational design, and by overhauling the new product development process and supporting infrastructure.

Keywords: Technology commercialization, Solutions, Hi-Tech companies, Japan, Management of technology

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Authors: H. Ait Abderrahmane, M. Fayed, H. D. Ng, G. H. Vatistas

Abstract:

The present paper expands details and confirms the transition mechanism between two subsequent polygonal patterns of the hollow-core vortex. Using power spectral analysis, we confirm in this work that the transition from any N-gon to (N+1)-gon pattern observed within a hollow-core vortex of shallow rotating flows occurs in two steps. The regime was quasi-periodic before the frequencies lock (synchronization). The ratios of locking frequencies were found to be equal to (N-1)/N.

Keywords: Patterns, quasi-periodic, swirling, synchronization, transition.

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Authors: Farshid Fathinia, Mohammad Parsazadeh, Amirhossein Heshmati

Abstract:

Turbulent forced convection flow in a 2-dimensional channel over periodic grooves is numerically investigated. Finite volume method is used to study the effect of turbulence model. The range of Reynolds number varied from 10000 to 30000 for the ribheight to channel-height ratio (B/H) of 2. The downstream wall is heated by a uniform heat flux while the upstream wall is insulated. The investigation is analyzed with different types of nanoparticles such as SiO2, Al2O3, and ZnO, with water as a base fluid are used. The volume fraction is varied from 1% to 4% and the nanoparticle diameter is utilized between 20nm to 50nm. The results revealed 114% heat transfer enhancement compared to the water in a grooved channel by using SiO2 nanoparticle with volume fraction and nanoparticle diameter of 4% and 20nm respectively.

Keywords: Forced convection, Periodic grooves, Nanofluids, Turbulent model, Heat transfer.

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Authors: Onesmus Muvengei, John Kihiu, Bernard Ikua

Abstract:

This paper numerically investigates the effects of input speed on the overall dynamic characteristics of a multi-body system with differently located revolute clearance joints without friction. A typical planar slider-crank mechanism is used as a demonstration case in which the effects of the input speed on the dynamic performance of the mechanism with a revolute clearance joint between the crank and connecting rod, and between the connecting rod and slider are separately investigated with comprehensive observations numerically presented. It is observed that, changing the driving speed of a multibody system makes the behavior of the system to change from either periodic to chaotic, or chaotic to periodic depending on which joint has clearance. The location of the clearance revolute joint and the operating speed of a multi-body system play a crucial role in predicting accurately the dynamic responses of the system. Therefore the dynamic behavior of one clearance revolute joint cannot be used as a general case for a mechanical system.

Keywords: Chaotic behavior, Contact-impact forces, Dynamic response, Multi-body mechanical system, Periodic behavior, Poincare maps, Quasi-periodic behavior, Revolute clearance joint

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Authors: Shunyi Li, Zhifang He, Xiangui Xue

Abstract:

An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.

Keywords: Stage-structured predator-prey system, Impulsive, Permanence, Bifurcation, Chaos.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Magdy G. Asaad

Abstract:

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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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: 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: M. H. Pol, A. Bidi, A. V. Hoseini

Abstract:

Estimation of natural frequency of structures is very important and isn-t usually calculated simply and sometimes complicated. Lack of knowledge about that caused hard damage and hazardous effects. In this paper, with using from two different models in FEM method and based on hydrodynamic mass of fluids, natural frequency of an especial bearing (Fig. 1) in an electric field (or, a periodic force) is calculated in different stiffness and different geometric. In final, the results of two models and analytical solution are compared.

Keywords: Natural frequency of the bearing, Hydrodynamic mass of fluid method.

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Authors: Muhammad Rizwan Azhar, Emadadeen Ali

Abstract:

In this paper, periodic force operation of a wastewater treatment process has been studied for the improved process performance. A previously developed dynamic model for the process is used to conduct the performance analysis. The static version of the model was utilized first to determine the optimal productivity conditions for the process. Then, feed flow rate in terms of dilution rate i.e. (D) is transformed into sinusoidal function. Nonlinear model predictive control algorithm is utilized to regulate the amplitude and period of the sinusoidal function. The parameters of the feed cyclic functions are determined which resulted in improved productivity than the optimal productivity under steady state conditions. The improvement in productivity is found to be marginal and is satisfactory in substrate conversion compared to that of the optimal condition and to the steady state condition, which corresponds to the average value of the periodic function. Successful results were also obtained in the presence of modeling errors and external disturbances.

Keywords: Dilution rate, nonlinear model predictive control, sinusoidal function, wastewater treatment.

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Authors: Aziza Altaibayeva, Ertan Gudekli, Ratbay Myrzakulov

Abstract:

In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: Quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times.

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Authors: Kejun Zhuang

Abstract:

In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.

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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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Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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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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