Showing papers on "Maxwell's equations published in 2009"

Classifying multiferroics: Mechanisms and effects

Abstract: Electricity and magnetism were combined into one common discipline in the 19th century, culminating in the Maxwell equations. But electric and magnetic ordering in solids are most often considered separately—and usually with good reason: the electric charges of electrons and ions are responsible for the charge effects, whereas electron spins govern magnetic properties There are, however, cases where these degrees of freedom couple strongly. For example, in the new, large field of spintronics, the effects of spins on the transport properties of solids (and vice versa) allow the possibility to control one by the other. The finding of a strong coupling of magnetic and electric degrees of freedom in insulators can be traced back to Pierre Curie, but the real beginning of this field started in 1959 with a short remark by Landau and Lifshitz in a volume of their Course of Theoretical Physics[1]: “Let us point out two more phenomena, which, in principle, could exist. One is piezomagnetism, which consists of linear coupling between a magnetic field in a solid and a deformation (analogous to piezoelectricity). The other is a linear coupling between magnetic and electric fields in a media, which would cause, for example, a magnetization proportional to an electric field. Both these phenomena could exist for certain classes of magnetocrystalline symmetry. We will not however discuss these phenomena in more detail because it seems that till present, presumably, they have not been observed in any substance.” The situation changed soon thereafter, when Dzyaloshinskii predicted [2], and Astrov observed [3], this type of coupling, which is now known as the linear magnetoelectric effect. This was rapidly followed by the discovery of many other compounds of this class and by a rather complete classification of possible symmetry groups allowing for the effect. A new twist in this problem was the idea that not only can strong cross-coupling of responses exist in solids (i.e., the appearance of magnetization M in an electric field E, or the inverse effect of electric polarization P generated by the application of magnetic field H), but that there may exist systems in which two types of ordering—(ferro)magnetism, the spontaneous orderFIG. 1: Multiferroics combine the properties of ferroelectrics and magnets. In the ideal case, the magnetization of a ferromagnet in a magnetic field displays the usual hysteresis (blue), and ferroelectrics have a similar response to an electric field (yellow). If we manage to create multiferroics that are simultaneously ferromagnetic and ferroelectric (green), then there is a magnetic response to an electric field, or, vice versa, the modification of polarization by magnetic field. And, in principle we have here the basis for making a 4-state logic state: (P + M+), (+−), (−+), (−−). (Illustration: Alan Stonebraker)

Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium

Abstract: We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin–orbit coupling of light which consists of (i) the Berry phase responsible for trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometrodynamical interrelations illuminate a dual physical nature of the phenomena.

On the Schrodinger-Maxwell equations under the effect of a general nonlinear term

Abstract: In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions.

Optimized Schwarz Methods for Maxwell's Equations

Abstract: Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for which overlap is essential for convergence. More recently, optimized Schwarz methods have been developed for elliptic partial differential equations. These methods use more effective transmission conditions between subdomains than the classical Dirichlet conditions, and optimized Schwarz methods can be used both with and without overlap for elliptic problems. We show here why the classical Schwarz method applied to both the time harmonic and time discretized Maxwell's equations converges without overlap: the method has the same convergence factor as a simple optimized Schwarz method for a scalar elliptic equation. Based on this insight, we develop an entire new hierarchy of optimized overlapping and nonoverlapping Schwarz methods for Maxwell's equations with greatly enhanced performance compared to the classical Schwarz method. We also derive for each algorithm asymptotic formulas for the optimized transmission conditions, which can easily be used in implementations of the algorithms for problems with variable coefficients. We illustrate our findings with numerical experiments.

Improved-Accuracy Source Reconstruction on Arbitrary 3-D Surfaces

Abstract: This paper presents a novel formulation of the source reconstruction problem on arbitrary three-dimensional (3-D) surfaces based on integral equations. Rigorous boundary integral field identities are employed to enforce that the two unknown currents are Maxwellian on the reconstruction surface; this leads to a dual integral-equation formulation, in contrast to the single-equation formulation found in literature. Numerical tests against reference currents allow a quantitative assessment of the improvements in accuracy afforded by the novel formulation, with important benefits in diagnostic applications.

Vortex and droplet engineering in a holographic superconductor

Abstract: We give a detailed account of the construction of nontrivial localized solutions in a $2+1$ dimensional model of superconductors using a $3+1$ dimensional gravitational dual theory of a black hole coupled to a scalar field The solutions are found in the presence of a background magnetic field We use numerical and analytic techniques to solve the full Maxwell-scalar equations of motion in the background geometry, finding condensate droplet solutions, and vortex solutions possessing a conserved winding number These solutions and their properties, which we uncover, help shed light on key features of the $(B,T)$ phase diagram

Weyl corrections to holographic conductivity

Abstract: For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk and thus obey universality relations at the classical level due to the uniqueness of the Maxwell action. We analyze corrections to these transport parameters due to higher-dimension operators in the bulk action, beyond the leading Maxwell term, of which the most significant involves a coupling to the bulk Weyl tensor. We show that the ensuing corrections to conductivity and the diffusion constant break the universal relation with the U(1) central charge observed at leading order, but are nonetheless subject to interesting bounds associated with causality in the boundary conformal field theory.

Relativistic models of magnetars: the twisted torus magnetic field configuration

Abstract: We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. Our method is based on the solution of the relativistic Grad-Shafranov equation, to which Maxwell's equations can be reduced. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher-order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.

Magnetically-actuated artificial cilia for microfluidic propulsion

Abstract: Natural cilia are hair-like microtubule-based structures that are able to move fluid at low Reynolds number through asymmetric motion. In this paper we follow a biomimetic approach to design artificial cilia lining the inner surface of microfluidic channels with the goal to propel fluid. The artificial cilia consist of polymer films filled with magnetic nanoparticles. The asymmetric, non-reciprocating motion is generated by tuning an external magnetic field. To obtain the magnetic field and associated magnetization local to the cilia we solve the Maxwell equations, from which the magnetic torques can be deduced. To obtain the ciliary motion we solve the dynamic equations of motion which are then fully coupled to the fluid dynamic equations that describe fluid flow around the cilia. By doing so we show that by properly tuning the applied magnetic field, asymmetric ciliary motion can be generated that is able to propel fluid in a microchannel. The results are presented in terms of three dimensionless parameters that fully delineate the asymmetry and cycle time as a function of the relative contribution of elastic, inertial, magnetic and viscous fluid forces.

Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations

Abstract: Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann’s H-theorem even for collisions between different particle species with unequal temperatures. The model collision operators are also written in the gyrophase-averaged form that can be applied to the gyrokinetic equation. Balance equations for the turbulent entropy density, the energy of electromagnetic fluctuations, the turbulent transport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokinetic equation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulent transport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.

Magnetic Field Analysis of Inset and Surface-Mounted Permanent-Magnet Synchronous Motors Using Schwarz–Christoffel Transformation

Abstract: In this paper, we apply an original numerical Schwarz-Christoffel (SC) transformation to analyze magnetic field originating from permanent magnets and the armature winding currents in a slotted air gap of an inset permanent-magnet synchronous motor. We obtained the solution of the SC integral numerically using Matlab SC Toolbox. We used this field solution to calculate both cogging torque and electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. The case without inter-polar piece, which is equivalent to a surface-mounted permanent-magnet motor, is also treated. The accuracy of the developed method is verified by comparing its results with those obtained from the developed numerical finite-element models.

Debye sources and the numerical solution of the time harmonic Maxwell equations

Abstract: In this paper, we develop a new representation for outgoing solutions to the timeharmonic Maxwell equations in unbounded domains in R 3 . This representation leads to a Fredholm integral equation of the second kind for solving the problem of scattering from a perfect conductor, which does not suffer from spurious resonances or low-frequency breakdown, although it requires the inversion of the scalar surface Laplacian on the domain boundary. In the course of our analysis, we give a new proof of the existence of nontrivial families of time-harmonic solutions with vanishing normal components that arise when the boundary of the domain is not simply connected. We refer to these ask-Neumann fields, since they generalize, to nonzero wave numbers, the classical harmonic Neumann fields. The existence ofk-Neumann fields was established earlier by Kress. © 2009 Wiley Periodicals, Inc.

Octonic representation of electromagnetic field equations

Abstract: In this paper we represent eight-component values “octons,” generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave equations for potentials and fields and to the system of Maxwell’s equations. The octonic algebra allows one to perform compact combined calculations simultaneously with scalars, vectors, pseudoscalars, and pseudovectors. Examples of such calculations are demonstrated by deriving the relations for energy, momentum, and Lorentz invariants of the electromagnetic field.

Direct solutions of the maxwell equations explain opposition phenomena observed for high-albedo solar system objects

Abstract: Several spectacular backscattering effects observed for particulate planetary surfaces have been interpreted in terms of the effect of weak localization (WL) of electromagnetic waves. However, the interference concept of WL explicitly relies on the notion of phase of an electromagnetic wave and is strictly applicable only when particles forming the surface are widely separated. Therefore, one needs a definitive quantitative proof of the WL nature of specific optical effects observed for densely packed particulate media. We use numerically exact computer solutions of the Maxwell equations to simulate electromagnetic scattering by realistic models consisting of large numbers of randomly positioned, densely packed particles. By increasing the particle packing density from zero to ~40%, we track the onset and evolution of the full suite of backscattering optical effects predicted by the low-density theory of WL, including the brightness and polarization opposition effects (BOE and POE). We find that all manifestations of WL, except the circular polarization ratio and POE, are remarkably immune to packing-density effects. Even POE can survive packing densities typical of planetary regolith surfaces. Our numerical data coupled with the results of unique observations at near-backscattering geometries demonstrate that the BOE and POE detected simultaneously for high-albedo solar system objects are caused by the effect of WL.

Thermally stimulated electromagnetic fields of solids

Abstract: Different ways to calculate the spectral properties of fluctuating electromagnetic fields produced by solids are reviewed, all of which essentially reduce to solving the Maxwell equations for a specified geometry and boundary conditions and then using the fluctuation--dissipation theorem. It is shown that in the practical case of plane-layered solids, all correlation characteristics of thermal fields can be expressed in terms of the Fresnel coefficients. The experimental results on thermally stimulated electromagnetic fields from solids are in qualitative and quantitative agreement with model calculations and theoretical expectations. The dispersion interaction between solid bodies in different thermodynamic states, the fluctuating fields as a means of body-to-body energy transfer, and the shift, broadening, and deexcitation of energy levels in a particle near a solid surface are discussed using the theory of thermally stimulated electromagnetic fields.

Higher-order effects and ultrashort solitons in left-handed metamaterials.

Abstract: Starting from Maxwell's equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrodinger equation, describing ultrashort solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.

A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations

Abstract: We present an explicit numerical method to solve the time-dependent Maxwell equations with arbitrary high order of accuracy in space and time on three-dimensional unstructured tetrahedral meshes. The method is based on the discontinuous Galerkin finite element approach, which allows for discontinuities at grid cell interfaces. The computation of the flux between the grid cells is based on the solution of generalized Riemann problems, which provides simultaneously a high-order accurate approximation in space and time. Within our approach, we expand the solution in a Taylor series in time, where subsequently the Cauchy–Kovalevskaya procedure is used to replace the time derivatives in this series by space derivatives. The numerical solution can thus be advanced in time in one single step with high order and does not need any intermediate stages, as needed, e.g. in classical Runge–Kutta-type schemes. This locality in space and time allows the introduction of time-accurate local time stepping (LTS) for unsteady wave propagation. Each grid cell is updated with its individual and optimal time step, as given by the local Courant stability criterion. On the basis of a numerical convergence study we show that the proposed LTS scheme provides high order of accuracy in space and time on unstructured tetrahedral meshes. The application to a well-acknowledged test case and comparisons with analytical reference solutions confirm the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

Current and Future Applications of 3-D Global Earth-Ionosphere Models Based on the Full-Vector Maxwell’s Equations FDTD Method

Abstract: Advances in computing technologies in recent decades have provided a means of generating and performing highly sophisticated computational simulations of electromagnetic phenomena. In particular, just after the turn of the twenty-first century, improvements to computing infrastructures provided for the first time the opportunity to conduct advanced, high-resolution three-dimensional full-vector Maxwell’s equations investigations of electromagnetic propagation throughout the global Earth-ionosphere spherical volume. These models, based on the finite-difference time-domain (FDTD) method, are capable of including such details as the Earth’s topography and bathymetry, as well as arbitrary horizontal/vertical geometrical and electrical inhomogeneities and anisotropies of the ionosphere, lithosphere, and oceans. Studies at this level of detail simply are not achievable using analytical methods. The goal of this paper is to provide an historical overview and future prospectus of global FDTD computational research for both natural and man-made electromagnetic phenomena around the world. Current and future applications of global FDTD models relating to lightning sources and radiation, Schumann resonances, hypothesized earthquake precursors, remote sensing, and space weather are discussed.

A high-order Discontinuous Galerkin method for the seismic wave propagation

Abstract: We are interested in the simulation of P-SV seismic wave propagation by a high-order Discontinuous Galerkin method based on centered fluxes at the interfaces combined with a leap-frog time-integration. This non-diffusive method, previously developed for the Maxwell equations, is particularly well adapted to complex topographies and fault discontinuities in the medium. We prove that the scheme is stable under a CFL type condition and that a discrete energy is preserved on an infinite domain. Convergence properties and efficiency of the method are studied through numerical simulations in two and three dimensions of space.

Charged relativistic spheres with generalized potentials

Abstract: A new class of exact solutions of the Einstein–Maxwell system is found in closed form. This is achieved by choosing a generalized form for one of the gravitational potentials and a particular form for the electric field intensity. For specific values of the parameters it is possible to write the new series solutions in terms of elementary functions. We regain well-known physically reasonable models. A physical analysis indicates that the model may be used to describe a charged sphere. The influence of the electromagnetic field on the gravitational interaction is highlighted. Copyright © 2008 John Wiley & Sons, Ltd.

A New Circuit Model for Carbon Nanotube Interconnects With Diameter-Dependent Parameters

Abstract: In this paper, a new circuit model for the propagation of electric signals along carbon nanotube interconnects is derived from a fluid model description of the nanotube electrodynamics. The conduction electrons are regarded as a 2-D charged fluid, interacting with the electromagnetic field produced by the ion lattice, the conduction electron themselves, and the external sources. This interaction may be assumed to be governed by a linearized Euler's equation, which provides the nanotube constitutive equation to be coupled to Maxwell equations. A derivation of a circuit model is then possible within the frame of the classical multiconductor transmission-line (TL) theory. The elementary cell of this TL model differs from those proposed in literature, due to the definition of the circuit variable corresponding to the voltage. When considering small nanotube radius, we obtain values for the kinetic inductance and quantum capacitance that are consistent with literature. These values are corrected here to take into account the influence of larger values of radius properly. Conversely, the value of the per unit length resistance is roughly half of the value usually adopted in literature. The multiconductor TL model is used to study the scaling law of the parameters with the number of carbon nanotubes in a bundle.

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

Abstract: An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell’s equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E×B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov–Maxwell system. Generalized ordering takes ρi⪡ρθi∼LE∼Lp⪡R [here ρi is the thermal ion Larmor radius and ρθi=B∕(Bθρi)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ρi∼1 is assumed for generality, and the relative fluctuation amplitudes eδϕ∕Ti∼δB∕B are kept up to the second order. Extending the electrostatic theory in the presence of high E×B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pullback transformation from the gyro...

On light propagation in premetric electrodynamics: the covariant dispersion relation

Abstract: The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism also emerges when the non-minimal coupling between the electromagnetic tensor and the torsion of Einstein–Cartan gravity is considered. Moreover, the premetric formalism can serve as a general covariant background of the electromagnetic properties of anisotropic media. In the current paper, we study wave propagation in the premetric electrodynamics. We derive a system of characteristic equations corresponded to premetric generalization of the Maxwell equation. This singular system is characterized by the adjoint matrix which turns to be of a very special form—proportional to a scalar quartic factor. We prove that a necessary condition for the existence of a non-trivial solution of the characteristic system is expressed by a unique scalar dispersion relation. In the tangential (momentum) space, it determines a fourth-order light hypersurface which replaces the ordinary light cone of the standard Maxwell theory. We derive an explicit form of the covariant dispersion relation and establish its algebraic and physical origin.