Advances in Mathematical Physics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2017 , Hindawi Publishing Corporation . All rights reserved. Symmetries and Properties of the Energy-Casimir Mapping in the Ball-Plate Problem Wed, 18 Jan 2017 10:11:55 +0000 http://www.hindawi.com/journals/amp/2017/5164602/ In this paper a system derived by an optimal control problem for the ball-plate dynamics is considered. Symplectic and Lagrangian realizations are given and some symmetries are studied. The image of the energy-Casimir mapping is described and some connections with the dynamics of the considered system are presented. Cristian Lăzureanu and Tudor Bînzar Copyright © 2017 Cristian Lăzureanu and Tudor Bînzar. All rights reserved. Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations Mon, 16 Jan 2017 08:55:58 +0000 http://www.hindawi.com/journals/amp/2017/3038179/ The paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous mechanical systems subjected to a harmonic load from noise induced by the nonlinearity of the system by employing the principal component analysis (PCA). Straight beams lying on Winkler foundations are analysed. Differential equations are obtained based on the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Levinson-Reddy hypotheses. Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA). A. V. Krysko, Jan Awrejcewicz, Irina V. Papkova, Olga Szymanowska, and V. A. Krysko Copyright © 2017 A. V. Krysko et al. All rights reserved. New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations Mon, 16 Jan 2017 05:59:15 +0000 http://www.hindawi.com/journals/amp/2017/3821870/ It is known that Genocchi polynomials have some advantages over classical orthogonal polynomials in approximating function, such as lesser terms and smaller coefficients of individual terms. In this paper, we apply a new operational matrix via Genocchi polynomials to solve fractional integro-differential equations (FIDEs). We also derive the expressions for computing Genocchi coefficients of the integral kernel and for the integral of product of two Genocchi polynomials. Using the matrix approach, we further derive the operational matrix of fractional differentiation for Genocchi polynomial as well as the kernel matrix. We are able to solve the aforementioned class of FIDE for the unknown function . This is achieved by approximating the FIDE using Genocchi polynomials in matrix representation and using the collocation method at equally spaced points within interval . This reduces the FIDE into a system of algebraic equations to be solved for the Genocchi coefficients of the solution . A few numerical examples of FIDE are solved using those expressions derived for Genocchi polynomial approximation. Numerical results show that the Genocchi polynomial approximation adopting the operational matrix of fractional derivative achieves good accuracy comparable to some existing methods. In certain cases, Genocchi polynomial provides better accuracy than the aforementioned methods. Jian Rong Loh, Chang Phang, and Abdulnasir Isah Copyright © 2017 Jian Rong Loh et al. All rights reserved. Analysis of Waterman’s Method in the Case of Layered Scatterers Mon, 16 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/amp/2017/7862462/ The method suggested by Waterman has been widely used in the last years to solve various light scattering problems. We analyze the mathematical foundations of this method when it is applied to layered nonspherical (axisymmetric) particles in the electrostatic case. We formulate the conditions under which Waterman’s method is applicable, that is, when it gives an infinite system of linear algebraic equations relative to the unknown coefficients of the field expansions which is solvable (i.e., the inverse matrix exists) and solutions of the truncated systems used in calculations converge to the solution of the infinite system. The conditions obtained are shown to agree with results of numerical computations. Keeping in mind the strong similarity of the electrostatic and light scattering cases and the agreement of our conclusions with the numerical calculations available for homogeneous and layered scatterers, we suggest that our results are valid for light scattering as well. Victor Farafonov, Vladimir Il’in, Vladimir Ustimov, and Evgeny Volkov Copyright © 2017 Victor Farafonov et al. All rights reserved. On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations Thu, 12 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/amp/2017/9401205/ We carry out a classification of Lie symmetries for the ()-dimensional nonlinear damped wave equation with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases. Usamah S. Al-Ali, Ashfaque H. Bokhari, A. H. Kara, and F. D. Zaman Copyright © 2017 Usamah S. Al-Ali et al. All rights reserved. The Neumann Problem for a Degenerate Elliptic System Near Resonance Wed, 11 Jan 2017 12:44:35 +0000 http://www.hindawi.com/journals/amp/2017/2925065/ This paper studies the following system of degenerate equations , , , , , Here is a bounded domain, and is the exterior normal vector on . The coefficient function may vanish in , with . We show that the eigenvalues of the operator are discrete. Secondly, when the linear part is near resonance, we prove the existence of at least two different solutions for the above degenerate system, under suitable conditions on , and . Yu-Cheng An and Hong-Min Suo Copyright © 2017 Yu-Cheng An and Hong-Min Suo. All rights reserved. Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate Wed, 04 Jan 2017 13:46:51 +0000 http://www.hindawi.com/journals/amp/2017/4514935/ A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results. Zizhen Zhang and Limin Song Copyright © 2017 Zizhen Zhang and Limin Song. All rights reserved. Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory Wed, 04 Jan 2017 12:03:16 +0000 http://www.hindawi.com/journals/amp/2017/1016530/ In this paper a new error function designed on 3-dimensional special Euclidean group SE(3) is proposed for the guidance of a UAV (Unmanned Aerial Vehicle). In the beginning, a detailed 6-DOF (Degree of Freedom) aircraft model is formulated including 12 nonlinear differential equations. Secondly the definitions of the adjoint representations are presented to establish the relationships of the Lie groups SO(3) and SE(3) and their Lie algebras so(3) and se(3). After that the general situation of the differential equations with matrices belonging to SO(3) and SE(3) is presented. According to these equations the features of the error function on SO(3) are discussed. Then an error function on SE(3) is devised which creates a new way of error functions constructing. In the simulation a trajectory tracking example is given with a target trajectory being a curve of elliptic cylinder helix. The result shows that a better tracking performance is obtained with the new devised error function. Yi Zhu, Xin Chen, and Chuntao Li Copyright © 2017 Yi Zhu et al. All rights reserved. A New Unconditionally Stable Method for Telegraph Equation Based on Associated Hermite Orthogonal Functions Thu, 29 Dec 2016 07:09:39 +0000 http://www.hindawi.com/journals/amp/2016/7045657/ The present paper proposes a new unconditionally stable method to solve telegraph equation by using associated Hermite (AH) orthogonal functions. Unlike other numerical approaches, the time variables in the given equation can be handled analytically by AH basis functions. By using the Galerkin’s method, one can eliminate the time variables from calculations, which results in a series of implicit equations. And the coefficients of results for all orders can then be obtained by the expanded equations and the numerical results can be reconstructed during the computing process. The precision and stability of the proposed method are proved by some examples, which show the numerical solution acquired is acceptable when compared with some existing methods. Di Zhang, Fusheng Peng, and Xiaoping Miao Copyright © 2016 Di Zhang et al. All rights reserved. The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises Wed, 28 Dec 2016 09:03:30 +0000 http://www.hindawi.com/journals/amp/2016/5164575/ The stochastic resonance (SR) characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated). In this paper, we consider a generalized Langevin equation (GLE) driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn) and Mittag-Leffler noise (M-Ln). Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works. Suchuan Zhong, Kun Wei, Lu Zhang, Hong Ma, and Maokang Luo Copyright © 2016 Suchuan Zhong et al. All rights reserved. A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos Wed, 21 Dec 2016 14:12:55 +0000 http://www.hindawi.com/journals/amp/2016/3142068/ A new no-equilibrium chaotic system is reported in this paper. Numerical simulation techniques, including phase portraits and Lyapunov exponents, are used to investigate its basic dynamical behavior. To confirm the chaotic behavior of this system, the existence of topological horseshoe is proven via the Poincaré map and topological horseshoe theory. Chunmei Wang, Chunhua Hu, Jingwei Han, and Shijian Cang Copyright © 2016 Chunmei Wang et al. All rights reserved. Stored Coulomb Self-Energy of a Uniformly Charged Rectangular Plate Sun, 18 Dec 2016 12:22:55 +0000 http://www.hindawi.com/journals/amp/2016/7207536/ A large number of electronic devices contain charged, flat plates (electrodes) as their components. The approximation of considering such components as infinitely large plates is not satisfactory for the current status of consumer electronics where size is now extremely small. In particular, the nanotechnology revolution has made the fabrication of truly finite systems with arbitrary shape and characteristic lengths that measure in nanometers possible. As a result the only accurate approach for such situations is to consider the system realistically as one with a finite size extent. In this work we calculate the amount of electrostatic energy that is stored in a charged finite size electrode that is modelled as a uniformly charged rectangular plate with arbitrary length and width. Nontrivial mathematical transformations allow us to derive a closed form exact expression for the Coulomb self-energy of such a system as a function of its length and width (therefore, shape, too). The exact result derived can be useful to understand the storage process of electrostatic energy as a function of size/shape in uniformly charged plate systems. The result also applies to calculations that deal with the properties of a finite two-dimensional electron gas within the jellium model where the finite jellium domain can have an arbitrary rectangular shape. Orion Ciftja Copyright © 2016 Orion Ciftja. All rights reserved. The Rational Solutions and Quasi-Periodic Wave Solutions as well as Interactions of -Soliton Solutions for 3 + 1 Dimensional Jimbo-Miwa Equation Thu, 15 Dec 2016 10:28:01 +0000 http://www.hindawi.com/journals/amp/2016/7241625/ The exact rational solutions, quasi-periodic wave solutions, and -soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant solution which is a special form of the -soliton solutions. At last, the interactions of the solitons are shown with the aid of -soliton solutions. Hongwei Yang, Yong Zhang, Xiaoen Zhang, Xin Chen, and Zhenhua Xu Copyright © 2016 Hongwei Yang et al. All rights reserved. Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations Thu, 15 Dec 2016 09:38:31 +0000 http://www.hindawi.com/journals/amp/2016/7854806/ An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method. A priori error estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method. M. Sameeh and A. Elsaid Copyright © 2016 M. Sameeh and A. Elsaid. All rights reserved. Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations Wed, 14 Dec 2016 13:25:22 +0000 http://www.hindawi.com/journals/amp/2016/4632163/ This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time-space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann-Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time-space fractional Kuramoto-Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method. Weishi Yin, Fei Xu, Weipeng Zhang, and Yixian Gao Copyright © 2016 Weishi Yin et al. All rights reserved. A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization Mon, 05 Dec 2016 14:06:57 +0000 http://www.hindawi.com/journals/amp/2016/4024836/ Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control. Viet-Thanh Pham, Christos Volos, Sundarapandian Vaidyanathan, and Xiong Wang Copyright © 2016 Viet-Thanh Pham et al. All rights reserved. Bright Solitons in a -Symmetric Chain of Dimers Sun, 04 Dec 2016 06:27:27 +0000 http://www.hindawi.com/journals/amp/2016/9514230/ We study the existence and stability of fundamental bright discrete solitons in a parity-time- (-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups. Omar B. Kirikchi, Alhaji A. Bachtiar, and Hadi Susanto Copyright © 2016 Omar B. Kirikchi et al. 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 http://www.hindawi.com/journals/amp/2016/6837308/ 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 http://www.hindawi.com/journals/amp/2016/5465263/ 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 http://www.hindawi.com/journals/amp/2016/1037849/ 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 http://www.hindawi.com/journals/amp/2016/8181927/ 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 http://www.hindawi.com/journals/amp/2016/9636491/ 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 http://www.hindawi.com/journals/amp/2016/4030658/ 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 http://www.hindawi.com/journals/amp/2016/6031523/ 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 http://www.hindawi.com/journals/amp/2016/9740410/ 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 http://www.hindawi.com/journals/amp/2016/3645129/ 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 http://www.hindawi.com/journals/amp/2016/8938970/ 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 http://www.hindawi.com/journals/amp/2016/2726394/ 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 http://www.hindawi.com/journals/amp/2016/1234642/ 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 http://www.hindawi.com/journals/amp/2016/8620473/ 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.