Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Homotopy Analysis of the Radiation Effect on MHD Flow with Heat and Mass Transfer due to a Point Sink Mon, 24 Oct 2016 12:29:11 +0000 An analytical solution of the magnetohydrodynamic, steady, and incompressible laminar boundary layer flow in the presence of heat and mass transfer as well as magnetic field on a cone due to a point sink by using the homotopy analysis method (HAM) has been studied under the radiative fluid properties. The HAM produces an analytical solution of the governing self-similar nonlinear two-point boundary layer equations. The effects of the suction/injection, magnetic, and radiation parameters over the obtained solution have been discussed. The effects of Prandtl number on temperature and Schmidt number on concentration profiles have also been studied. It has been observed that the temperature profiles exhibit an increasing trend with radiation in case of injection while an opposite trend is observed in case of suction. The results obtained in the present study have also been compared numerically as well as graphically with the corresponding results obtained by using other methods. An excellent agreement has been found between them. The analytical solution obtained by the HAM is very near to the exact solution for a properly selected initial guess, auxiliary, and convergence control parameters and for higher orders of deformations. C. N. Guled and B. B. Singh Copyright © 2016 C. N. Guled and B. B. Singh. All rights reserved. Virtual Correlations in Single Qutrit Mon, 24 Oct 2016 07:26:56 +0000 We construct the positive invertible map of the mixed states of a single qutrit onto the antisymmetrized bipartite qutrit states (quasifermions). It is shown that using this one-to-one correspondence between qutrit states and states of two three-dimensional quasifermions one may attribute hidden entanglement to a single mixed state of qutrit. Alexey A. Strakhov and Vladimir I. Man’ko Copyright © 2016 Alexey A. Strakhov and Vladimir I. Man’ko. All rights reserved. Multidimensional Schrödinger Equation and Spectral Properties of Heavy-Quarkonium Mesons at Finite Temperature Sun, 23 Oct 2016 12:50:10 +0000 The -radial Schrödinger equation is analytically solved at finite temperature. The analytic exact iteration method (AEIM) is employed to obtain the energy eigenvalues and wave functions for all states and . The application of present results to the calculation of charmonium and bottomonium masses at finite temperature is also presented. The behavior of the charmonium and bottomonium masses is in qualitative agreement with other theoretical methods. We conclude that the solution of the Schrödinger equation plays an important role at finite temperature that the analysis of the quarkonium states gives a key input to quark-gluon plasma diagnostics. M. Abu-Shady Copyright © 2016 M. Abu-Shady. All rights reserved. Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System Wed, 19 Oct 2016 14:30:52 +0000 The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures of the shock and rarefaction curves in the phase plane. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data. Pengpeng Ji and Chun Shen Copyright © 2016 Pengpeng Ji and Chun Shen. All rights reserved. Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction Mon, 17 Oct 2016 14:01:09 +0000 We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with a combination of a normal compliance and a normal damped response law associated with a slip rate-dependent version of Coulomb’s law of dry friction. We derive a variational formulation and an existence and uniqueness result of the weak solution of the problem is presented. Next, we introduce a fully discrete approximation of the variational problem based on a finite element method and on an implicit time integration scheme. We study this fully discrete approximation schemes and bound the errors of the approximate solutions. Under regularity assumptions imposed on the exact solution, optimal order error estimates are derived for the fully discrete solution. Finally, after recalling the solution of the frictional contact problem, some numerical simulations are provided in order to illustrate both the behavior of the solution related to the frictional contact conditions and the theoretical error estimate result. Mikaël Barboteu and David Danan Copyright © 2016 Mikaël Barboteu and David Danan. All rights reserved. Two-Phase Flow in Wire Coating with Heat Transfer Analysis of an Elastic-Viscous Fluid Mon, 17 Oct 2016 13:05:37 +0000 This work considers two-phase flow of an elastic-viscous fluid for double-layer coating of wire. The wet-on-wet (WOW) coating process is used in this study. The analytical solution of the theoretical model is obtained by Optimal Homotopy Asymptotic Method (OHAM). The expression for the velocity field and temperature distribution for both layers is obtained. The convergence of the obtained series solution is established. The analytical results are verified by Adomian Decomposition Method (ADM). The obtained velocity field is compared with the existing exact solution of the same flow problem of second-grade fluid and with analytical solution of a third-grade fluid. Also, emerging parameters on the solutions are discussed and appropriate conclusions are drawn. Zeeshan Khan, Rehan Ali Shah, Saeed Islam, and Bilal Jan Copyright © 2016 Zeeshan Khan et al. All rights reserved. Conformal Vector Fields on Doubly Warped Product Manifolds and Applications Mon, 17 Oct 2016 06:33:10 +0000 This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered. H. K. El-Sayied, Sameh Shenawy, and Noha Syied Copyright © 2016 H. K. El-Sayied et al. All rights reserved. Generating -Commutator Identities and the -BCH Formula Sun, 16 Oct 2016 14:15:39 +0000 Motivated by the physical applications of -calculus and of -deformations, the aim of this paper is twofold. Firstly, we prove the -deformed analogue of the celebrated theorem by Baker, Campbell, and Hausdorff for the product of two exponentials. We deal with the -exponential function , where denotes, as usual, the th -integer. We prove that if and are any noncommuting indeterminates, then , where is a sum of iterated -commutators of and (on the right and on the left, possibly), where the -commutator has always the innermost position. When , this expansion is consistent with the known result by Schützenberger-Cigler: . Our result improves and clarifies some existing results in the literature. Secondly, we provide an algorithmic procedure for obtaining identities between iterated -commutators (of any length) of and . These results can be used to obtain simplified presentation for the summands of the -deformed Baker-Campbell-Hausdorff Formula. Andrea Bonfiglioli and Jacob Katriel Copyright © 2016 Andrea Bonfiglioli and Jacob Katriel. All rights reserved. Stochastic Effects for the Reaction-Duffing Equation with Wick-Type Product Sun, 16 Oct 2016 13:00:08 +0000 We construct new explicit solutions of the Wick-type stochastic reaction-Duffing equation arising from mathematical physics with the help of the white noise theory and the system technique. Based on these exact solutions, we also discuss the influences of stochastic effects for dynamical behaviors according to functions , , and Brownian motion which are the solitary wave group velocities. Jin Hyuk Choi, SeungGwan Lee, and Hyunsoo Kim Copyright © 2016 Jin Hyuk Choi et al. All rights reserved. Radiation Effects in Flow through Porous Medium over a Rotating Disk with Variable Fluid Properties Sun, 16 Oct 2016 08:35:27 +0000 The present study investigates the radiation effects in flow through porous medium over a permeable rotating disk with velocity slip and temperature jump. Fluid properties density , viscosity , and thermal conductivity are taken to be dependent on temperature. Particular case considering these fluid properties’ constant is also discussed. The governing partial differential equations are converted into nonlinear normal differential equation using similarity alterations. Transformed system of equations is solved numerically by using Runge-Kutta method with shooting technique. Effects of various parameters such as porosity parameter , suction parameter , rotational Reynolds number Re, Knudsen number Kn, Prandtl number Pr, radiation parameter , and relative temperature difference parameter on velocity profiles along radial, tangential, and axial direction and temperature distribution are investigated for both variable fluid properties and constant fluid properties. Results obtained are analyzed and depicted through graphs and table. Shalini Jain and Shweta Bohra Copyright © 2016 Shalini Jain and Shweta Bohra. All rights reserved. Anomalous Localized Resonance Phenomena in the Nonmagnetic, Finite-Frequency Regime Tue, 11 Oct 2016 14:46:40 +0000 The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that when a given source is placed near the interface, the electric and magnetic fields start to have very fast and large oscillations around the interface as the absorption in the materials becomes very small while they remain smooth and regular away from the interface. In this paper, we discuss the phenomenon of anomalous localized resonance (ALR) in the context of an infinite slab of homogeneous, nonmagnetic material () with permittivity for some small loss surrounded by positive, nonmagnetic, homogeneous media. We explicitly characterize the limit value of the product between frequency and the width of slab beyond which the ALR phenomenon does not occur and analyze the situation when the phenomenon is observed. In addition, we also construct sources for which the ALR phenomenon never appears. Daniel Onofrei and Andrew E. Thaler Copyright © 2016 Daniel Onofrei and Andrew E. Thaler. All rights reserved. Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids Tue, 11 Oct 2016 10:56:41 +0000 This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions. Sudi Mungkasi Copyright © 2016 Sudi Mungkasi. All rights reserved. New Periodic Solutions for a Class of Zakharov Equations Thu, 29 Sep 2016 12:45:36 +0000 Through applying the Jacobian elliptic function method, we obtain the periodic solution for a series of nonlinear Zakharov equations, which contain Klein-Gordon Zakharov equations, Zakharov equations, and Zakharov-Rubenchik equations. Cong Sun and Shuguan Ji Copyright © 2016 Cong Sun and Shuguan Ji. All rights reserved. Homogenized Model of Two-Phase Flow with Local Nonequilibrium in Double Porosity Media Thu, 29 Sep 2016 12:05:13 +0000 We consider two-phase flow in a heterogeneous porous medium with highly permeable fractures and low permeable periodic blocks. The flow in the blocks is assumed to be in local capillary disequilibrium and described by Barenblatt’s relaxation relationships for the relative permeability and capillary pressure. It is shown that the homogenization of such equations leads to a new macroscopic model that includes two kinds of long-memory effects: the mass transfer between the blocks and fractures and the memory caused by the microscopic Barenblatt disequilibrium. We have obtained a general relationship for the double nonequilibrium capillary pressure which represents great interest for applications. Due to the nonlinear coupling and the nonlocality in time, the macroscopic model remains incompletely homogenized in general case. The completely homogenized model was obtained for two different regimes. The first case corresponds to a linearized flow in the blocks. In the second case, we assume a low contrast in the block-fracture permeability. Numerical results for the two-dimensional problem are presented for two test cases to demonstrate the effectiveness of the methodology. Brahim Amaziane, Mikhail Panfilov, and Leonid Pankratov Copyright © 2016 Brahim Amaziane et al. All rights reserved. Approximate Solution of Volterra-Stieltjes Linear Integral Equations of the Second Kind with the Generalized Trapezoid Rule Tue, 27 Sep 2016 10:09:13 +0000 The numerical solution of linear Volterra-Stieltjes integral equations of the second kind by using the generalized trapezoid rule is established and investigated. Also, the conditions on estimation of the error are determined and proved. A selected example is solved employing the proposed method. Avyt Asanov, Elman Hazar, Mustafa Eroz, Kalyskan Matanova, and Elmira Abdyldaeva Copyright © 2016 Avyt Asanov et al. All rights reserved. Remarks on Chern-Simons-Higgs Equations in Thu, 22 Sep 2016 13:46:23 +0000 We prove global existence of solutions to Chern-Simons-Higgs equations under the gauge condition . We also find stationary solutions. Hyungjin Huh and Guanghui Jin Copyright © 2016 Hyungjin Huh and Guanghui Jin. All rights reserved. The Strict AKNS Hierarchy: Its Structure and Solutions Thu, 08 Sep 2016 09:16:48 +0000 We discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space of than that in the AKNS case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy. G. F. Helminck Copyright © 2016 G. F. Helminck. All rights reserved. Lie Subalgebras of the Matrix Quantum Pseudodifferential Operators Wed, 07 Sep 2016 16:52:29 +0000 We give a complete description of the anti-involutions that preserve the principal gradation of the algebra of matrix quantum pseudodifferential operators and we describe the Lie subalgebras of their minus fixed points. Karina Batistelli and Carina Boyallian Copyright © 2016 Karina Batistelli and Carina Boyallian. All rights reserved. Fractal Dimension versus Process Complexity Wed, 07 Sep 2016 11:33:22 +0000 We look at small Turing machines (TMs) that work with just two colors (alphabet symbols) and either two or three states. For any particular such machine and any particular input , we consider what we call the space-time diagram which is basically the collection of consecutive tape configurations of the computation . In our setting, it makes sense to define a fractal dimension for a Turing machine as the limiting fractal dimension for the corresponding space-time diagrams. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time, if and only if its dimension is 2, and its dimension is 1, if and only if it runs in superpolynomial time and it uses polynomial space. If a TM runs in time , we have empirically verified that the corresponding dimension is , a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on one side versus the time complexity of a computation on the other side. Joost J. Joosten, Fernando Soler-Toscano, and Hector Zenil Copyright © 2016 Joost J. Joosten et al. All rights reserved. Two Kinds of Darboux-Bäcklund Transformations for the -Deformed KdV Hierarchy with Self-Consistent Sources Wed, 07 Sep 2016 09:28:21 +0000 Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for the -deformed th KdV hierarchy with self-consistent sources (-NKdVHSCS) by using the -deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for two -deformed th KdV equations with self-consistent sources (-NKdVESCS) with different degree. In addition, the soliton solution to the first nontrivial equation of -KdVHSCS is also obtained. Hongxia Wu, Liangjuan Gao, Jingxin Liu, and Yunbo Zeng Copyright © 2016 Hongxia Wu et al. All rights reserved. Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller Sun, 04 Sep 2016 09:40:43 +0000 Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of dislocated and ordinary feedback control. The random feedback control method, which does not require any adjustable control parameters of the model, just only slightly changes the random intensity. Finally, numerical simulations are presented to verify the effectiveness of the proposed controllers. Jie Ran, Yanmin Liu, Jun He, and Xiang Li Copyright © 2016 Jie Ran et al. All rights reserved. On the Definition of Energy for a Continuum, Its Conservation Laws, and the Energy-Momentum Tensor Wed, 31 Aug 2016 16:18:18 +0000 We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame and that, however, they can be given a rigorous meaning. Then, we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in general space-time. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially on the fields. Mayeul Arminjon Copyright © 2016 Mayeul Arminjon. All rights reserved. Classical Logic and Quantum Logic with Multiple and Common Lattice Models Wed, 31 Aug 2016 10:19:25 +0000 We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and nondistributive ortholattices. In particular, we prove that both classical logic and quantum logic are sound and complete with respect to each of these lattices. We also show that there is one common nonorthomodular lattice that is a model of both quantum and classical logic. In technical terms, that enables us to run the same classical logic on both a digital (standard, two-subset, 0-1-bit) computer and a nondigital (say, a six-subset) computer (with appropriate chips and circuits). With quantum logic, the same six-element common lattice can serve us as a benchmark for an efficient evaluation of equations of bigger lattice models or theorems of the logic. Mladen Pavičić Copyright © 2016 Mladen Pavičić. All rights reserved. Characterizations of Fuzzy Ideals in Coresiduated Lattices Tue, 30 Aug 2016 08:24:20 +0000 The notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices. Yan Liu and Mucong Zheng Copyright © 2016 Yan Liu and Mucong Zheng. All rights reserved. Curing Black Hole Singularities with Local Scale Invariance Mon, 29 Aug 2016 07:21:03 +0000 We show that Weyl-invariant dilaton gravity provides a description of black holes without classical space-time singularities. Singularities appear due to the ill behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are as follows: (1) singularities signal a phase transition from broken to unbroken phase of Weyl symmetry; (2) instead of a singularity, there is a “baby universe” or a white hole inside a black hole; (3) in the baby universe scenario, there is a critical mass after which reducing mass makes the black hole larger as viewed by outside observers; (4) if a black hole could be connected with white hole through the “singularity,” this would require breakdown of (classical) geometric description; (5) the singularity of Schwarzschild BH solution is nongeneric and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information loss puzzle. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point. Predrag Dominis Prester Copyright © 2016 Predrag Dominis Prester. All rights reserved. The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures Sun, 28 Aug 2016 14:19:01 +0000 A new type of two-component Casimir-Qiao-Liu type hierarchy (2-CQLTH) is produced from a new spectral problem and their bi-Hamiltonian structures are constructed. Particularly, a new completely integrable two-component Casimir-Qiao-Liu type equation (2-CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished. Juhui Zhang and Yuqin Yao Copyright © 2016 Juhui Zhang and Yuqin Yao. All rights reserved. A Numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments Thu, 25 Aug 2016 12:09:40 +0000 A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a number and the resulting model is called an -Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of the -Model, then we will be able to find that of -Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed number . Maria Cristina Carrisi, Rita Enoh Tchame, Marcel Obounou, and Sebastiano Pennisi Copyright © 2016 Maria Cristina Carrisi et al. All rights reserved. From Boole to Leggett-Garg: Epistemology of Bell-Type Inequalities Thu, 25 Aug 2016 11:22:12 +0000 In 1862, George Boole derived an inequality for variables that represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole’s, that according to them represents a demarcation between macroscopic realism and quantum mechanics. We show that a wide gulf separates the “sense impressions” and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett and Garg. If the gulf can be bridged, one may indeed derive the said inequality, which is then clearly a demarcation between possible and impossible experience: it cannot be violated and is not violated by quantum theory. This implies that the Leggett-Garg inequality does not mean that the SQUID flux is not there when nobody looks, as Leggett and Garg suggest, but instead that the probability measures may not be what Leggett and Garg have assumed them to be, when no data can be secured that directly relate to them. We show that similar considerations apply to other quantum interpretation-puzzles such as two-slit experiments. Karl Hess, Hans De Raedt, and Kristel Michielsen Copyright © 2016 Karl Hess et al. All rights reserved. Two-Dimensional Nonlinear Propagation of Ion Acoustic Waves through KPB and KP Equations in Weakly Relativistic Plasmas Wed, 24 Aug 2016 08:11:15 +0000 Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons. M. G. Hafez, M. R. Talukder, and M. Hossain Ali Copyright © 2016 M. G. Hafez et al. All rights reserved. Higher Spin Symmetries of the Free Schrödinger Equation Sun, 21 Aug 2016 11:18:39 +0000 It is shown that the Schrödinger symmetry algebra of a free particle in spatial dimensions can be embedded into a representation of the higher spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrödinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of nonrelativistic generators. We show also how to convert Vasiliev’s equations into an explicit nonrelativistic covariant form, such that they might apply to nonrelativistic systems. Our procedure reveals that the space of solutions of the Schrödinger equation can be regarded also as a supersymmetric module. Mauricio Valenzuela Copyright © 2016 Mauricio Valenzuela. All rights reserved.