Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. The Interactions of -Soliton Solutions for the Generalized ()-Dimensional Variable-Coefficient Fifth-Order KdV Equation Thu, 26 Nov 2015 09:39:37 +0000 A generalized ()-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the ()-dimensional KdV equation. The -soliton solutions of the ()-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient ; when , the soliton fusion and fission will happen; when , the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method. Xiangrong Wang, Xiaoen Zhang, Yong Zhang, and Huanhe Dong Copyright © 2015 Xiangrong Wang et al. All rights reserved. Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport Wed, 25 Nov 2015 12:15:16 +0000 The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster. Igor Medved’ and Robert Černý Copyright © 2015 Igor Medved’ and Robert Černý. All rights reserved. Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations Wed, 25 Nov 2015 08:26:13 +0000 We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis. X. Wang, F. Liu, and X. Chen Copyright © 2015 X. Wang et al. All rights reserved. Hypersurface Constrained Elasticae in Lorentzian Space Forms Tue, 24 Nov 2015 13:18:23 +0000 We study geodesics in hypersurfaces of a Lorentzian space form , which are critical curves of the -bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics. Óscar J. Garay, Álvaro Pámpano, and Changhwa Woo Copyright © 2015 Óscar J. Garay et al. All rights reserved. A Regime Switching Model of Schooling Choice as a Job Search Process Tue, 24 Nov 2015 08:06:29 +0000 We propose a regime switching model of schooling choice as a job search process. We adopt a two-state Markov process and the derived coupled Bellman equations are solved by seeking the root of an auxiliary algebraic equation. Some numerical examples are also considered. Yong Hyun Shin and Ho-Seok Lee Copyright © 2015 Yong Hyun Shin and Ho-Seok Lee. All rights reserved. Dynamics of a General Stochastic Nonautonomous Lotka-Volterra Model with Delays and Impulsive Perturbations Sun, 22 Nov 2015 11:20:09 +0000 A stochastic nonautonomous N-species Lotka-Volterra model with delays and impulsive perturbations is investigated. For this model, sufficient conditions for extinction, nonpersistence in the mean, weak persistence and stochastic permanence are given, respectively. The influences of the stochastic noises, and the impulsive perturbations on the properties of the stochastic model are also discussed. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results. Qing Wang, Yongguang Yu, and Shuo Zhang Copyright © 2015 Qing Wang et al. All rights reserved. Construction of Analytic Solution for Time-Fractional Boussinesq Equation Using Iterative Method Sun, 22 Nov 2015 07:25:30 +0000 This paper is aimed at constructing analytical solution for both linear and nonlinear time-fractional Boussinesq equations by an iterative method. By the iterative process, we can obtain the analytic solution of the fourth-order time-fractional Boussinesq equation in , , and , the sixth-order time-fractional Boussinesq equation, and the th-order time-fractional Boussinesq equation in . Through these examples, it shows that the method is simple and effective. Fei Xu, Yixian Gao, and Weipeng Zhang Copyright © 2015 Fei Xu et al. All rights reserved. On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative Sun, 22 Nov 2015 06:49:22 +0000 The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative , , , , where , are Caputo fractional derivatives, , , , and . Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to guarantees not only the global existence of solutions on the interval , but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to . Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with -Laplacian on the half-axis follow as a special case of our results. Hailong Ye and Rui Huang Copyright © 2015 Hailong Ye and Rui Huang. All rights reserved. Thermal Ground State and Nonthermal Probes Wed, 18 Nov 2015 09:19:04 +0000 The Euclidean formulation of SU(2) Yang-Mills thermodynamics admits periodic, (anti)self-dual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar field , effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state of , the Yang-Mills theory conjectured to underlie the fundamental description of thermal photon gases. Thierry Grandou and Ralf Hofmann Copyright © 2015 Thierry Grandou and Ralf Hofmann. All rights reserved. Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems Thu, 12 Nov 2015 06:24:56 +0000 An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms. Jeong Ryeol Choi Copyright © 2015 Jeong Ryeol Choi. All rights reserved. Stability Criteria for Volterra Integrodynamic System Wed, 11 Nov 2015 08:29:06 +0000 We study conditions under which the solutions of linear Volterra integrodynamic system of the form are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system. Nusrat Yasmin, Awais Younus, Usman Ali, and Safia Mirza Copyright © 2015 Nusrat Yasmin et al. All rights reserved. Entropic Lower Bound for Distinguishability of Quantum States Thu, 05 Nov 2015 14:14:40 +0000 For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are all pure, acquiring the entropic lower bound requires only the density operator and the number of the possible states. This entropic bound shows a relation between the von Neumann entropy and the distinguishability. Seungho Yang, Jinhyoung Lee, and Hyunseok Jeong Copyright © 2015 Seungho Yang et al. All rights reserved. Memory Effects on Nonlinear Temperature and Pressure Wave Propagation in the Boundary between Two Fluid-Saturated Porous Rocks Thu, 05 Nov 2015 13:35:46 +0000 The evolution of strong transients of temperature and pressure in two adjacent fluid-saturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti (1996). We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quantities but also “time averaged” quantities. These boundary effects are here analyzed by using a “memory formalism”; that is, we replace the ordinary punctual time-derivatives with Caputo fractional time-derivatives. We therefore obtain a nonlinear fractional model, whose explicit solution is shown, and finally discuss its geological importance. R. Garra, E. Salusti, and R. Droghei Copyright © 2015 R. Garra et al. All rights reserved. Synthesis of Relativistic Wave Equations: The Noninteracting Case Thu, 05 Nov 2015 09:15:13 +0000 We study internal structure of the Duffin-Kemmer-Petiau equations for spin 0 and spin 1 mesons. We show that in the noninteracting case full covariant solutions of the and DKP equations are generalized solutions of the Dirac equation. Andrzej Okniński Copyright © 2015 Andrzej Okniński. All rights reserved. The Rabi Oscillation in Subdynamic System for Quantum Computing Wed, 04 Nov 2015 12:04:31 +0000 A quantum computation for the Rabi oscillation based on quantum dots in the subdynamic system is presented. The working states of the original Rabi oscillation are transformed to the eigenvectors of subdynamic system. Then the dissipation and decoherence of the system are only shown in the change of the eigenvalues as phase errors since the eigenvectors are fixed. This allows both dissipation and decoherence controlling to be easier by only correcting relevant phase errors. This method can be extended to general quantum computation systems. Bi Qiao and Gu Jiayin Copyright © 2015 Bi Qiao and Gu Jiayin. All rights reserved. Mathematical Properties of the Hyperbolicity of Circulant Networks Mon, 02 Nov 2015 12:09:05 +0000 If is a geodesic metric space and , a geodesic triangle   is the union of the three geodesics , , and in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . The study of the hyperbolicity constant in networks is usually a very difficult task; therefore, it is interesting to find bounds for particular classes of graphs. A network is circulant if it has a cyclic group of automorphisms that includes an automorphism taking any vertex to any other vertex. In this paper we obtain several sharp inequalities for the hyperbolicity constant of circulant networks; in some cases we characterize the graphs for which the equality is attained. Juan C. Hernández, José M. Rodríguez, and José M. Sigarreta Copyright © 2015 Juan C. Hernández et al. All rights reserved. Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region Wed, 28 Oct 2015 08:07:54 +0000 The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor and rotation rate tensor and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors and are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors and , in which the scalar coefficients depend on simultaneous invariants of these tensors. Igor Vigdorovich and Holger Foysi Copyright © 2015 Igor Vigdorovich and Holger Foysi. All rights reserved. Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products Thu, 22 Oct 2015 12:11:22 +0000 We characterize the spacelike slices of a Lorentzian warped product as the only constant mean curvature spacelike surfaces under suitable geometrical and physical assumptions. As a consequence of our study, we derive a Bernstein-type result which widely improves and extends the state-of-the-art results in this setting. Juan A. Aledo and Rafael M. Rubio Copyright © 2015 Juan A. Aledo and Rafael M. Rubio. All rights reserved. Compound Synchronization of Four Chaotic Complex Systems Thu, 22 Oct 2015 11:27:55 +0000 The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control scheme. Junwei Sun, Yi Shen, and Guangzhao Cui Copyright © 2015 Junwei Sun et al. All rights reserved. Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)-Dimensional Nonlinear Schrödinger Equation with Dual-Power Law Nonlinearity Wed, 21 Oct 2015 09:33:35 +0000 The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented. Qing Meng, Bin He, and Zhenyang Li Copyright © 2015 Qing Meng et al. All rights reserved. Towards Noncommutative Linking Numbers via the Seiberg-Witten Map Mon, 19 Oct 2015 06:35:28 +0000 Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of new knots at the th order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels. H. García-Compeán, O. Obregón, and R. Santos-Silva Copyright © 2015 H. García-Compeán et al. All rights reserved. Geometrical Applications of Split Octonions Sun, 18 Oct 2015 13:07:54 +0000 It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1)-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group . This group generates specific rotations of (3 + 4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentz-type rotations towards the extra time-like coordinates. It is shown how the algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zero-norm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters. Merab Gogberashvili and Otari Sakhelashvili Copyright © 2015 Merab Gogberashvili and Otari Sakhelashvili. All rights reserved. Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective Sun, 18 Oct 2015 07:02:11 +0000 This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass. José Velhinho Copyright © 2015 José Velhinho. All rights reserved. One-Dimensional Coulomb Multiparticle Systems Tue, 13 Oct 2015 07:41:44 +0000 We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature case there is sufficiently complete picture and we give a short review. For Gibbs distribution the situation is more difficult and we present two related results. V. A. Malyshev and A. A. Zamyatin Copyright © 2015 V. A. Malyshev and A. A. Zamyatin. All rights reserved. Long-Time Behavior of Solution for a Reactor Model Sun, 11 Oct 2015 12:28:28 +0000 In this paper, we would consider the dynamical behaviors of the chemical model represented by Satnoianu et al. (2001). Using the Kuratowski measure of noncompactness method, we prove the existence of global attractor for the weak solution semiflow of system. Finally, several numerical experiments confirm the theoretical results. Yantao Guo, Jianwei Shen, and Qianqian Zheng Copyright © 2015 Yantao Guo et al. All rights reserved. Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing Thu, 08 Oct 2015 14:01:49 +0000 Magnetic particle imaging (MPI) is a tomographic imaging technique that allows the determination of the 3D spatial distribution of superparamagnetic iron oxide nanoparticles. Due to the complex dynamic nature of these nanoparticles, a time-consuming calibration measurement has to be performed prior to image reconstruction. During the calibration a small delta sample filled with the particle suspension is measured at all positions in the field of view where the particle distribution will be reconstructed. Recently, it has been shown that the calibration procedure can be significantly shortened by sampling the field of view only at few randomly chosen positions and applying compressed sensing to reconstruct the full MPI system matrix. The purpose of this work is to reduce the number of necessary calibration scans even further. To this end, we take into account symmetries of the MPI system matrix and combine this knowledge with the compressed sensing method. Experiments on 2D MPI data show that the combination of symmetry and compressed sensing allows reducing the number of calibration scans compared to the pure compressed sensing approach by a factor of about three. A. Weber and T. Knopp Copyright © 2015 A. Weber and T. Knopp. All rights reserved. The Periodic Boundary Value Problem for the Weakly Dissipative -Hunter-Saxton Equation Mon, 05 Oct 2015 08:44:47 +0000 We study the periodic boundary value problem for the weakly dissipative -Hunter-Saxton equation. We establish the local well-posedness in Besov space , which extends the previous regularity range to the critical case. Zhengyong Ouyang, Xiangdong Wang, and Haiwu Rong Copyright © 2015 Zhengyong Ouyang et al. All rights reserved. A Numerical Method for Solving Fractional Differential Equations by Using Neural Network Sun, 04 Oct 2015 07:06:37 +0000 We present a new method for solving the fractional differential equations of initial value problems by using neural networks which are constructed from cosine basis functions with adjustable parameters. By training the neural networks repeatedly the numerical solutions for the fractional differential equations were obtained. Moreover, the technique is still applicable for the coupled differential equations of fractional order. The computer graphics and numerical solutions show that the proposed method is very effective. Haidong Qu and Xuan Liu Copyright © 2015 Haidong Qu and Xuan Liu. All rights reserved. Existence of Multiple Positive Solutions for Choquard Equation with Perturbation Wed, 30 Sep 2015 13:58:25 +0000 This paper is concerned with the following Choquard equation with perturbation: , , where , , and . This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functions , we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation. Tao Xie, Lu Xiao, and Jun Wang Copyright © 2015 Tao Xie et al. All rights reserved. Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation Thu, 10 Sep 2015 11:16:13 +0000 The relations between -operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with -operators of nonlinear equations directly and quickly. Exact periodic wave solution of a (3+1)-dimensional generalized shallow water equation is obtained with the help of the -operators and a general Riemann theta function in terms of the Hirota method, which illustrate that bilinear -operators can provide a method for seeking exact periodic solutions of nonlinear integrable equations. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions. Jingzhu Wu, Xiuzhi Xing, and Xianguo Geng Copyright © 2015 Jingzhu Wu et al. All rights reserved.