http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 28 Mar 2013 15:12:31 +0000 http://www.hindawi.com/isrn/mp/2013/149169/ Strongly nonlinear stochastic processes can be found in many applications in physics and the life sciences. In particular, in physics, strongly nonlinear stochastic processes play an important role in understanding nonlinear Markov diffusion processes and have frequently been used to describe order-disorder phase transitions of equilibrium and nonequilibrium systems. However, diffusion processes represent only one class of strongly nonlinear stochastic processes out of four fundamental classes of time-discrete and time-continuous processes evolving on discrete and continuous state spaces. Moreover, strongly nonlinear stochastic processes appear both as Markov and non-Markovian processes. In this paper the full spectrum of strongly nonlinear stochastic processes is presented. Not only are processes presented that are defined by nonlinear diffusion and nonlinear Fokker-Planck equations but also processes are discussed that are defined by nonlinear Markov chains, nonlinear master equations, and strongly nonlinear stochastic iterative maps. Markovian as well as non-Markovian processes are considered. Applications range from classical fields of physics such as astrophysics, accelerator physics, order-disorder phase transitions of liquids, material physics of porous media, quantum mechanical descriptions, and synchronization phenomena in equilibrium and nonequilibrium systems to problems in mathematics, engineering sciences, biology, psychology, social sciences, finance, and economics. T. D. Frank Copyright © 2013 T. D. Frank. All rights reserved. Mon, 11 Mar 2013 09:05:45 +0000 http://www.hindawi.com/isrn/mp/2013/651684/ We construct the higher order terms of curvatures in Lagrangians of the scale factor in the D-dimensional Robertson-Walker metric, which are linear in the second derivative of the scale factor with respect to cosmic time. It is shown that they are composed of the Lovelock tensors at the first step; iterative construction yields arbitrarily high order terms. The relation to the former work on higher order gravity is discussed. Despite the absence of scalar degrees of freedom in cosmological models which come from our Lagrangian, it is shown that an inflationary behavior of the scale factor can be found. The application to the thick brane solutions is also studied. Nahomi Kan, Koichiro Kobayashi, and Kiyoshi Shiraishi Copyright © 2013 Nahomi Kan et al. All rights reserved. Mon, 25 Feb 2013 18:53:10 +0000 http://www.hindawi.com/isrn/mp/2013/146704/ The modified simple equation method is significant for finding the exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring in the modified simple equation (MSE) method for solving NLEEs via the Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony (GZK-BBM) equation and the right-handed noncommutative Burgers' (nc-Burgers) equations and achieve the exact solutions involving parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. It is established that the MSE method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics. Kamruzzaman Khan, M. Ali Akbar, and Norhashidah Hj. Mohd. Ali Copyright © 2013 Kamruzzaman Khan et al. All rights reserved. Sun, 03 Feb 2013 15:09:12 +0000 http://www.hindawi.com/isrn/mp/2013/487270/ We provide an overview on the application of the exterior calculus of differential forms to the ab initio formulation of lattice field theories, with a focus on irregular or “random” lattices. F. L. Teixeira Copyright © 2013 F. L. Teixeira. All rights reserved. Tue, 25 Sep 2012 10:51:43 +0000 http://www.hindawi.com/isrn/mp/2012/327298/ On the real line initially there are infinite number of particles on the positive half line, each having one of -negative velocities . Similarly, there are infinite number of antiparticles on the negative half line, each having one of -positive velocities . Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of —the coordinate of the last collision before between particle and antiparticle. V. A. Malyshev, A. D. Manita, and A. A. Zamyatin Copyright © 2012 V. A. Malyshev et al. All rights reserved. Sun, 23 Sep 2012 09:51:57 +0000 http://www.hindawi.com/isrn/mp/2012/630801/ This work is concerned with the lattice Boltzmann computation of two-dimensional incompressible viscous flow past a square cylinder confined in a channel. It is known that the nature of the flow past cylindrical obstacles is very complex. In the present work, computations are carried out both for steady and unsteady flows using lattice Boltzmann method. Effects of Reynolds number, blockage ratio, and channel length are studied in detail. As good care has been taken to include appropriate measures in the computational method, these results enjoy good credibility. To sum up, the present study reveals many interesting features of square cylinder problem and demonstrates the capability of the lattice Boltzmann method to capture these features. D. Arumuga Perumal, Gundavarapu V. S. Kumar, and Anoop K. Dass Copyright © 2012 D. Arumuga Perumal et al. All rights reserved. Sun, 16 Sep 2012 11:27:19 +0000 http://www.hindawi.com/isrn/mp/2012/401515/ The objective of this paper is to investigate an unsteady flow of a viscous incompressible flow past an infinite isothermal vertical oscillating plate, in the presence of thermal radiation and chemical reaction. The fluid considered here is a gray, absorbing-emitting radiation but a nonscattering medium. The plate temperature is arised to 𝑇𝑤, and the concentration level near the plate is raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the finite element method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature, and concentration are studied for different physical parameters like thermal Grashof number, mass Grashof number, radiation parameter, prandtl number, chemical reaction parameter, Schmidt number, phase angle, and time are studied graphically. The skin-friction coefficient, the Nusselt number, and the Sherwood number at the plate are discussed, and their numerical values for various values of physical parameters are presented through tables. S. Sivaiah, G. Murali, and M. C. K. Reddy Copyright © 2012 S. Sivaiah et al. All rights reserved. Tue, 11 Sep 2012 15:14:39 +0000 http://www.hindawi.com/isrn/mp/2012/920475/ An interesting discovery in the last two years in the field of mathematical physics has been the exceptional 𝑋ℓ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have the lowest degree ℓ=1,2,…, and yet they form complete sets with respect to some positive-definite measure. In this paper, we study one important aspect of these new polynomials, namely, the behaviors of their zeros as some parameters of the Hamiltonians change. Most results are of heuristic character derived by numerical analysis. Choon-Lin Ho and Ryu Sasaki Copyright © 2012 Choon-Lin Ho and Ryu Sasaki. All rights reserved. Thu, 06 Sep 2012 16:17:04 +0000 http://www.hindawi.com/isrn/mp/2012/869070/ The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics. The generalized Lukovsky-Miles modal equations are derived. Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions. Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form. Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors. A good agreement is shown. M. O. Chernova, I. A. Lukovsky, and A. N. Timokha Copyright © 2012 M. O. Chernova et al. All rights reserved. Sun, 02 Sep 2012 11:09:47 +0000 http://www.hindawi.com/isrn/mp/2012/760239/ We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex conjugation operator and the Pauli spin matrices, corresponding to the irreducible representation of the Lorentz group. Then we derive the complex two-component eigenfunctions of the Majorana equation and the related quantum fields in a concise way, by exploiting the so-called chirality conjugation operator that involves the spin-flip operator. Subsequently, the four-component spinor solutions of the real Majorana equation are derived, and their intrinsic relations with the spinors of the complex two-component version of the Majorana equation are revealed and discussed extensively. Eckart Marsch Copyright © 2012 Eckart Marsch. All rights reserved. Thu, 23 Aug 2012 14:13:56 +0000 http://www.hindawi.com/isrn/mp/2012/185469/ In the present paper, we have obtained an exact biperiodic, one-phase solution of the Kawahara evolution equation. Two classes of real periodic waves generated by the biperiodic solution have been analyzed. A modification of the bilinear-transformation method has been applied allowing to provide a single solution of the residual equation derived from the bidifferential reduction of the considered nonintegrable equation. It is shown that the spatial displacements are individual for each separate harmonic of the real periodic solutions. Ognyan Yordanov Kamenov and Anna P. Angova Copyright © 2012 Ognyan Yordanov Kamenov and Anna P. Angova. All rights reserved. Thu, 16 Aug 2012 14:07:10 +0000 http://www.hindawi.com/isrn/mp/2012/869069/ We present interesting properties of null geodesics of static charged black holes in Einstein-Born-Infeld gravity. These null geodesics represents the path for gravitons. In addition, we also study the path of photons for the Born-Infeld black hole which are null geodesics of an effective geometry. We will present how the bending of light is effected by the non-linear parameter 𝛽 of the theory. Some other properties, such as the horizon radius and the temperature are also discussed in the context of the nonlinear parameter 𝛽. Sharmanthie Fernando Copyright © 2012 Sharmanthie Fernando. All rights reserved. Wed, 15 Aug 2012 08:56:18 +0000 http://www.hindawi.com/isrn/mp/2012/837241/ Employing the classical Lie method, we obtain the symmetries of the ZK-BBM equation. Applying the given Lie symmetry, we obtain the similarity reduction, group invariant solution, and new exact solutions. We also obtain the conservation laws of ZK-BBM equation of the corresponding Lie symmetry. Wenbin Zhang, Jiangbo Zhou, and Sunil Kumar Copyright © 2012 Wenbin Zhang et al. All rights reserved. Wed, 15 Aug 2012 07:56:30 +0000 http://www.hindawi.com/isrn/mp/2012/659289/ We consider a nonlinear degenerate coupled beams system with weak damping. We show using the Nakao method that the solution of this system decays exponentially when the time tends to infinity. R. F. C. Lobato, D. C. Pereira, and M. L. Santos Copyright © 2012 R. F. C. Lobato et al. All rights reserved. Thu, 09 Aug 2012 15:19:01 +0000 http://www.hindawi.com/isrn/mp/2012/965164/ This paper deals with the cosmological models for the static spherically symmetric spacetime for perfect fluid with anisotropic stress energy tensor in general relativity by introducing the generating functions 𝑔(𝑟) and 𝑤(𝑟) and also discussing their physical and geometric properties. D. D. Pawar, V. R. Patil, and S. N. Bayaskar Copyright © 2012 D. D. Pawar et al. All rights reserved. Thu, 09 Aug 2012 13:37:29 +0000 http://www.hindawi.com/isrn/mp/2012/374670/ Exact analytic solutions are obtained for the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders. The fractional calculus approach in the governing equations of a second grade fluid is used. The exact analytic solutions are constructed by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constantly accelerating shear. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. Moreover, they can be easily specialized to give similar solutions for second grade and Newtonian fluids. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between the three models, is underlined by graphical illustrations. M. Kamran, M. Imran, and M. Athar Copyright © 2012 M. Kamran et al. All rights reserved. Tue, 07 Aug 2012 10:21:26 +0000 http://www.hindawi.com/isrn/mp/2012/973968/ The second derivative of two vector functions is related to the divergence of the vector functions with first order operators. Namely, 𝐏⋅∇2𝐐−𝐐⋅∇2𝐏=∇⋅[𝐏(∇⋅𝐐)−𝐐(∇⋅𝐏)+𝐏×∇×𝐐−𝐐×∇×𝐏]. M. Fernández-Guasti Copyright © 2012 M. Fernández-Guasti. All rights reserved. Sun, 05 Aug 2012 08:30:44 +0000 http://www.hindawi.com/isrn/mp/2012/168315/ Nonsimilar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating or nonrotating perfect gas in presence of a constant azimuthal magnetic field. The density of the gas is assumed to be varying and obeying an exponential law. In order to obtain the solutions, the angular velocity of the ambient medium is assumed to be decreasing exponentially as the distance from the axis increases. The shock wave moves with variable velocity and the total energy of the wave is nonconstant. The effects of variation of Alfven-Mach number and time are obtained. Also, a comparison between the solutions in the cases of rotating and non-rotating media with or without magnetic field is made. J. P. Vishwakarma and G. Nath Copyright © 2012 J. P. Vishwakarma and G. Nath. All rights reserved. Mon, 30 Jul 2012 12:18:01 +0000 http://www.hindawi.com/isrn/mp/2012/467520/ The objective of this paper is to show that the group 𝑆𝐸(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry. Carol Linton, William Holderbaum, and James Biggs Copyright © 2012 Carol Linton et al. All rights reserved. Mon, 30 Jul 2012 09:46:45 +0000 http://www.hindawi.com/isrn/mp/2012/230245/ The problem of construction of self-adjoint Hamiltonian for quantum system consisting of three pointlike interacting particles (two fermions with mass 1 plus a particle of another nature with mass 𝑚>0) was studied in many works. In most of these works, a family of one-parametric symmetrical operators {𝐻𝜀,𝜀∈ℝ1} is considered as such Hamiltonians. In addition, the question about the self-adjointness of 𝐻𝜀 is equivalent to the one concerning the self-adjointness of some auxiliary operators {𝒯𝑙,𝑙=0,1,…} acting in the space 𝐿2(ℝ1+,𝑟2𝑑𝑟). In this work, we establish a simple general criterion of self-adjointness for operators 𝒯𝑙 and apply it to the cases 𝑙=0 and 𝑙=1. It turns out that the operator 𝒯𝑙=0 is self-adjoint for any 𝑚, while the operator 𝒯𝑙=1 is self-adjoint for 𝑚>𝑚0, where the value of 𝑚0 is given explicitly in the paper. Robert Adol'fovich Minlos Copyright © 2012 Robert Adol'fovich Minlos. All rights reserved. Sun, 15 Jul 2012 10:16:08 +0000 http://www.hindawi.com/isrn/mp/2012/530473/ We construct a one-parameter family of coherent states of Barut-Girdrardello type performing a resolution of the identity of the classical Hardy space of complex-valued square integrable functions on the real line, whose Fourier transform is supported by the positive real semiaxis. Zouhaïr Mouayn Copyright © 2012 Zouhaïr Mouayn. All rights reserved. Thu, 05 Jul 2012 13:31:42 +0000 http://www.hindawi.com/isrn/mp/2012/601749/ We investigate the 2D behavior of one-fold self-intersecting, topologically stabilized center-vortex loops in the confining phase of an SU(2) Yang-Mills theory. This coarse-graining is described by curve-shrinking evolution of center-vortex loops immersed in a flat 2D plane driving the renormalization-group flow of an effective “action.” We observe that the system evolves into a highly ordered state at finite noise level, and we speculate that this feature is connected with 2D planar high 𝑇𝑐 superconductivity in FeAs systems. Julian Moosmann and Ralf Hofmann Copyright © 2012 Julian Moosmann and Ralf Hofmann. All rights reserved. Thu, 05 Jul 2012 09:56:40 +0000 http://www.hindawi.com/isrn/mp/2012/896156/ The present paper focuses on the characterization of compact sets of Minkowski space with a non-Euclidean 𝑠-topology which is defined in terms of Lorentz metric. As an application of this study, it is proved that the 2-dimensional Minkowski space with 𝑠-topology is not simply connected. Also, it is obtained that the 𝑛-dimensional Minkowski space with 𝑠-topology is separable, first countable, path-connected, nonregular, nonmetrizable, nonsecond countable, noncompact, and non-Lindelöf. Gunjan Agrawal and Sampada Shrivastava Copyright © 2012 Gunjan Agrawal and Sampada Shrivastava. All rights reserved. Wed, 20 Jun 2012 16:37:33 +0000 http://www.hindawi.com/isrn/mp/2012/704612/ We examine homogeneous and anisotropic Bianchi type I cosmological model with viscous stiff matter and time-varying cosmological term Λ which scales with Hubble parameter H. The resulting model approaches isotropy. The cosmological term Λ relaxes to a genuine cosmological constant, and the model in the absence of bulk viscosity tends to a deSitter universe asymptotically. Our scenario presents an initial epoch with decelerating expansion followed by late-time acceleration consistent with observations. Bulk viscosity advances the accelerating phase in the model and prevents the matter density to vanish for large times. Raj Bali, Pratibha Singh, and J. P. Singh Copyright © 2012 Raj Bali et al. All rights reserved. Mon, 28 May 2012 15:45:18 +0000 http://www.hindawi.com/isrn/mp/2012/236783/ We consider coarse-graining applied to nonselfintersecting planar centervortex loops as they emerge in the confining phase of an SU(2) Yang-Mills theory. Well-established properties of planar curve-shrinking predict that a suitably defined, geometric effective action exhibits (mean-field) critical behavior when the conformal limit of circular points is reached. This suggests the existence of an asymptotic mass gap. We demonstrate that the initially sharp mean center-of-mass position in a given ensemble of curves develops a variance under the flow as is the case for a position eigenstate in free-particle quantum mechanics under unitary time evolution. A possible application of these concepts is an approach to high-𝑇𝑐 superconductivity based (a) on the nonlocal nature of the electron (1 fold selfintersecting center-vortex loop) and (b) on planar curve-shrinking flow representing the decrease in thermal noise in a cooling cuprate. Julian Moosmann and Ralf Hofmann Copyright © 2012 Julian Moosmann and Ralf Hofmann. All rights reserved. Thu, 05 Apr 2012 12:09:01 +0000 http://www.hindawi.com/isrn/mp/2012/201525/ The approximately analytical bound state solutions of the l-wave Schrödinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary principal and orbital quantum numbers n and l with two different values of the potential screening parameter α. It is found that our results are in good agreement with the those obtained by other methods for short potential range, lowest values of orbital quantum number l, and α. Two special cases of much interest are investigated like the s-wave case and Hulthén potential case. Sameer M. Ikhdair Copyright © 2012 Sameer M. Ikhdair. All rights reserved. Wed, 04 Apr 2012 11:49:58 +0000 http://www.hindawi.com/isrn/mp/2012/908386/ New exact solutions for the motion of a fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) second grade fluid due to longitudinal and torsional oscillations of an infinite circular cylinder are determined by means of Laplace and finite Hankel transforms. These solutions are presented in series form in term of generalized 𝐺𝑎,𝑏,𝑐(⋅,𝑡) functions and satisfy all imposed initial and boundary conditions. In special cases, solutions for ordinary second grade and Newtonian fluids are obtained. Furthermore, other equivalent forms of solutions for ordinary second grade and Newtonian fluids are presented and written as sum of steady-state and transient solutions. The solutions for Newtonian fluid coincide with the well-known classical solutions. Finally, by means of graphical illustrations, the influence of pertinent parameters on fluid motion as well as comparison among different models is discussed. Muhammad Jamil, Najeeb Alam Khan, and Abdul Rauf Copyright © 2012 Muhammad Jamil et al. All rights reserved. Wed, 28 Mar 2012 11:10:14 +0000 http://www.hindawi.com/isrn/mp/2012/197068/ We construct the approximate solutions of the time-fractional Schrödinger equations, with zero and nonzero trapping potential, by homotopy analysis method (HAM). The fractional derivatives, in the Caputo sense, are used. The method is capable of reducing the size of calculations and handles nonlinear-coupled equations in a direct manner. The results show that HAM is more promising, convenient, efficient and less computational than differential transform method (DTM), and easy to apply in spaces of higher dimensions as well. Najeeb Alam Khan, Muhammad Jamil, and Asmat Ara Copyright © 2012 Najeeb Alam Khan et al. All rights reserved. Thu, 22 Mar 2012 09:31:50 +0000 http://www.hindawi.com/isrn/mp/2012/341612/ We have obtained and presented spatially homogeneous Bianchi types II, VIII, and IX string cosmological models with bulk viscosity in a theory of gravitation proposed by Sen (1957) based on Lyra (1951) geometry. It is observed that only vacuum cosmological model exists in case of Bianchi type IX universe. Some physical and geometrical properties of the models are also discussed. V. U. M. Rao, K. V. S. Sireesha, and M. Vijaya Santhi Copyright © 2012 V. U. M. Rao et al. All rights reserved. Mon, 05 Mar 2012 09:16:12 +0000 http://www.hindawi.com/isrn/mp/2012/531250/ The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by a transverse varying magnetic field, under the influence of capillary, inertia, and Lorentz force, has been developed. The problem is modelized. The basic equations formulated, solved, and, upon applying appropriate boundary conditions, the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the nonaxisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform field and varying transverse one. The axial field is stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here, the high compressibility increases rapidly the magnetodynamic stable domains and leads to shrinking those of instability. Samia S. Elazab, Samy A. Rahman, Alfaisal A. Hasan, and Nehad A. Zidan Copyright © 2012 Samia S. Elazab et al. All rights reserved.