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## Maxwell's Equations (maxwell + equation)
## Selected Abstracts## A parametric study of multi-phase and multi-species transport in the cathode of PEM fuel cells INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2008Nada ZamelAbstract In this study, a mathematical model is developed for the cathode of PEM fuel cells, including multi-phase and multi-species transport and electrochemical reaction under the isothermal and steady-state conditions. The conservation equations for mass, momentum, species and charge are solved using the commercial software COMSOL Multiphysics. The catalyst layer is modeled as a finite domain and assumed to be composed of a uniform distribution of supported catalyst, liquid water, electrolyte and void space. The Stefan,Maxwell equation is used to model the multi-species diffusion in the gas diffusion and catalyst layers. Owing to the low relative species' velocity, Darcy's law is used to describe the transport of gas and liquid phases in the gas diffusion and catalyst layers. A serpentine flow field is considered to distribute the oxidant over the active cathode electrode surface, with pressure loss in the flow direction along the channel. The dependency of the capillary pressure on the saturation is modeled using the Leverette function and the Brooks and Corey relation. A parametric study is carried out to investigate the effects of pressure drop in the flow channel, permeability, inlet relative humidity and shoulder/channel width ratio on the performance of the cell and the transport of liquid water. An inlet relative humidity of 90 and 80% leads to the highest performance in the cathode. Owing to liquid water evaporation, the relative humidity in the catalyst layer reaches 100% with an inlet relative humidity of 90 and 80%, resulting in a high electrolyte conductivity. The electrolyte conductivity plays a significant role in determining the overall performance up to a point. Further, the catalyst layer is found to be important in controlling the water concentration in the cell. The cross-flow phenomenon is shown to enhance the removal of liquid water from the cell. Moreover, a shoulder/channel width ratio of 1:2 is found to be an optimal ratio. A decrease in the shoulder/channel ratio results in an increase in performance and an increase in cross flow. Finally, the Leverette function leads to lower liquid water saturations in the backing and catalyst layers than the Brooks and Corey relation. The overall trend, however, is similar for both functions. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## High harmonic generation by two color field-mixing in n-type low-doped GaAs PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 5 2003D. Persano AdornoAbstract Monte Carlo simulations for high harmonic generation by two mixed electric fields linearly polarized with frequency in the far-infrared range in GaAs crystal are examined. The wave-mixed signal conversion efficiency is calculated by the use of the appropriate Maxwell equation for the propagation of an electromagnetic wave along a given direction in a medium. We show how the efficiency of the harmonics and their polarization depend on: (i) the frequencies and the intensities of the incident waves; (ii) the angle between the polarization of the two incident fields. [source] ## Magnetic susceptibility: Further insights into macroscopic and microscopic fields and the sphere of Lorentz CONCEPTS IN MAGNETIC RESONANCE, Issue 1 2003C.J. DurrantAbstract To make certain quantitative interpretations of spectra from NMR experiments carried out on heterogeneous samples, such as cells and tissues, we must be able to estimate the magnetic and electric fields experienced by the resonant nuclei of atoms in the sample. Here, we analyze the relationships between these fields and the fields obtained by solving the Maxwell equations that describe the bulk properties of the materials present. This analysis separates the contribution to these fields of the molecule in which the atom in question is bonded, the "host" fields, from the contribution of all the other molecules in the system, the "external" fields. We discuss the circumstances under which the latter can be found by determining the macroscopic fields in the sample and then removing the averaged contribution of the host molecule. We demonstrate that the results produced by the, so-called, "sphere of Lorentz" construction are of general validity in both static and time-varying cases. This analytic construct, however, is not "mystical" and its justification rests not on any sphericity in the system but on the local uniformity and isotropy, i.e., spherical symmetry, of the medium when averaged over random microscopic configurations. This local averaging is precisely that which defines the equations that describe the macroscopic fields. Hence, the external microscopic fields, in a suitably averaged sense, can be estimated from the macroscopic fields. We then discuss the calculation of the external fields and that of the resonant nucleus in NMR experiments. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part A 18A: 72,95, 2003 [source] ## An approach to the non-active power concept in terms of the poynting-park vector EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 5 2001A. FerreroThis paper reconsiders the approach to the electric systems in terms of Maxwell equations, and reconsiders in particular the energy transfer involved in an electric system in terms of the flux of the Poynting vector. This approach is extended to the three-phase systems, and the Park transformation is reconsidered by applying it to the Poynting vector. In this way a correct physical meaning can be assigned to the non-active components of the Park instantaneous power by tracing them back to the components of the Poynting vector. [source] ## Statistical theory of weak field thermoremanent magnetization in multidomain particle ensembles GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2003Karl FabianSUMMARY A non-equilibrium statistical theory of multidomain thermoremanent magnetization (TRM) is developed, which describes thermal magnetization changes as continuous inhomogeneous Markov processes. The proposed theory relies on three very general physical properties of TRM: (a) The probability that a magnetization state Sj is transformed during an infinitesimal temperature change into state Si depends only on external conditions and on Sj, but not on previously assumed states. (b) Due to time inversion symmetry of the Maxwell equations, the magnetic energies are invariant with respect to inversion of all spins in zero field. (c) The probability that an energy barrier between two magnetization states is overcome during a thermal process is governed by Boltzmann statistics. From these properties, the linearity of TRM with field is derived for generic multidomain particle ensembles. The general validity of Thellier's law of additivity of partial TRM's in weak fields is established and a method for proving a large class of similar additivity laws is developed. The theory allows consistent treatment of blocking and unblocking of remanence in multidomain particle ensembles and naturally explains apparent differences between blocking and unblocking temperatures. [source] ## Performance of a parallel implementation of the FMM for electromagnetics applications INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2003G. SylvandAbstract This paper describes the parallel fast multipole method implemented in EADS integral equations code. We will focus on the electromagnetics applications such as CEM and RCS computation. We solve Maxwell equations in the frequency domain by a finite boundary-element method. The complex dense system of equations obtained cannot be solved using classical methods when the number of unknowns exceeds approximately 105. The use of iterative solvers (such as GMRES) and fast methods (such as the fast multipole method (FMM)) to speed up the matrix,vector product allows us to break this limit. We present the parallel out-of-core implementation of this method developed at CERMICS/INRIA and integrated in EADS industrial software. We were able to solve unprecedented industrial applications containing up to 25 million unknowns. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A new parallelization strategy for solving time-dependent 3D Maxwell equations using a high-order accurate compact implicit scheme, INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2006Eugene KashdanAbstract With progress in computer technology there has been renewed interest in a time-dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second-order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high-order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd-order accurate explicit scheme for approximation of spatial derivatives with the 4th-order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl-based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three-dimensional time-dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## The electromagnetic effect of cooling fins INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2006S. B. ChiuAbstract The electromagnetic effect of cooling fins is studied by solving Maxwell equations numerically using a FDTD method under high-frequency operating conditions. The fin is attached to a square IC chip to form a package. The overall size of the package is 25 mm × 25 mm × 17.5 mm. A smooth compact pulse with a reference frequency of either 1 or 2.5 GHz is used as the excitation source of EM waves. Six fin configurations are investigated. Computational results indicate that a fin can act as an antenna. For the present type of excitation source, resonance could occur roughly at frequencies of 2.5, 5 and 7.5 GHz, depending on the source reference frequency and fin geometries. Thus, fin effects should be considered in the electrical design phase since noises could be induced in the circuit due to the presence of fins. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Numerical modelling of anisotropy and eddy current effects in ferromagnetic laminations using a co-energy formulation INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2001L. R. DupréAbstract The paper deals with a numerical model for the evaluation of electromagnetic fields in one steel lamination under the influence of a rotating magnetic flux, taking into account anisotropy effects. For this purpose a detailed material model, described by a differential permeability tensor, is included in the macroscopic electromagnetic field calculations in one lamination. Here, by geometrical and physical considerations, the governing Maxwell equations are reduced to a system of parabolic PDEs for the components of the magnetic field vector, under appropriate boundary and initial conditions. We present a suitable numerical approximation based upon a finite element,finite difference method, which properly takes into account the material characteristics. The study leads to a more realistic numerical modelling of the electromagnetic phenomena inside electric and magnetic conducting laminations due to anisotropy effects. Numerical results are compared with those from simplified analytical formulae. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Multi-periodic eigensolutions to the Dirac operator and applications to the generalized Helmholtz equation on flat cylinders and on the n -torus MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2009Denis ConstalesAbstract In this paper, we study the solutions to the generalized Helmholtz equation with complex parameter on some conformally flat cylinders and on the n -torus. Using the Clifford algebra calculus, the solutions can be expressed as multi-periodic eigensolutions to the Dirac operator associated with a complex parameter ,,,. Physically, these can be interpreted as the solutions to the time-harmonic Maxwell equations on these manifolds. We study their fundamental properties and give an explicit representation theorem of all these solutions and develop some integral representation formulas. In particular, we set up Green-type formulas for the cylindrical and toroidal Helmholtz operator. As a concrete application, we explicitly solve the Dirichlet problem for the cylindrical Helmholtz operator on the half cylinder. Finally, we introduce hypercomplex integral operators on these manifolds, which allow us to represent the solutions to the inhomogeneous Helmholtz equation with given boundary data on cylinders and on the n -torus. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## On a hierarchy of models for electrical conduction in biological tissues MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2006M. AmarAbstract In this paper we derive a hierarchy of models for electrical conduction in a biological tissue, which is represented by a periodic array of period , of conducting phases surrounded by dielectric shells of thickness ,, included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process , , 0, followed by a homogenization limit with respect to ,. These models are then compared with regard to their physical meaning and mathematical issues. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Solution of axisymmetric Maxwell equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2003Franck AssousAbstract In this article, we study the static and time-dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in (Math. Meth. Appl. Sci. 2002; 25: 49), we investigate the decoupled problems induced in a meridian half-plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H1 component-wise. It is proven that the singular parts are related to singularities of Laplace-like or wave-like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space,time regularity results for the electromagnetic field. This paper is the continuation of (Modél. Math. Anal. Numér. 1998; 32: 359, Math. Meth. Appl. Sci. 2002; 25: 49). Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A well-posed problem for electromagnetic media with quadrupoles MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2003Carlo Alberto BoselloAbstract In this paper, we consider a non-local electromagnetic medium for which the quadrupole term in the electric induction is not negligible. After giving an outline of the physical model, the problem of Maxwell equations for such a medium is addressed by proving existence and uniqueness of solutions and a principle of constrained minimum is shown to hold as a consequence of some thermodynamical restrictions. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Theoretical tools to solve the axisymmetric Maxwell equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2002F. AssousAbstract In this paper, the mathematical tools, which are required to solve the axisymmetric Maxwell equations, are presented. An in-depth study of the problems posed in the meridian half-plane, numerical algorithms, as well as numerical experiments, based on the implementation of the theory described hereafter, shall be presented in forthcoming papers. In the present paper, the attention is focused on the (orthogonal) splitting of the electromagnetic field in a regular part and a singular part, the former being in the Sobolev space H1 component-wise. It is proven that the singular fields are related to singularities of Laplace-like operators, and, as a consequence, that the space of singular fields is finite dimensional. This paper can be viewed as the continuation of References (J. Comput. Phys. 2000; 161: 218,249, Modél. Math. Anal. Numér, 1998; 32: 359,389) Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Preconditioners for the discretized time-harmonic Maxwell equations in mixed form NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2007Chen GreifAbstract We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators, but are augmentation free and Schur complement free. We provide a complete spectral analysis, and show that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations are accompanied by numerical results that demonstrate the scalability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Dynamical model for coherent optical manipulation of a single spin state in a charged quantum dot PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 2 2009Gabriela SlavchevaAbstract The optically-induced coherent spin dynamics of a single spin confined in a charged quantum dot (QD) is theoretically studied employing coupled vector Maxwell-pseudospin formalism. Generalized pseudospin master equation is derived for description of the time evolution of spin coherences and spin populations including spin population transfer and dissipation in the system through spin relaxation processes. The equation is solved in the time domain self-consistently with the vector Maxwell equations for the optical wave propagation coupled to it via macroscopic medium polarisation. Using the model the long-lived electron spin coherence left behind a single resonant ultrashort optical excitation of the electron-trion transition in a charged QD is simulated in the low- and high-intensity Rabi oscillations regime. Signatures of the polarised photoluminescence (PL), predicted by the model, such as the appearance of a second echo pulse after the excitation and characteristic PL trace shape, are discussed for realization of high-fidelity schemes for coherent readout of a single spin polarisation state. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Magnetic fields in the early Universe ASTRONOMISCHE NACHRICHTEN, Issue 1 2010K. SubramanianAbstract We give a pedagogical introduction to two aspects of magnetic fields in the early Universe. We first focus on how to formulate electrodynamics in curved space time, defining appropriate magnetic and electric fields and writing Maxwell equations in terms of these fields. We then specialize to the case of magnetohydrodynamics in the expanding Universe. We emphasize the usefulness of tetrads in this context. We then review the generation of magnetic fields during the inflationary era, deriving in detail the predicted magnetic and electric spectra for some models. We discuss potential problems arising from back reaction effects and from the large variation of the coupling constants required for such field generation (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Effective thermal conductivity behavior of filled vulcanized perfluoromethyl vinyl ether rubber JOURNAL OF APPLIED POLYMER SCIENCE, Issue 5 2008Li WangAbstract The effective thermal conductivity behavior of vulcanized perfluoromethyl vinyl ether (PMVE) rubber filled with various inorganic fillers was investigated and analyzed with thermal conductivity models. Experimental results showed that there was no significant improvement in the thermal conductivity of PMVE rubber if the intrinsic thermal conductivity of the fillers was greater than 100 times that of the rubber matrix, and this agreed with the prediction of Maxwell's equation. The thermal conductivity of PMVE rubber filled with larger size silicon carbide (SiC) particles was greater than that of PMVE filled with smaller size SiC because of the lower interfacial thermal resistance, and there existed a transition filler loading at about 60 vol %. It was also found that flocculent graphite was the most effective thermally conductive filler among the fillers studied. A modified form of Agari's equation with a parameter independent on the units used was proposed. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] ## Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma CONTRIBUTIONS TO PLASMA PHYSICS, Issue 4 2006N. I. GrishanovAbstract Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Influence of line routing and terminations on transient overvoltages in LV power installations EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 8 2009Ibrahim A. MetwallyAbstract IEC 62305-4 gives the rules for the selection and the installation of surge protective devices (SPDs), where the maximum enhancement factor is considered to be equal to 2 in the worst case of open-circuit condition. The objective of the present paper is to check this relation for equipment connected to low-voltage (LV) power system. The LV power system is considered as TN-S system with different routings in three- and six-storey buildings. The terminals of apparatus are substituted by a variety of different loads, namely, resistances, inductances, and capacitances. All Maxwell's equations are solved by the method of moments (MoM) and the voltage is calculated at the apparatus terminals. The SPD itself is simulated by a voltage source at the ground floor. The results reveal that the voltage at the apparatus terminals may overshoot the SPD protection level by a factor of 3 irrespective of the number of floors and loops. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Computer solutions of Maxwell's equations in homogeneous media INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2003O. PironneauAbstract This document is the material support for a talk given for JSIAM on the current methods for the computation of radar cross sections. The talk covers more than just computations of RCS and extends to any problem which involves the numerical solution of Maxwell's equations in homogeneous media. The talk is based on a review of the most recent papers in leading journals and on the author's experience. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Power and temperature distribution during microwave thawing, simulated by using Maxwell's equations and Lambert's law INTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 1 2005Chang Min LiuSummary The microwave thawing of frozen food was simulated by using an equation to describe heat conduction. This was based on the fact that the thermal and dielectric properties of food vary with temperature. The microwave power absorbed was modelled by using Maxwell's equations and Lambert's law. The power and temperature distributions calculated using both models were compared. Although Lambert's law is theoretically less applicable for simulating the transmitted microwave power, it provided an effective numerical approach for calculating temperature distribution during microwave thawing, which proved compatible with experimental results. [source] ## Synthetic-aperture assessment of a dispersive surface INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2004Margaret CheneyAbstract This article considers Synthetic Aperture Radar and other synthetic-aperture imaging systems in which a backscattered wave is measured from a variety of locations. We focus on the case in which the ground-reflectivity function depends on frequency as well as on position. We begin with a (linearized) mathematical model, based on a scalar approximation to Maxwell's equations, which includes the effects of the source waveform and the antenna beam pattern. The model can also accommodate other effects such as antenna steering and motion. For this mathematical model, we use the tools of microlocal analysis to develop and analyze a three-dimensional inversion algorithm that uses measurements made on a surface and determines the frequency-dependent ground reflectivity. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol 14, 28,34, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20004 [source] ## Higher order explicit time integration schemes for Maxwell's equations INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5-6 2002Holger SpachmannAbstract The finite integration technique (FIT) is an efficient and universal method for solving a wide range of problems in computational electrodynamics. The conventional formulation in time-domain (FITD) has a second-order accuracy with respect to spatial and temporal discretization and is computationally equivalent with the well-known finite difference time-domain (FDTD) scheme. The dispersive character of the second-order spatial operators and temporal integration schemes limits the problem size to electrically small structures. In contrast higher-order approaches result not only in low-dispersive schemes with modified stability conditions but also higher computational costs. In this paper, a general framework of explicit Runge,Kutta and leap-frog integrators of arbitrary orders N is derived. The powerful root-locus method derived from general system theory forms the basis of the theoretical mainframe for analysing convergence, stability and dispersion characteristics of the proposed integrators. As it is clearly stated, the second- and fourth-order leap-frog scheme are highly preferable in comparison to any other higher order Runge,Kutta or leap-frog scheme concerning stability, efficiency and energy conservation. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Time domain global modelling of EM propagation in semiconductor using irregular grids INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2002Hsiao-Ping TsaiAbstract A two-dimensional finite volume time domain (FVTD) method using a triangular grid is applied to the analysis of electromagnetic wave propagation in a semiconductor. Maxwell's equations form the basis of all electromagnetic phenomena in semiconductors and the drift-diffusion model is employed to simulate charge transport phenomena in the semiconductor. The FVTD technique is employed to solve Maxwell's equations on an irregular grid and the finite box method is implemented on the same grid to solve the drift-diffusion model for carrier concentration. The locations of unknowns have been chosen to allow linking coupled Maxwell's equations and transport equations in a seamless way. To achieve suitable accuracy and computational efficiency, using irregular grid topology allows a finer mesh in doped region and at junction, and a coarser mesh in substrate and insulting regions. The proposed scheme has been implemented and verified by characterizing electromagnetic wave propagation at microwave frequency in a semiconductor slab with arbitrary doping profile. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Simulation of EM wave propagation in magnetoelectric media using TLM INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2001Christos ChristopoulosAbstract In this paper, the simulation of general frequency-dependent magnetoelectric material properties in time-domain TLM is described. The formulation is developed from Maxwell's equations and the constitutive relations using bilinear ,,-transform methods leading to a general Padé system. The approach is applicable to all frequency-dependent linear materials including those displaying anisotropic and bianisotropic behaviour. The method is validated by the example of a chiral slab having an analytic solution. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## On a model for electromagnetic processes inside and outside a ferromagnetic body MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2008Martin BrokateAbstract One-dimensional Maxwell's equations are considered in a ferromagnetic body surrounded by vacuum. Existence and uniqueness of solution for the resulting system of partial differential equations with hysteresis on the whole real line is proved under suitable constitutive hypotheses. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Transmission problems for Maxwell's equations with weakly Lipschitz interfaces MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2006Andreas AxelssonAbstract We prove sufficient conditions on material constants, frequency and Lipschitz regularity of interface for well posedness of a generalized Maxwell transmission problem in finite energy norms. This is done by embedding Maxwell's equations in an elliptic Dirac equation, by constructing the natural trace space for the transmission problem and using Hodge decompositions for operators d and , on weakly Lipschitz domains to prove stability. We also obtain results for boundary value problems and transmission problems for the Hodge,Dirac equation and prove spectral estimates for boundary singular integral operators related to double layer potentials. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## The diffraction in a class of unbounded domains connected through a hole MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2003Yu. V. ShestopalovAbstract In this paper, the unique solvability, Fredholm property, and the principle of limiting absorption are proved for a boundary value problem for the system of Maxwell's equations in a semi-infinite rectangular cylinder coupled with a layer by an aperture of arbitrary shape. Conditions at infinity are taken in the form of the Sveshnikov,Werner partial radiation conditions. The method of solution employs Green's functions of the partial domains and reduction to vector pseudodifferential equations considered in appropriate vectorial Sobolev spaces. Singularities of Green's functions are separated both in the domain and on its boundary. The smoothness of solutions is established. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Boundary value problems for Dirac operators and Maxwell's equations in non-smooth domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002Marius MitreaAbstract We study the well-posedness of the half-Dirichlet and Poisson problems for Dirac operators in three-dimensional Lipschitz domains, with a special emphasis on optimal Lebesgue and Sobolev-Besov estimates. As an application, an elliptization procedure for the Maxwell system is devised. Copyright © 2002 John Wiley & Sons, Ltd. [source] |