Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities Wed, 30 Nov 2016 13:59:14 +0000 We consider the standing wave solutions for nonlinear fractional Schrödinger equations with focusing Hartree type and power type nonlinearities. We first establish the constrained minimization problem via applying variational method. Under certain conditions, we then show the existence of standing waves. Finally, we prove that the set of minimizers for the initial value problem of this minimization problem is stable. Na Zhang and Jie Xin Copyright © 2016 Na Zhang and Jie Xin. All rights reserved. Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures Tue, 29 Nov 2016 12:45:39 +0000 We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM), a submanifold of a 5-dimensional pseudo-Euclidean (5dPE) equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structures and are introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example, is not supposed to be the model of any gravitational field in the General Relativity Theory (GRT). Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories. Waldyr A. Rodrigues and Samuel A. Wainer Copyright © 2016 Waldyr A. Rodrigues and Samuel A. Wainer. All rights reserved. Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry Mon, 28 Nov 2016 13:48:32 +0000 The importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed. M. I. Wanas, Nabil L. Youssef, W. El Hanafy, and S. N. Osman Copyright © 2016 M. I. Wanas et al. All rights reserved. An Efficient Numerical Method for the Solution of the Schrödinger Equation Wed, 23 Nov 2016 13:55:52 +0000 The development of a new five-stage symmetric two-step fourteenth-algebraic order method with vanished phase-lag and its first, second, and third derivatives is presented in this paper for the first time in the literature. More specifically we will study the development of the new method, the determination of the local truncation error (LTE) of the new method, the local truncation error analysis which will be based on test equation which is the radial time independent Schrödinger equation, the stability and the interval of periodicity analysis of the new developed method which will be based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, and the efficiency of the new obtained method based on its application to the coupled Schrödinger equations. Licheng Zhang and Theodore E. Simos Copyright © 2016 Licheng Zhang and Theodore E. Simos. All rights reserved. Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales Wed, 23 Nov 2016 11:32:52 +0000 Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives. Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item. Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a -Laplacian conformable fractional differential equation boundary value problem on time scale , , , where denotes the conformable fractional derivative of of order at , is the forward jump operator, , and . By establishing a proper variational setting, we obtain three existence results. Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results. Yanning Wang, Jianwen Zhou, and Yongkun Li Copyright © 2016 Yanning Wang et al. All rights reserved. Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications Thu, 17 Nov 2016 13:46:41 +0000 We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation in tangle space which is a set of real tangles with analytic structure and describe the recombination as the action of some enzymes on tangle space. Soo Hwan Kim Copyright © 2016 Soo Hwan Kim. All rights reserved. Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem Sun, 13 Nov 2016 08:45:04 +0000 We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis. Lung-Hui Chen Copyright © 2016 Lung-Hui Chen. All rights reserved. On the Possibility of the Jerk Derivative in Electrical Circuits Wed, 09 Nov 2016 08:08:07 +0000 A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics. Some mechanical and acoustic systems can be interpreted as jerky dynamics. In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order . We consider fractional LC and RL electrical circuits with for different source terms. The LC circuit has a frequency dependent on the order of the fractional differential equation , since it is defined as , where is the fundamental frequency. For , the system is described by a third-order differential equation with frequency , and assuming the dynamics are described by a fourth differential equation for jerk dynamics with frequency . J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, and V. H. Olivares-Peregrino Copyright © 2016 J. F. Gómez-Aguilar et al. All rights reserved. On the Splitting of the Einstein Field Equations with respect to General Threading of Spacetime Thu, 03 Nov 2016 07:06:55 +0000 Based on general threading of the spacetime , we obtain a new and simple splitting of both the Einstein field equations (EFE) and the conservation laws in . As an application, we obtain the splitting of EFE in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particular, we state the perturbation Friedmann equations in an almost FLRW universe. Aurel Bejancu and Hani Reda Farran Copyright © 2016 Aurel Bejancu and Hani Reda Farran. All rights reserved. Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics Mon, 31 Oct 2016 05:56:50 +0000 Mathematical modeling has become an indispensable part of systems biology which is a discipline that has become increasingly popular in recent years. In this context, our understanding of bistable signaling pathways in terms of mathematical modeling is of particular importance because such bistable components perform crucial functions in living cells. Bistable signaling pathways can act as switches or memory functions and can determine cell fate. In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. How to determine these order parameters for bistable signaling pathways at saddle-node bifurcation points is shown. The procedure is outlined in general and an explicit example is worked out in detail. Till D. Frank Copyright © 2016 Till D. Frank. All rights reserved. Numerical Simulation of Entropy Growth for a Nonlinear Evolutionary Model of Random Markets Sun, 30 Oct 2016 13:47:49 +0000 In this communication, the generalized continuous economic model for random markets is revisited. In this model for random markets, agents trade by pairs and exchange their money in a random and conservative way. They display the exponential wealth distribution as asymptotic equilibrium, independently of the effectiveness of the transactions and of the limitation of the total wealth. In the current work, entropy of mentioned model is defined and then some theorems on entropy growth of this evolutionary problem are given. Furthermore, the entropy increasing by simulation on some numerical examples is verified. Mahdi Keshtkar, Hamidreza Navidi, and Elyas Shivanian Copyright © 2016 Mahdi Keshtkar et al. All rights reserved. Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation Thu, 27 Oct 2016 13:05:19 +0000 A composite droplet made of two miscible fluids in a narrow tube generally moves under the action of capillarity until complete mixture is attained. This physical situation is analysed here on a combined theoretical and numerical analysis. The mathematical framework consists of the two-phase flow phase-field equation set, an advection-diffusion chemical concentration equation, and closure relationships relating the surface tensions to the chemical concentration. The numerical framework is composed of the COMSOL Laminar two-phase flow phase-field method coupled with an advection-diffusion chemical concentration equation. Through transient studies, we show that the penetrating length of the bidroplet system into the capillary tube is linear at early-time regime and exponential at late-time regime. Through parametric studies, we show that the rate of penetration of the bidroplet system into the capillary tube is proportional to a time-dependent exponential function. We also show that this speed obeys the Poiseuille law at the early-time regime. A series of position, speed-versus-property graphs are included to support the analysis. Finally, the overall results are contrasted with available experimental data, grouped together to settle a general mathematical description of the phenomenon, and explained and concluded on this basis. M. I. Khodabocus, M. Sellier, and V. Nock Copyright © 2016 M. I. Khodabocus et al. All rights reserved. Discrete Spectrum of 2 + 1-Dimensional Nonlinear Schrödinger Equation and Dynamics of Lumps Thu, 27 Oct 2016 07:33:49 +0000 We consider a natural integrable generalization of nonlinear Schrödinger equation to dimensions. By studying the associated spectral operator we discover a rich discrete spectrum associated with regular rationally decaying solutions, the lumps, which display interesting nontrivial dynamics and scattering. Particular interest is placed in the dynamical evolution of the associated pulses. For all cases under study we find that the relevant dynamics corresponds to a central configuration of a certain -body problem. Javier Villarroel, Julia Prada, and Pilar G. Estévez Copyright © 2016 Javier Villarroel et al. All rights reserved. On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances Wed, 26 Oct 2016 13:24:55 +0000 The response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. Lagrange’s equations are used in order to derive the governing equations of motion. One of the important perturbation techniques MS (multiple scales) is utilized to achieve the approximate analytical solutions of these equations and to identify the resonances of the system. Besides, the amplitude and the phase variables are renowned to study the steady-state solutions and to recognize their stability conditions. The time history for the attained solutions and the projections of the phase plane are presented to interpret the behavior of the dynamical system. The mentioned model is considered one of the important scientific applications like in instrumentation, addressing the oscillations occurring in sawing buildings and the most of various applications of pendulum dampers. T. S. Amer, M. A. Bek, and I. S. Hamada Copyright © 2016 T. S. Amer et al. 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.