Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Adaptive Fractional Differentiation Harris Corner Detection Algorithm for Vision Measurement of Surface Roughness Thu, 17 Apr 2014 13:57:39 +0000 The Harris algorithm via fractional order derivative (the adaptive fractional differentiation Harris corner detection algorithm), which adaptively adjusts the fractal dimension parameter, has been investigated for an analysis of image processing relevant to surface roughness by vision measurements. The comparative experiments indicate that the algorithm allows the edge information in the high frequency areas to be enhanced, thus overcoming shortcomings. The algorithm permits real-time measurements of surface roughness to be performed with high precision, superior to the conventional Harris algorithm. Rui-Yin Tang and Zhou-Mo Zeng Copyright © 2014 Rui-Yin Tang and Zhou-Mo Zeng. All rights reserved. Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip Thu, 17 Apr 2014 11:36:19 +0000 This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase. O. D. Makinde and M. S. Tshehla Copyright © 2014 O. D. Makinde and M. S. Tshehla. All rights reserved. A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation Thu, 17 Apr 2014 07:18:21 +0000 We introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly. Jiraporn Janwised, Ben Wongsaijai, Thanasak Mouktonglang, and Kanyuta Poochinapan Copyright © 2014 Jiraporn Janwised et al. All rights reserved. Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain Wed, 16 Apr 2014 14:15:58 +0000 From the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. Their applications to the electrostatics in fractal media are discussed and their local forms in the Cantor-type cylindrical coordinates are also obtained. Yang-Yang Li, Yang Zhao, Gong-Nan Xie, Dumitru Baleanu, Xiao-Jun Yang, and Kai Zhao Copyright © 2014 Yang-Yang Li et al. All rights reserved. A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations Tue, 15 Apr 2014 16:33:48 +0000 The shifted Jacobi-Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm. A. H. Bhrawy and M. A. Alghamdi Copyright © 2014 A. H. Bhrawy and M. A. Alghamdi. All rights reserved. Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media Mon, 14 Apr 2014 08:56:38 +0000 We investigate the local fractional linear transport equations arising in fractal porous media by using the local fractional variational iteration method. Their approximate solutions within the nondifferentiable functions are obtained and their graphs are also shown. Meng Li, Xiao-Feng Hui, Carlo Cattani, Xiao-Jun Yang, and Yang Zhao Copyright © 2014 Meng Li et al. All rights reserved. On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current Mon, 14 Apr 2014 00:00:00 +0000 The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves. Dali Guo, Bo Tao, and Xiaohui Zeng Copyright © 2014 Dali Guo et al. All rights reserved. Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras Sun, 13 Apr 2014 14:43:28 +0000 Let be the Hilbert space effect algebra on a Hilbert space with , two positive numbers with and a bijective map. We show that if holds for all , then there exists a unitary or an antiunitary operator on such that for every . Qing Yuan and Kan He Copyright © 2014 Qing Yuan and Kan He. All rights reserved. On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation Thu, 10 Apr 2014 10:08:38 +0000 We study the modified Hunter-Saxton equation which arises in modelling of nematic liquid crystals. We obtain local conservation laws using the nonlocal conservation method and multiplier approach. In addition, using the relationship between conservation laws and Lie-point symmetries, some reductions and exact solutions are obtained. Sait San and Emrullah Yaşar Copyright © 2014 Sait San and Emrullah Yaşar. All rights reserved. Fractal Theory and Contact Dynamics Modeling Vibration Characteristics of Damping Blade Mon, 07 Apr 2014 13:58:50 +0000 The contact surface structure of dry friction damper is complicate, irregular, and self-similar. In this paper, contact surface structure is described with the fractal theory and damping blade is simplified as 2-DOF cantilever beam model with lumped masses. By changing the position of the damper, lacing and shroud structure are separately simulated to study vibration absorption effect of damping blade. The results show that both shroud structure and lacing could not only dissipate energy but also change stiffness of blade. Under the same condition of normal pressure and contact surface, the damping effect of lacing is stronger than that of shroud structure. Meanwhile, the effect on changing blade stiffness of shroud structure is stronger than that of lacing. This paper proposed that there is at least one position of the blade, at which the damper dissipates the most vibration energy during a vibration cycle. Ruishan Yuan, Qin Zhou, Qiang Zhang, and Yonghui Xie Copyright © 2014 Ruishan Yuan et al. All rights reserved. Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures Mon, 07 Apr 2014 13:48:06 +0000 The point for which the limit does not exist is called divergence point. Recently, multifractal structure of the divergence points of self-similar measures has been investigated by many authors. This paper is devoted to the study of some Moran measures with the support on the homogeneous Moran fractals associated with the sequences of which the frequency of the letter exists; the Moran measures associated with this kind of structure are neither Gibbs nor self-similar and than complex. Such measures possess singular features because of the existence of so-called divergence points. By the box-counting principle, we analyze multifractal structure of the divergence points of some homogeneous Moran measures and show that the Hausdorff dimension of the set of divergence points is the same as the dimension of the whole Moran set. JiaQing Xiao and YouMing He Copyright © 2014 JiaQing Xiao and YouMing He. All rights reserved. Numerical Analysis of Nanofluids in Differentially Heated Enclosure Undergoing Orthogonal Rotation Sun, 06 Apr 2014 14:10:51 +0000 Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2 nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction, , and the rotational speeds,  rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1% of the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds. H. Saleh and I. Hashim Copyright © 2014 H. Saleh and I. Hashim. All rights reserved. Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling Mon, 31 Mar 2014 16:38:50 +0000 Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu) and alumina (Al2O3) as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively. O. D. Makinde, S. Khamis, M. S. Tshehla, and O. Franks Copyright © 2014 O. D. Makinde et al. All rights reserved. On Fuzzy Fractional Laplace Transformation Sun, 30 Mar 2014 10:16:38 +0000 Fuzzy and fractional differential equations are used to model problems with uncertainty and memory. Using the fractional fuzzy Laplace transformation we have solved the fuzzy fractional eigenvalue differential equation. By illustrative examples we have shown the results. Ahmad Jafarian, Alireza Khalili Golmankhaneh, and Dumitru Baleanu Copyright © 2014 Ahmad Jafarian et al. All rights reserved. Description of Dispersive Wave Emission and Supercontinuum Generation in Silicon Waveguides Using Split-Step Fourier and Runge-Kutta Integration Methods Thu, 27 Mar 2014 11:27:24 +0000 Based on solving numerically the generalized nonlinear Schrödinger equation describing the propagation of high order femtosecond soliton in silicon waveguide under certain parametric conditions by the split-step Fourier and Runge-Kutta integration methods, dispersive wave emission and supercontinuum generation in silicon waveguides are numerically investigated by propagating femtosecond solitons. The numerical results show that the efficient dispersive wave emission can be generated in silicon waveguide, which plays an important role in the process of the supercontinuum generation with the form of Cherenkov radiation, and it is also shown that the high order low-energy solitons and short waveguides are efficient for the dispersive wave emission. Xuefeng Li Copyright © 2014 Xuefeng Li. All rights reserved. Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method Tue, 25 Mar 2014 15:18:39 +0000 The unsteady viscous flow over a continuously shrinking surface with mass suction is investigated using the optimal homotopy asymptotic method (OHAM). The nonlinear differential equation is obtained by means of the similarity transformation. The dual solutions exist for a certain range of mass suction and unsteadiness parameters. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration. Vasile Marinca and Remus-Daniel Ene Copyright © 2014 Vasile Marinca and Remus-Daniel Ene. All rights reserved. Scales of Time Where the Quantum Discord Allows an Efficient Execution of the DQC1 Algorithm Sun, 23 Mar 2014 09:17:39 +0000 The power of one qubit deterministic quantum processor (DQC1) (Knill and Laflamme (1998)) generates a nonclassical correlation known as quantum discord. The DQC1 algorithm executes in an efficient way with a characteristic time given by , where is an qubit unitary gate. For pure states, quantum discord means entanglement while for mixed states such a quantity is more than entanglement. Quantum discord can be thought of as the mutual information between two systems. Within the quantum discord approach the role of time in an efficient evaluation of is discussed. It is found that the smaller the value of is, where is the time of execution of the DQC1 algorithm and is the scale of time where the nonclassical correlations prevail, the more efficient the calculation of is. A Mösbauer nucleus might be a good processor of the DQC1 algorithm while a nuclear spin chain would not be efficient for the calculation of . M. Ávila, G. H. Sun, and A. L. Salas-Brito Copyright © 2014 M. Ávila et al. All rights reserved. Two Conservative Difference Schemes for Rosenau-Kawahara Equation Tue, 18 Mar 2014 08:57:19 +0000 Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results. Jinsong Hu, Youcai Xu, Bing Hu, and Xiaoping Xie Copyright © 2014 Jinsong Hu et al. All rights reserved. Dimension Spectrum for Sofic Systems Mon, 10 Mar 2014 11:50:45 +0000 We study the dimension spectrum of sofic system with the potential functions being matrix valued. For finite-coordinate dependent positive matrix potential, we set up the entropy spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. We extend this method to nonnegative matrix and give a series of examples of the sofic-affine set on which we can compute the spectrum concretely. Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen, and Mei-Shao Lin Copyright © 2014 Jung-Chao Ban et al. All rights reserved. Simulation of Impinging Cooling Performance with Pin Fins and Mist Cooling Adopted in a Simplified Gas Turbine Transition Piece Sun, 09 Mar 2014 07:21:36 +0000 The gas turbine transition piece was simplified to a one-four cylinder double chamber model with a single row of impinging holes in the outer wall. Heat transfer augmentation in the coolant chamber was achieved through the use of pin fin structure and mist cooling, which could increase the turbulence and heat transfer efficiency. The present research is focused on heat transfer and pressure characteristics of the impinging cooling in the coolant chamber using FLUENT software. With the given diameter of impinging hole, pin fin diameter ratios have been numerically studied in ranges from 1 to 2. Three different detached were simulated. The impinging cooling performance in all cases was compared between single-phase and two-phase (imported appropriate mist) flow in the coolant chamber. All the simulation results reveal that the factors of and have significant effects on the convective heat transfer. After the pin fin structure was taken, the resulting temperature decrease of 38.77 K at most compared with the result of structure without pin fins. And with the mist injecting into the cooling chamber, the area weighted average temperature got a lower value without excess pressure loss, which could satisfy the more stringent requirements in engineering. Tao Xu, Hang Xiu, Junlou Li, Haichao Ge, Qing Shao, Guang Yang, and Zhenglei Yu Copyright © 2014 Tao Xu et al. All rights reserved. Dynamical Processes and Systems of Fractional Order Sun, 02 Mar 2014 09:08:12 +0000 Ming Li, Carlo Cattani, Massimo Scalia, S. C. Lim, and Wen-Sheng Chen Copyright © 2014 Ming Li et al. All rights reserved. A New Boundary Model for Simulating Complex and Flexible Wall Bounded Domain in Dissipative Particle Dynamics Sun, 02 Mar 2014 08:26:43 +0000 Despite extensive area of applications, simulation of complex wall bounded problems or any deformable boundary is still a challenge in a Dissipative Particle Dynamics simulation. This limitation is rooted in the soft force nature of DPD and the fact that we need to use an antipenetration model for escaped particles. In the present paper, we propose a new model of antipenetration which preserves the conservation of linear momentum on the boundaries and enables us to simulate complex and flexible boundaries. Finally by performing numerical simulations, we demonstrate the validity of our new model. Saeid Mokhtarian, Ahmadreza Pishevar, and Mohammad Said Saidi Copyright © 2014 Saeid Mokhtarian et al. All rights reserved. Stabilization of the Wave Equation with Boundary Time-Varying Delay Wed, 26 Feb 2014 12:38:34 +0000 We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system. Hao Li, Changsong Lin, Shupeng Wang, and Yanmei Zhang Copyright © 2014 Hao Li et al. All rights reserved. Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise Wed, 12 Feb 2014 08:13:58 +0000 We consider a class of stochastic fractional equations driven by fractional noise on , with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise. Xichao Sun and Junfeng Liu Copyright © 2014 Xichao Sun and Junfeng Liu. All rights reserved. On a Periodic Solution of the 4-Body Problems Tue, 11 Feb 2014 11:36:56 +0000 We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition. Jian Chen and Bingyu Li Copyright © 2014 Jian Chen and Bingyu Li. All rights reserved. Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows Sun, 02 Feb 2014 12:35:38 +0000 The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated soils under uniform radial water flow backgrounds. The arising convection-dispersion equation given in terms of the stream functions is analyzed using classical Lie point symmetries. A number of exotic Lie point symmetries are admitted. Group invariant solutions are classified according to the elements of the one-dimensional optimal systems. We analyzed the group invariant solutions which satisfy the physical boundary conditions. M. M. Potsane and R. J. Moitsheki Copyright © 2014 M. M. Potsane and R. J. Moitsheki. All rights reserved. The Study of Fractional Order Controller with SLAM in the Humanoid Robot Tue, 28 Jan 2014 07:36:08 +0000 We present a fractional order PI controller (FOPI) with SLAM method, and the proposed method is used in the simulation of navigation of NAO humanoid robot from Aldebaran. We can discretize the transfer function by the Al-Alaoui generating function and then get the FOPI controller by Power Series Expansion (PSE). FOPI can be used as a correction part to reduce the accumulated error of SLAM. In the FOPI controller, the parameters () need to be tuned to obtain the best performance. Finally, we compare the results of position without controller and with PI controller, FOPI controller. The simulations show that the FOPI controller can reduce the error between the real position and estimated position. The proposed method is efficient and reliable for NAO navigation. Shuhuan Wen, Xiao Chen, Yongsheng Zhao, Ahmad B. Rad, Kamal Mohammed Othman, and Ethan Zhang Copyright © 2014 Shuhuan Wen et al. All rights reserved. The Deng Algorithm in Higher Dimensions Thu, 09 Jan 2014 11:55:11 +0000 We extend an algorithm of Deng in spherically symmetric spacetimes to higher dimensions. We show that it is possible to integrate the generalised condition of pressure isotropy and generate exact solutions to the Einstein field equations for a shear-free cosmological model with heat flow in higher dimensions. Three new metrics are identified which contain results of four dimensions as special cases. We show graphically that the matter variables are well behaved and the speed of sound is causal. Y. Nyonyi, S. D. Maharaj, and K. S. Govinder Copyright © 2014 Y. Nyonyi et al. All rights reserved. Application of Successive Linearisation Method to Squeezing Flow with Bifurcation Thu, 02 Jan 2014 12:24:37 +0000 This paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper. S. S. Motsa, O. D. Makinde, and S. Shateyi Copyright © 2014 S. S. Motsa et al. All rights reserved. Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems Mon, 30 Dec 2013 08:10:00 +0000 We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method. P. G. Dlamini, S. S. Motsa, and M. Khumalo Copyright © 2013 P. G. Dlamini et al. All rights reserved.