Longitudinal wave propagation in bars with variable cross section

Zusammenfassung Eine Störmethode wird angewandt, um die Feldgleichungen für die Wellenausbreitung in Längsrichtung in Balken mit veränderlichem Querschnitt zu entwickeln.

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This work was supported by the United States Atomic Energy Commission and the Engineering Research Institute, Iowa State University.     

Mathematical modeling of electromagnetic wave propagation in nonlinear electrodynamics

The eikonal method for an electromagnetic wave propagating according to the laws of non-linear electrodynamics in vacuum in external electromagnetic and gravitational fields is developed. A mathematical model of the propagation of electromagnetic signals in the parameterized post-Maxwellian electrodynamics in vacuum is constructed. As an example of using the proposed method, the angles of the nonlinear electrodynamical and gravitational curvature of the normal wave rays propagating in the field of a charged collapsar are calculated.     

Investigation of electromagnetic wave diffraction from an inhomogeneous partially shielded solid

Diffraction of electromagnetic wave from a partially shielded inhomogeneous dielectric is considered. The original boundary value problem for Maxwell’s equations is shown to have at most one quasi-classical solution. The problem is reduced to a system of integro-differential equations on the solid and the screens. The matrix integro-differential operator is treated in Sobolev spaces and is shown to be a continuously invertible operator. As a result, convergence of the Galerkin method is proved in the chosen functional spaces.     

The mathematical modeling of the electric field in the media with anisotropic objects

We present a numerical scheme for modeling the electric field in the media with tensor conductivity. This scheme is based on vector finite element method in frequency domain. The numerical computations of the electric field in the anisotropic medium are done. The conductivity of the anisotropic medium is positive defined dense tensor in general case. We consider the electric field from anisotropic layer, inclined anisotropic layer and some anisotropic objects in isotropic half-space.     

The new type of non-polarized symmetric electromagnetic waves in planar nonlinear waveguide

Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear medium. The wave propagation problem is reduced to a transmission eigenvalue problem. Eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and therefore, guide waves. The found guide regime is novel in the theory of nonlinear waveguides. Numerical results are presented.     

Time domain study of the Drude–Born–Fedorov model for a class of heterogeneous chiral materials

We deal with the well‐posedness of the transient Maxwell equations in a particular class of heterogeneous isotropic chiral material modeled by the Drude–Born–Fedorov constitutive relations with different boundary conditions. A new formulation of the underlying evolution problems allows us to establish existence and uniqueness results. The selfadjointness of the curl operator multiplied by a piecewise smooth function in an appropriated Hilbert space is also proved. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotic behaviour of the energy for electromagnetic systems in the presence of small inhomogeneities

In this article we consider solutions to the time-harmonic and time-dependent Maxwell's systems with piecewise constant coefficients with a finite number of small inhomogeneities in ?³. In time-harmonic case and for such solutions, we derive the asymptotic expansions due to the presence of small inhomogeneities embedded in the entire space. Further, we analyse the behaviour of the electromagnetic energy caused by the presence of these inhomogeneities. For a general time-dependent case, we show that the local electromagnetic energy, trapped in the total collection of these well-separated inhomogeneities, decays towards zero as the shape parameter decreases to zero or as time increases.     

Shape derivative of the volume integral operator in electromagnetic scattering by homogeneous bodies

We study the shape derivative of the strongly singular volume integral operator that describes time‐harmonic electromagnetic scattering from homogeneous medium. We show the existence and a representation of the derivative, and we deduce a characterization of the shape derivative of the solution to the diffraction problem as a solution to a volume integral equation of the second kind.     

Analysis of the energy‐conserved S‐FDTD scheme for variable coefficient Maxwell's equations in disk domains

In this paper, we analyze the energy‐conserved splitting finite‐difference time‐domain (FDTD) scheme for variable coefficient Maxwell's equations in two‐dimensional disk domains. The approach is energy‐conserved, unconditionally stable, and effective. We strictly prove that the EC‐S‐FDTD scheme for the variable coefficient Maxwell's equations in disk domains is of second order accuracy both in time and space. It is also strictly proved that the scheme is energy‐conserved, and the discrete divergence‐free is of second order convergence. Numerical experiments confirm the theoretical results, and practical test is simulated as well to demonstrate the efficiency of the proposed EC‐S‐FDTD scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

On singularities of solution of Maxwell's equations in axisymmetric domains with conical points

Boundary value problems (BVP) in three‐dimensional axisymmetric domains can be treated more efficiently by partial Fourier analysis. Partial Fourier analysis is applied to time‐harmonic Maxwell's equations in three‐dimensional axisymmetric domains with conical points on the rotation axis thereby reducing the three dimensional BVP to an infinite sequence of 2D BVPs on the plane meridian domain Ω_a?? of . The regularity of the solutions u _n (n∈?₀:={0, 1, 2,…}) of the two dimensional BVPs is investigated and it is proved that the asymptotic behaviour of the solutions u _n near an angular point on the rotation axis can be characterized by singularity functions related to the solutions of some associated Legendre equations. By means of numerical experiments, it is shown that the solutions u _n for n∈?₀\{1} belong to the Sobolev space H² irrespective of the size of the solid angle at the conical point. However, the regularity of the coefficient u ₁ depends on the size of the solid angle at the conical point. The singular solutions of the three dimensional BVP are obtained by Fourier synthesis. Copyright © 2006 John Wiley & Sons, Ltd.     

Exterior problem of magnetic field in Darwin model and its numerical solution

In this paper, we consider the solutions of magnetic field in the Darwin model to the Maxwell's equations in 2D unbounded domain. We first deduce the variational formulation and prove the well‐posedness of the weak solution, and then prove the existence and uniqueness of the infinite element solution. Error estimate and the numerical examples are provided. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Maxwell meets Korn: A new coercive inequality for tensor fields in with square‐integrable exterior derivative

For a bounded domain with connected Lipschitz boundary, we prove the existence of some c > 0, such that holds for all square‐integrable tensor fields , having square‐integrable generalized “rotation” tensor fields and vanishing tangential trace on ?Ω, where both operations are to be understood row‐wise. Here, in each row, the operator curl is the vector analytical reincarnation of the exterior derivative d in . For compatible tensor fields T, that is, T = ? v, the latter estimate reduces to a non‐standard variant of Korn's first inequality in , namely for all vector fields , for which ? v_n,n = 1, … ,N, are normal at ?Ω. Copyright © 2012 John Wiley & Sons, Ltd.     

Mathematical modeling of coupled turbulent flow and solidification in a single belt caster with electromagnetic brake

A mathematical model has been developed to simulate turbulent fluid flow and solidification in the presence of a DC magnetic field in an extended nozzle for metal delivery to a single belt caster. This paper reports on predicted effects of DC magnetic field conditions in modifying flows and solidification behavior in the metal delivery system. It is shown that the application of a DC magnetic brake to the proposed system can result in a reasonably uniform feeding of melt onto the cooled moving belt. This, in turn, optimises the rate of even shell growth along the chilled substrate. In order to account for the effects of turbulence, a revised low-Reynolds k–ε turbulent model was employed. A Darcy-porosity approach was used to simulate fluid flow within the mushy solidification region. Simulations were carried out for plain carbon steel strip casting. The fully coupled transport equations were numerically solved using the finite volume method. The computed flow patterns were compared with those reported in the literature. The performance of the magnetic flow control device proposed in this work is evaluated and compared with flow modifications obtained by inserting a ceramic filter within the reservoir.     

A block‐centered finite difference method for Darcy–Forchheimer model with variable Forchheimer number

A block‐centered finite difference scheme is introduced to solve the nonlinear Darcy–Forchheimer equation with variable Forchheimer number, in which the velocity and pressure can be approximated simultaneously. For variable Forchheimer number the second‐order error estimates for both pressure and velocity are established on nonuniform rectangular grid. An iteration process is given to solve the nonlinear system. Numerical experiments using the scheme show the consistency of the convergence rates of the presented methods with the theoretical analysis. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1603–1622, 2015     

Dynamic analysis of a rumor propagation model with Lévy noise

In this paper, we are concerned with a rumor propagation model with L vy noise. We first prove that there exists a positive global solution. Then, the asymptotic behaviors around the rumor‐free equilibrium and rumor‐epidemic equilibrium are obtained. Lastly, simulations verify our results.     

Asymptotic stability of traveling wave fronts in nonlocal reaction–diffusion equations with delay

This paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction–diffusion equations with delay. Under monostable assumption, we prove that the traveling wave front is exponentially stable by means of the (technical) weighted energy method, when the initial perturbation around the wave is suitable small in a weighted norm. The exponential convergent rate is also obtained. Finally, we apply our results to some population models and obtain some new results, which recover, complement and/or improve a number of existing ones.     

Mathematical modeling and comparison of air standard Dual and Dual-Atkinson cycles with friction,heat transfer and variable specific-heats of the working fluid

Based on finite-time thermodynamics, a comparative performance analysis of air standard Dual and Dual-Atkinson cycles with heat-transfer loss, friction like term losses and variable specific-heats of the working fluid have been performed. Also the effects of heat loss, as characterized by a percentage of the fuel’s energy, friction and variable specific-heats of the working fluid, on performance of the mentioned irreversible cycles are analyzed. Moreover, detailed numerical examples show the relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the thermal efficiency of cycles. Results show the importance of consideration of heat loss effects on the both cycles’ performance. Also performance comparison of two cycles show that heat efficiency and power output of a Dual-Atkinson cycle are higher than a Dual cycle’s ones. The results obtained from this paper will provide guidance for the design of Dual-Atkinson engines.     

Existence of CMC and Constant Areal Time Foliations in T 2 Symmetric Spacetimes with Vlasov Matter

Abstract

The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a two-dimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the Einstein–Vlasov system when conformal or areal coordinates are introduced.     

Green's function approach to study the propagation of SH‐wave in piezoelectric layer influenced by a point source

Green's function technique serves as a powerful tool to find the particle displacements due to SH‐wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH‐wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT‐5H ceramics, Barium titanate (BaTiO₃) ceramics, Silicon dioxide (SiO₂) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe₂O₄), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well‐known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.