Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Investigating the Nanoparticles Penetration Efficiency through Horizontal Tubes Using an Experimental Approach Mon, 02 Mar 2015 09:54:03 +0000 It is a complex transfer process of nanoparticles in a tube. In this paper, in order to quantify the penetration efficiency of nanoparticles in different flows condition through horizontal tubes, the experiments have been carried out with particles diameter between 6 nm and 560 nm in various lengths of sampling tube. The results were in good agreement with the theory of Gormley and Kennedy and the experiment results of Kumar et al. for particles size smaller than 100 nm. Particles penetration rate increases with increasing of the Schmidt number (Sc), and it decreases with increasing Reynolds and tube length. Particles deposition on the wall induces the changes of the mass and average diameter of particles continuously. Therefore, a nondimensional parameter (ς) defined dependency on Reynolds number and particle residence time in tube has been used to express total mass penetration efficiency and mean size growth rate through a straight tube. Zhaoqin Yin and Zhongping Dai Copyright © 2015 Zhaoqin Yin and Zhongping Dai. All rights reserved. Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study Mon, 02 Mar 2015 09:53:51 +0000 This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows. Xingtuan Yang, Nan Gui, Gongnan Xie, Jie Yan, Jiyuan Tu, and Shengyao Jiang Copyright © 2015 Xingtuan Yang et al. All rights reserved. On the Deformation Retract of Eguchi-Hanson Space and Its Folding Sun, 22 Feb 2015 12:04:38 +0000 We introduce the deformation retract of the Eguchi-Hanson space using Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The deformation retract of the Eguchi-Hanson space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced. H. Rafat and Nasr Ahmed Copyright © 2015 H. Rafat and Nasr Ahmed. All rights reserved. Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms Sun, 22 Feb 2015 11:45:59 +0000 We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense. Erhan Pişkin Copyright © 2015 Erhan Pişkin. All rights reserved. The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder Wed, 18 Feb 2015 12:18:40 +0000 The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field. Bülent Yılmaz Copyright © 2015 Bülent Yılmaz. All rights reserved. Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds Mon, 16 Feb 2015 06:45:11 +0000 We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds . We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere. Shenyang Tan, Tiren Huang, and Wenbin Zhang Copyright © 2015 Shenyang Tan et al. All rights reserved. On Homogeneous Parameter-Dependent Quadratic Lyapunov Function for Robust Filtering Design in Switched Linear Discrete-Time Systems with Polytopic Uncertainties Sun, 15 Feb 2015 08:59:54 +0000 This paper is concerned with the problem of robust filter design for switched linear discrete-time systems with polytopic uncertainties. The condition of being robustly asymptotically stable for uncertain switched system and less conservative noise-attenuation level bounds are obtained by homogeneous parameter-dependent quadratic Lyapunov function. Moreover, a more feasible and effective method against the variations of uncertain parameter robust switched linear filter is designed under the given arbitrary switching signal. Lastly, simulation results are used to illustrate the effectiveness of our method. Guochen Pang and Kanjian Zhang Copyright © 2015 Guochen Pang and Kanjian Zhang. All rights reserved. Orbital Stability of Solitary Traveling Waves of Moderate Amplitude Mon, 09 Feb 2015 14:05:40 +0000 We consider the orbital stability of solitary traveling wave solutions of an equation describing the free surface waves of moderate amplitude in the shallow water regime. Firstly, we rewrite this equation in Hamiltonian form and construct two invariants of motion. Then using the abstract stability theorem of solitary waves proposed by Grillakis et al. (1987), we prove that the solitary traveling waves of the equation under consideration are orbital stable. Zhengyong Ouyang Copyright © 2015 Zhengyong Ouyang. All rights reserved. A Brief Observational History of the Black-Hole Spacetimes Sun, 08 Feb 2015 08:50:39 +0000 In this year (2015), black holes (BHs) celebrate their 100th birthday, if their birth is taken to be triggered by a handwritten letter from Martin Schwarzschild to Albert Einstein, in connection with his newly found spherically symmetric vacuum solution. Wolfgang Kundt Copyright © 2015 Wolfgang Kundt. All rights reserved. Behavior of a Free Dual-Spin Gyrostat with Different Ratios of Inertia Moments Sun, 08 Feb 2015 07:26:16 +0000 The attitude motion is studied of asymmetric dual-spin gyrostats which may be modeled as free systems of two rigid bodies, one asymmetric and one axisymmetric. Exact analytical solutions of the attitude motion are presented for all possible ratios of inertia moments of these bodies. The dynamics of free gyrostats with zero internal torque is considered. The dimensionless nonlinear equations of the gyrostat are written in Serret-Andoyer canonical variables. The previously known exact solutions are complemented by new several solutions in terms of Jacobi elliptic functions. The results of the study can be useful for the analysis of dual-spin spacecraft dynamics. Vladimir Aslanov Copyright © 2015 Vladimir Aslanov. All rights reserved. The Ellipsoidal Vortex: A Novel Approach to Geophysical Turbulence Sun, 08 Feb 2015 07:19:56 +0000 We review the development of the ellipsoidal vortex model within the field of geophysical fluid dynamics. This vortex model is built on the classical potential theory of ellipsoids and applies to large-scale fluid flows, such as those found in the atmosphere and oceans, where the dynamics are strongly affected by the Earth's rotation. In this large-scale limit the governing equations reduce to the quasi-geostrophic system, where all the dynamics depends on a single scalar field, the potential vorticity, which is a dynamical marker for vortices. The solution of this system is achieved by the inversion of a Poisson equation, that in the case of an ellipsoidal vortex can be solved exactly. From this ellipsoidal solution equilibria have been determined and their stability properties have been studied. Many studies have shown that this ellipsoidal vortex model, while being conceptually simple, is an extremely powerful tool in eliciting some of the fundamental characteristics of turbulent geophysical flows. William J. McKiver Copyright © 2015 William J. McKiver. All rights reserved. Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity Sun, 08 Feb 2015 07:18:12 +0000 The paper focuses on the problem of monochromatic electromagnetic TM wave propagation in a two-layer circular cylindrical dielectric waveguide. The space outside the waveguide is filled with isotropic medium having constant permittivity. The inner core of the waveguide is filled with isotropic medium having constant permittivity; the cladding of the core is filled with isotropic inhomogeneous nonlinear permittivity (the nonlinear term is expressed by Kerr law). Existence of guided modes which depend harmonically on z (the waveguide axis coincides with z-axis) is proved and their localization is found. Numerical results including different type of nonlinearities are presented. A comparison with the linear case is given. The existence of a new propagation regime is predicted. E. Yu. Smol’kin and D. V. Valovik Copyright © 2015 E. Yu. Smol’kin and D. V. Valovik. All rights reserved. On a Conjecture regarding Fisher Information Thu, 05 Feb 2015 08:47:39 +0000 Fisher’s information measure plays a very important role in diverse areas of theoretical physics. The associated measures and , as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product has been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimension . We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies for . Angelo Plastino, Guido Bellomo, and Angel Ricardo Plastino Copyright © 2015 Angelo Plastino et al. All rights reserved. Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering Mon, 02 Feb 2015 06:12:00 +0000 The environment of the ellipsoidal system, significantly more complex than the spherical one, provides the necessary settings for tackling boundary value problems in anisotropic space. However, the theory of Lamé functions and ellipsoidal harmonics affiliated with the ellipsoidal system is rather complicated. A turning point would reside in the existence of expressions interlacing these two different systems. Still, there is no simple way, if at all, to bridge the gap. The present paper addresses this issue. We provide explicit formulas of specific ellipsoidal harmonics expressed in terms of their counterparts in the classical spherical system. These expressions are then put into practice in the framework of physical applications. Michael Doschoris and Panayiotis Vafeas Copyright © 2015 Michael Doschoris and Panayiotis Vafeas. 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.