Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging Sat, 31 Jan 2015 12:40:00 +0000 Unique determination issues about inverse problems for elliptic partial differential equations in divergence form are summarized and discussed. The inverse problems include medical imaging problems including electrical impedance tomography (EIT), diffuse optical tomography (DOT), and inverse scattering problem (ISP) which is an elliptic inverse problem closely related with DOT and EIT. If the coefficient inside the divergence is isotropic, many uniqueness results are known. However, it is known that inverse problem with anisotropic coefficients has many possible coefficients giving the same measured data for the inverse problem. For anisotropic coefficient with anomaly with or without jumps from known or unknown background, nonuniqueness of the inverse problems is discussed and the relation to cloaking or illusion of the anomaly is explained. The uniqueness and nonuniqueness issues are discussed firstly for EIT and secondly for ISP in similar arguments. Arguing the relation between source-to-detector map and Dirichlet-to-Neumann map in DOT and the uniqueness and nonuniqueness of DOT are also explained. Kiwoon Kwon Copyright © 2015 Kiwoon Kwon. All rights reserved. Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone Thu, 29 Jan 2015 13:45:14 +0000 Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations. Yuan Wang, Xiaochuan Luo, and Sai Li Copyright © 2015 Yuan Wang et al. All rights reserved. A Novel Approach to Solve Quasiexactly Solvable Pauli Equation Thu, 29 Jan 2015 11:21:13 +0000 The spectra for some specific forms of external magnetic fields in Pauli equation are obtained in the framework of the asymptotic iteration method (AIM). AIM is applied to find the solution of Pauli equation. When the method is applied to quasiexactly solvable systems, it not only easily gives the corresponding spectrum, but also produces accurate results for the eigenvalues of the system having sl(2) symmetry. Ramazan Koç, Eser Olğar, and Haydar Mutaf Copyright © 2015 Ramazan Koç et al. All rights reserved. Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions Tue, 27 Jan 2015 14:23:09 +0000 This study presents 1D analytical solutions for the ensemble variance of reactive scalars in one-dimensional turbulent flows, in case of stationary conditions, homogeneous mean scalar gradient and turbulence, Dirichlet boundary conditions, and first order kinetics reactions. Simplified solutions and sensitivity analysis are also discussed. These solutions represent both analytical tools for preliminary estimations of the concentration variance and upwind spatial reconstruction schemes for CFD (Computational Fluid Dynamics)—RANS (Reynolds-Averaged Navier-Stokes) codes, which estimate the turbulent fluctuations of reactive scalars. Andrea Amicarelli, Annalisa Di Bernardino, Franco Catalano, Giovanni Leuzzi, and Paolo Monti Copyright © 2015 Andrea Amicarelli et al. All rights reserved. Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation Sun, 18 Jan 2015 12:53:25 +0000 Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained. The resulting Hamiltonian structure of one negative integrable coupling is derived from the variational identity. Binlu Feng and Yufeng Zhang Copyright © 2015 Binlu Feng and Yufeng Zhang. All rights reserved. Local System Matrix Compression for Efficient Reconstruction in Magnetic Particle Imaging Sun, 18 Jan 2015 06:21:26 +0000 Magnetic particle imaging (MPI) is a quantitative method for determining the spatial distribution of magnetic nanoparticles, which can be used as tracers for cardiovascular imaging. For reconstructing a spatial map of the particle distribution, the system matrix describing the magnetic particle imaging equation has to be known. Due to the complex dynamic behavior of the magnetic particles, the system matrix is commonly measured in a calibration procedure. In order to speed up the reconstruction process, recently, a matrix compression technique has been proposed that makes use of a basis transformation in order to compress the MPI system matrix. By thresholding the resulting matrix and storing the remaining entries in compressed row storage format, only a fraction of the data has to be processed when reconstructing the particle distribution. In the present work, it is shown that the image quality of the algorithm can be considerably improved by using a local threshold for each matrix row instead of a global threshold for the entire system matrix. T. Knopp and A. Weber Copyright © 2015 T. Knopp and A. Weber. All rights reserved. The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface Wed, 14 Jan 2015 11:45:10 +0000 We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary condition data on the shared boundary at each time step. There exists a significant and sophisticated numerical analysis of such methods. However, computations for practical applications are often carried out under conditions under which it is unclear if rigorous results apply while relatively few iterations are used per time step. To examine this situation, we derive exact matrix expressions for the propagation of the error due to incomplete iteration that can be readily evaluated for specific discretization parameters. Using the formulas, we show that the universal validity of several tenants of the practitioner’s conventional wisdom are not universally valid. B. Sheehan, D. Estep, S. Tavener, J. Cary, S. Kruger, A. Hakim, A. Pletzer, J. Carlsson, and S. Vadlamani Copyright © 2015 B. Sheehan et al. All rights reserved. Existence Results for the Periodic Thomas-Fermi-Dirac-von Weizsäcker Equations Wed, 14 Jan 2015 07:20:37 +0000 We consider the Thomas-Fermi-Dirac-von Weizsäcker equation = , , where is a parameter, , is 1-periodic in , for , and 0 is in a spectral gap of the operator . Using a new infinite-dimensional linking theorem, we prove that, for sufficiently small , this equation has a nontrivial solution. Shaowei Chen, Lishan Lin, and Liqin Xiao Copyright © 2015 Shaowei Chen et al. All rights reserved. Loop Quantization of a 3D Abelian BF Model with σ-Model Matter Wed, 14 Jan 2015 07:16:14 +0000 The main goal of this work is to explore the symmetries and develop the dynamics associated with a 3D Abelian BF model coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. Background independence, on which the model is founded, strongly constrains its nature. We adapt to the present model the techniques of Loop Quantum Gravity in order to construct its physical Hilbert space and its observables. Diego C. M. Mendonça and Olivier Piguet Copyright © 2015 Diego C. M. Mendonça and Olivier Piguet. All rights reserved. Continuum Model for Traffic Flow considering Safe Driving Awareness Heterogeneity Tue, 13 Jan 2015 13:15:46 +0000 This paper defines the concepts of region representative vehicle and driver and region representative safe driving awareness and its heterogeneity, and, based on these concepts and a new car-following model proposed, it proposes a new continuum model for traffic flow considering region representative safe driving awareness heterogeneity. Analyses show that the new continuum model follows traffic flow anisotropy principle, and the following insights can be gotten: (1) the bigger the difference of the preceding region representative safe driving awareness coefficient minus the following region representative safe driving awareness coefficient is, the less the probability of the wrong-way travel (the negative velocity) problem in the new continuum model is; (2) when the preceding region representative safe driving awareness coefficient is not less than the following region representative safe driving awareness coefficient, there is no wrong-way travel problem in the new continuum model, and vice versa. Youzhi Zeng and Ning Zhang Copyright © 2015 Youzhi Zeng and Ning Zhang. All rights reserved. A Statistical Cohomogeneity One Metric on the Upper Plane with Constant Negative Curvature Tue, 30 Dec 2014 10:23:42 +0000 we analyze the geometrical structures of statistical manifold S consisting of all the wrapped Cauchy distributions. We prove that S is a simply connected manifold with constant negative curvature . However, it is not isometric to the hyperbolic space because S is noncomplete. In fact, S is approved to be a cohomogeneity one manifold. Finally, we use several tricks to get the geodesics and explore the divergence performance of them by investigating the Jacobi vector field. Limei Cao, Didong Li, Erchuan Zhang, Zhenning Zhang, and Huafei Sun Copyright © 2014 Limei Cao et al. All rights reserved. Bifurcation Problems for Generalized Beam Equations Mon, 22 Dec 2014 07:23:29 +0000 We investigate a class of bifurcation problems for generalized beam equations and prove that the one-parameter family of problems have exactly two bifurcation points via a unified, elementary approach. The proof of the main results relies heavily on calculus facts rather than such complicated arguments as Lyapunov-Schmidt reduction technique or Morse index theory from nonlinear functional analysis. Fosheng Wang Copyright © 2014 Fosheng Wang. All rights reserved. Non-Hermitian Lagrangian for Quasirelativistic Fermions Sun, 21 Dec 2014 00:10:21 +0000 We present a Lorentz-symmetry violating Lagrangian for free fermions, which is local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian but not local. A specific feature of the model is that the dispersion relation is relativistic in both the IR and the UV but not in an intermediate regime, set by a given mass scale. The consistency of the model is shown by the study of properties expected in analogy with the Dirac Lagrangian. Jean Alexandre Copyright © 2014 Jean Alexandre. All rights reserved. Symmetry and Group Theory and Its Application to Few-Body Physics Thu, 18 Dec 2014 11:12:45 +0000 Xiao-Yan Gu, Fabien Gatti, Shi-Hai Dong, and Jian-Qiang Sun Copyright © 2014 Xiao-Yan Gu et al. All rights reserved. Fundamental Solutions for Periodic Media Sun, 14 Dec 2014 06:42:17 +0000 Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate. Sergey V. Kuznetsov Copyright © 2014 Sergey V. Kuznetsov. All rights reserved. Lie Symmetry Reductions and Exact Solutions to the Rosenau Equation Sun, 14 Dec 2014 00:10:45 +0000 The Lie symmetry analysis is performed on the Rosenau equation which arises in modeling many physical phenomena. The similarity reductions and exact solutions are presented. Then the exact analytic solutions are considered by the power series method. Ben Gao and Hongxia Tian Copyright © 2014 Ben Gao and Hongxia Tian. All rights reserved. Investigations on Vehicle Rollover Prevention Using LQG Regulator Tue, 09 Dec 2014 08:40:06 +0000 This paper presents results of an initial investigation into vehicle roll model and control strategies suitable for preventing vehicle untripped rollovers. For vehicles that are deemed to be susceptible to wheel-liftoff, various control strategies are implemented in simulation. In this study, the authors propose a method for rollover prevention that does not require such accurate contact information. The validity of the stability margin is shown, and it is used to realize rollover prevention in the direction of the roll. The primary assumption in their implementation is that the vehicle in question is equipped with a conventional controller system. Binda Mridula Balakrishnan and Marimuthu Rajaram Copyright © 2014 Binda Mridula Balakrishnan and Marimuthu Rajaram. All rights reserved. Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions Wed, 26 Nov 2014 00:10:07 +0000 We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented. Jessada Tariboon, Sotiris K. Ntouyas, and Chatthai Thaiprayoon Copyright © 2014 Jessada Tariboon et al. All rights reserved. Shear Wave Propagation in Multilayered Medium including an Irregular Fluid Saturated Porous Stratum with Rigid Boundary Wed, 12 Nov 2014 06:11:08 +0000 The present investigation is concerned with the study of propagation of shear waves in an anisotropic fluid saturated porous layer over a semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformation. Numerically, the effect of irregularity present is analysed. It is seen that the phase velocity is significantly influenced by the wave number and the depth of the irregularity. The variations of dimensionless phase velocity against dimensionless wave number are shown graphically for the different size of rectangular irregularities with the help of MATLAB. Ravinder Kumar, Dinesh Kumar Madan, and Jitander Singh Sikka Copyright © 2014 Ravinder Kumar et al. All rights reserved. On the Deformation Retract of Kerr Spacetime and Its Folding Mon, 10 Nov 2014 00:00:00 +0000 The deformation retract of the Kerr spacetime is introduced using Lagrangian equations. The equatorial geodesics of the Kerr space have been discussed. The retraction of this space into itself and into geodesics has been presented. The deformation retract of this space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced. H. Rafat Copyright © 2014 H. Rafat. All rights reserved. Solution Theory of Ginzburg-Landau Theory on BCS-BEC Crossover Sun, 02 Nov 2014 11:22:59 +0000 We establish strong solution theory of time-dependent Ginzburg-Landau (TDGL) systems on BCS-BEC crossover. By the properties of Besov, Sobolev spaces, and Fourier functions and the method of bootstrapping argument, we deduce that the global existence of strong solutions to time-dependent Ginzburg-Landau systems on BCS-BEC crossover in various spatial dimensions. Shuhong Chen and Zhong Tan Copyright © 2014 Shuhong Chen and Zhong Tan. All rights reserved. Some Propositions on Generalized Nevanlinna Functions of the Class Thu, 23 Oct 2014 07:15:55 +0000 Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the class does not exceed . This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the class has a uniform asymptotic expansion at a real point or at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceed . Also, an explicit formula for the negative index of a real rational function is given by using relations among Loewner, Bézout, and Hankel matrices. These results will provide first tools for the solution of the indefinite truncated moment problems together with the multiple Nevanlinna-Pick interpolation problems in the class based on the so-called Hankel vector approach. Yan-Ping Song, Hui-Feng Hao, Yong-Jian Hu, and Gong-Ning Chen Copyright © 2014 Yan-Ping Song et al. All rights reserved. Hybrid Dislocated Control and General Hybrid Projective Dislocated Synchronization for Memristor Chaotic Oscillator System Thu, 16 Oct 2014 06:13:07 +0000 Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic oscillator system. For the different dimensions, the memristor chaotic oscillator system and the other chaotic system have realized general hybrid projective dislocated synchronization. Numerical simulations are given to show the effectiveness of these methods. Junwei Sun, Chun Huang, and Guangzhao Cui Copyright © 2014 Junwei Sun et al. All rights reserved. Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity Mon, 15 Sep 2014 09:33:33 +0000 We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities. H. Chachou Samet, M. Benarous, M. Asad-uz-zaman, and U. Al Khawaja Copyright © 2014 H. Chachou Samet et al. All rights reserved. Exact Solutions of the Time Fractional BBM-Burger Equation by Novel -Expansion Method Thu, 11 Sep 2014 10:23:57 +0000 The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method. Muhammad Shakeel, Qazi Mahmood Ul-Hassan, Jamshad Ahmad, and Tauseef Naqvi Copyright © 2014 Muhammad Shakeel et al. All rights reserved. Low Temperature Expansion in the Lifshitz Formula Tue, 09 Sep 2014 00:00:00 +0000 The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We rederive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the asymptotic expansions for . The paper includes the derivations and should provide a self-contained representation. M. Bordag Copyright © 2014 M. Bordag. All rights reserved. On Generalized Jordan Prederivations and Generalized Prederivations of Lie Superalgebras Tue, 02 Sep 2014 13:05:24 +0000 The concepts of (generalized) -prederivations and (generalized) Jordan -prederivations on a Lie superalgebra are introduced. It is proved that Jordan -prederivations (resp., generalized Jordan -prederivations) are -prederivations (resp., generalized -prederivations) on a Lie superalgebra under some conditions. In particular, Jordan -prederivations are -prederivations on a Lie superalgebra. Yao Ma and Liangyun Chen Copyright © 2014 Yao Ma and Liangyun Chen. All rights reserved. -Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation Mon, 01 Sep 2014 06:09:27 +0000 The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK) equation. By using Hirota method, the analytic one-, two-, three-, and -soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media. Jian Zhou, Xiang-Gui Li, and Deng-Shan Wang Copyright © 2014 Jian Zhou et al. All rights reserved. An Alternative Approach to Energy Eigenvalue Problems of Anharmonic Potentials Wed, 27 Aug 2014 08:24:33 +0000 Energy eigenvalues of quartic and sextic type anharmonic potentials are obtained by using an alternative method called asymptotic Taylor expansion method (ATEM) which is an approximate approach based on the asymptotic Taylor series expansion of a function. It is shown that the energy eigenvalues found by ATEM are in excellent agreement with the existing results. Okan Ozer and Halide Koklu Copyright © 2014 Okan Ozer and Halide Koklu. All rights reserved. Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source Sun, 24 Aug 2014 12:37:37 +0000 This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of a -Laplacian equation with a localized reaction. We obtain the Fujita exponent of the equation. Yulan Wang, Xiaojun Song, and Chao Ye Copyright © 2014 Yulan Wang et al. All rights reserved.