Advances in Mathematical Physics
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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
http://www.hindawi.com/journals/amp/2016/7036728/
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 selfsimilar nonlinear twopoint 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
http://www.hindawi.com/journals/amp/2016/7213197/
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 onetoone correspondence between qutrit states and states of two threedimensional 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 HeavyQuarkonium Mesons at Finite Temperature
Sun, 23 Oct 2016 12:50:10 +0000
http://www.hindawi.com/journals/amp/2016/4935940/
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 quarkgluon plasma diagnostics.
M. AbuShady
Copyright © 2016 M. AbuShady. 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
http://www.hindawi.com/journals/amp/2016/4808610/
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
http://www.hindawi.com/journals/amp/2016/1562509/
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 ratedependent 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.

TwoPhase Flow in Wire Coating with Heat Transfer Analysis of an ElasticViscous Fluid
Mon, 17 Oct 2016 13:05:37 +0000
http://www.hindawi.com/journals/amp/2016/9536151/
This work considers twophase flow of an elasticviscous fluid for doublelayer coating of wire. The wetonwet (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 secondgrade fluid and with analytical solution of a thirdgrade 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
http://www.hindawi.com/journals/amp/2016/6508309/
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. ElSayied, Sameh Shenawy, and Noha Syied
Copyright © 2016 H. K. ElSayied et al. All rights reserved.

Generating Commutator Identities and the BCH Formula
Sun, 16 Oct 2016 14:15:39 +0000
http://www.hindawi.com/journals/amp/2016/9598409/
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 SchützenbergerCigler: . 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 BakerCampbellHausdorff Formula.
Andrea Bonfiglioli and Jacob Katriel
Copyright © 2016 Andrea Bonfiglioli and Jacob Katriel. All rights reserved.

Stochastic Effects for the ReactionDuffing Equation with WickType Product
Sun, 16 Oct 2016 13:00:08 +0000
http://www.hindawi.com/journals/amp/2016/9062343/
We construct new explicit solutions of the Wicktype stochastic reactionDuffing 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
http://www.hindawi.com/journals/amp/2016/9671513/
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 RungeKutta 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, FiniteFrequency Regime
Tue, 11 Oct 2016 14:46:40 +0000
http://www.hindawi.com/journals/amp/2016/4156072/
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
http://www.hindawi.com/journals/amp/2016/7528625/
This paper presents a numerical entropy production (NEP) scheme for twodimensional 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
http://www.hindawi.com/journals/amp/2016/6219251/
Through applying the Jacobian elliptic function method, we obtain the periodic solution for a series of nonlinear Zakharov equations, which contain KleinGordon Zakharov equations, Zakharov equations, and ZakharovRubenchik equations.
Cong Sun and Shuguan Ji
Copyright © 2016 Cong Sun and Shuguan Ji. All rights reserved.

Homogenized Model of TwoPhase Flow with Local Nonequilibrium in Double Porosity Media
Thu, 29 Sep 2016 12:05:13 +0000
http://www.hindawi.com/journals/amp/2016/3058710/
We consider twophase 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 longmemory 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 blockfracture permeability. Numerical results for the twodimensional 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 VolterraStieltjes Linear Integral Equations of the Second Kind with the Generalized Trapezoid Rule
Tue, 27 Sep 2016 10:09:13 +0000
http://www.hindawi.com/journals/amp/2016/1798050/
The numerical solution of linear VolterraStieltjes 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 ChernSimonsHiggs Equations in
Thu, 22 Sep 2016 13:46:23 +0000
http://www.hindawi.com/journals/amp/2016/9830474/
We prove global existence of solutions to ChernSimonsHiggs 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
http://www.hindawi.com/journals/amp/2016/3649205/
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
http://www.hindawi.com/journals/amp/2016/9218693/
We give a complete description of the antiinvolutions 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
http://www.hindawi.com/journals/amp/2016/5030593/
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 spacetime 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 spacetime diagrams. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the abovespecified 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 SolerToscano, and Hector Zenil
Copyright © 2016 Joost J. Joosten et al. All rights reserved.

Two Kinds of DarbouxBäcklund Transformations for the Deformed KdV Hierarchy with SelfConsistent Sources
Wed, 07 Sep 2016 09:28:21 +0000
http://www.hindawi.com/journals/amp/2016/8153752/
Two kinds of DarbouxBäcklund transformations (DBTs) are constructed for the deformed th KdV hierarchy with selfconsistent 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 selfconsistent 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 NeimarkSacker Bifurcation in Delayed Species Model Using Feedback Controller
Sun, 04 Sep 2016 09:40:43 +0000
http://www.hindawi.com/journals/amp/2016/2028037/
Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the NeimarkSacker 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 EnergyMomentum Tensor
Wed, 31 Aug 2016 16:18:18 +0000
http://www.hindawi.com/journals/amp/2016/9679460/
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 energymomentum 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 energymomentum tensors from a Lagrangian through the principle of stationary action in general spacetime. 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
http://www.hindawi.com/journals/amp/2016/6830685/
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, twosubset, 01bit) computer and a nondigital (say, a sixsubset) computer (with appropriate chips and circuits). With quantum logic, the same sixelement 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
http://www.hindawi.com/journals/amp/2016/6423735/
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
http://www.hindawi.com/journals/amp/2016/6095236/
We show that Weylinvariant dilaton gravity provides a description of black holes without classical spacetime 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 BiIntegrable Couplings of TwoComponent CasimirQiaoLiu Type Hierarchy and Their Hamiltonian Structures
Sun, 28 Aug 2016 14:19:01 +0000
http://www.hindawi.com/journals/amp/2016/6347961/
A new type of twocomponent CasimirQiaoLiu type hierarchy (2CQLTH) is produced from a new spectral problem and their biHamiltonian structures are constructed. Particularly, a new completely integrable twocomponent CasimirQiaoLiu type equation (2CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of block matrix Lie algebra, the biintegrable couplings of the 2CQLTH are constructed and their biHamiltonian 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
http://www.hindawi.com/journals/amp/2016/1307813/
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 selfgenerating 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 LeggettGarg: Epistemology of BellType Inequalities
Thu, 25 Aug 2016 11:22:12 +0000
http://www.hindawi.com/journals/amp/2016/4623040/
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 LeggettGarg 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 interpretationpuzzles such as twoslit experiments.
Karl Hess, Hans De Raedt, and Kristel Michielsen
Copyright © 2016 Karl Hess et al. All rights reserved.

TwoDimensional Nonlinear Propagation of Ion Acoustic Waves through KPB and KP Equations in Weakly Relativistic Plasmas
Wed, 24 Aug 2016 08:11:15 +0000
http://www.hindawi.com/journals/amp/2016/9352148/
Twodimensional threecomponent plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The wellknown KadomtsevPetviashviliBurgers and KadomtsevPetviashvili 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, electronpositron and ionelectron 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
http://www.hindawi.com/journals/amp/2016/5739410/
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 higherorder 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.