Showing papers on "Maxwell's equations published in 2013"

Dual electromagnetism: Helicity, spin, momentum, and angular momentum

Abstract: The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.

Electromagnetic Duality Symmetry and Helicity Conservation for the Macroscopic Maxwell's Equations

Abstract: In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwell’s equations by the presence of charges, can be restored for the macroscopic Maxwell’s equations. The restoration of this symmetry is shown to be independent of the geometry of the problem. These results provide a tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We illustrate its use by determining the helicity content of the natural modes of structures possessing spatial inversion symmetries and by elucidating the root causes for some surprising effects in the scattering off magnetic spheres.

Coupled hydromechanical and electromagnetic disturbances in unsaturated porous materials.

Abstract: A theory of cross-coupled flow equations in unsaturated soils is necessary to predict (1) electroosmotic flow with application to electroremediation and agriculture, (2) the electroseismic and the seismoelectric effects to develop new geophysical methods to characterize the vadose zone, and (3) the streaming current, which can be used to investigate remotely ground water flow in unsaturated conditions in the capillary water regime. To develop such a theory, the cross-coupled generalized Darcy and Ohm constitutive equations of transport are extended to unsaturated conditions. This model accounts for inertial effects and for the polarization of porous materials. Rather than using the zeta potential, like in conventional theories for the saturated case, the key parameter used here is the quasi-static volumetric charge density of the pore space, which can be directly computed from the quasi-static permeability. The apparent permeability entering Darcy's law is also frequency dependent with a critical relaxation time that is, in turn, dependent on saturation. A decrease of saturation increases the associated relaxation frequency. The final form of the equations couples the Maxwell equations and a simplified form of two-fluid phases Biot theory accounting for water saturation. A generalized expression of the Richard equation is derived, accounting for the effect of the vibration of the skeleton during the passage of seismic waves and the electrical field. A new expression is obtained for the effective stress tensor. The model is tested against experimental data regarding the saturation and frequency dependence of the streaming potential coupling coefficient. The model is also adapted for two-phase flow conditions and a numerical application is shown for water flooding of a nonaqueous phase liquid (NAPL, oil) contaminated aquifer. Seismoelectric conversions are mostly taking place at the NAPL (oil)/water encroachment front and can be therefore used to remotely track the position of this front. This is not the case for other geophysical methods.

Computations of Electromagnetic Wave Scattering From Penetrable Composite Targets Using a Surface Integral Equation Method With Multiple Traces

Abstract: We present a surface integral equation domain decomposition method (SIE-DDM) for time harmonic electromagnetic wave scattering from bounded composite targets. The proposed SIE-DDM starts by partitioning the composite object into homogeneous sub-regions with constant material properties. Each of the sub-regions is comprised of two sub-domains (the interior of the penetrable object, and the exterior free space), separated on the material interface. The interior and the exterior boundary value problems are coupled to each other through the Robin transmission conditions, which are prescribed on the material/domain interface. A generalized combined field integral equation is employed for both the interior and the exterior sub-domains. Convergence studies of the proposed SIE-DDM are included for both single homogeneous objects and composite penetrable objects. Furthermore, a complex large-scale simulation is conducted to demonstrate the capability of the proposed method to model multi-scale electrically large targets.

Force Calculations in 3-D Cylindrical Structures Using Fourier Analysis and the Maxwell Stress Tensor

Abstract: Analytical modeling is still a very effective manner to calculate the magnetic fields in permanent magnet devices. From these magnetic fields, device quantities, e.g., force, emf, or inductance, can be calculated. This paper presents a semianalytical technique, based on a 2-D Fourier series to represent the magnetic field, to describe the force components due to permanent magnets in 3-D cylindrical structures. The Maxwell stress tensor method is selected to calculate these force components in the cylindrical coordinate system. The method is analytically evaluated by inserting the analytical expressions describing the magnetic fields. The obtained force equations avoid the use of numerical integration of the magnetic fields resulting in a fast and accurate force calculation method. An example of a 3-D cylindrical structure is modeled and validated by means of a magnetostatic finite element analysis (FEA), and excellent agreement is found.

Nondiffracting accelerating waves: Weber waves and parabolic momentum

Abstract: Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a specific class of nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape. They are expressed in an analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solutions of the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic, electromagnetic and elastic waves to surface waves in fluids and membranes.

Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.

Abstract: This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin formulation for the discretization in space and a second-order leapfrog scheme for the integration in time. The numerical treatment of the dispersive model relies on an auxiliary differential equation approach similar to that which is adopted in the finite difference time-domain method. Stability estimates are derived through energy considerations and convergence is proved for both the semidiscrete and the fully discrete schemes.

The MLPG analyses of large deflections of magnetoelectroelastic plates

Abstract: The von Karman plate theory of large deformations is applied to express the strains, which are then used in the constitutive equations for magnetoelectroelastic solids. The in-plane electric and magnetic fields can be ignored for plates. A quadratic variation of electric and magnetic potentials along the thickness direction of the plate is assumed. The number of unknown terms in the quadratic approximation is reduced, satisfying the Maxwell equations. Bending moments and shear forces are considered by the Reissner–Mindlin theory, and the original three-dimensional (3D) thick plate problem is reduced to a two-dimensional (2D) one. A meshless local Petrov–Galerkin (MLPG) method is applied to solve the governing equations derived based on the Reissner–Mindlin theory. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the centre of a circle surrounding it. The weak form on small subdomains with a Heaviside step function as the test function is applied to derive the local integral equations. After performing the spatial MLS approximation, a system of algebraic equations for certain nodal unknowns is obtained. Both stationary and time-harmonic loads are then analyzed numerically.

Nonlinear graphene plasmonics:Amplitude equation for surface plasmons

Abstract: Using perturbation expansion of Maxwell equations, an amplitude equation is derived for nonlinear transverse magnetic (TM) and transverse electric (TE) surface plasmon waves supported by graphene. The equation describes the interplay between in-plane beam diffraction and nonlinearity due to light intensity induced corrections to graphene conductivity and susceptibility of dielectrics. For strongly localized TM plasmons, graphene is found to bring the superior contribution to the overall nonlinearity. In contrast, nonlinear response of the substrate and cladding dielectrics can become dominant for weakly localized TE plasmons.

Enhancement of Near Cloaking for the Full Maxwell Equations

Abstract: Recently published methods for the quasi-static limit of the Helmholtz equation is extended to consider near cloaking for the full Maxwell equations. Effective near cloaking structures are described for the electromagnetic scattering problem at a fixed frequency. These structures are, prior to using the transformation optics, layered structures designed so that their first scattering coefficients vanish. As a result, any target inside the cloaking region has near-zero scattering cross section for a band of frequencies. Analytical results show that this construction significantly enhances the cloaking effect for the full Maxwell equations.

Fast Evaluation of Time–Harmonic Maxwell's Equations Using the Reduced Basis Method

Abstract: The reduced basis method (RBM) generates low- order models for the solution of parametrized partial differential equations to allow for efficient evaluation in many-query and real-time contexts. We show the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction in frequency domain. Using rigorous error estimators, the RBM achieves low-order models under variation of material parameters and geometry. The RBM reduces model order by a factor of 50 to 100 and reduces compute time by a factor of 200 and more for numerical experiments using standard circuit elements.

Nonlocal Theory of Radiation-Matter Interaction : Boundary-Condition-Less Treatment of Maxwell Equations

Abstract: Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schri:idinger and Maxwell equations selfconsistently. The case of linear response is' described in detail. As a manifes­ tation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for a two-level atom in vacuum. The interaction of electromagnetic (EM) radiation with matter has been studied in various aspects for quite a long time. The relevant phenomena range, in the scale of wavelength, from rf wave (NMR, for example) to gamma ray (Mossbauer effect): They are related with the absorption, reflection, transmission, propagation, refrac­ tion, scattering, diffraction, emission, etc. of EM wave in linear and nonlinear manner. For the theoretical treatment of these phenomena, we need Schrodinger equation for the description of matter and Maxwell equations in classical or quantized form for radiation field. When the Maxwell equations are treated in classical form, this is called semiclassical treatment of radiation-matter interaction. Though it has a certain limitation, the semiclassical treatment can be appliedto most of the phenom­ ena mentioned above. For the treatment of the interaction of EM radiation with solids, it is usual to employ a susceptibility function to describe the solid, and solve the Maxwell equa­ tions containing that susceptibility as an integral kernel. In doing so, we must consider the boundary conditions (BC) arising from the shape of the sample in question. However, we do not consider BC's in treating microscopic systems such as an atom or small molecule. This would mean that the use of BC(s is in general not compulsory, although we are so much accustomed to it. In this respect, there has been a long debated problem of additional boundary condition (ABC) in relation with exciton polaritons in semiconductors or insulators, where the nonlocal nature of the medium allows the existence of two or more eigenmodes of the coupled exciton-EM radiation. After the long history of the ABC problem,r>- 4 > we now have a recipe to derive the appropriate form(s) of ABC(s) from a microscopic model of the medium including the details of the surface. 5 >-s> Another form of the microscopic solution of the ABC problem has been given as an ABC-free formulation, 9 >-n> where one needs

Three-dimensional electromagnetic breathers in carbon nanotubes with the field inhomogeneity along their axes

Abstract: We study the propagation of extremely short electromagnetic three-dimensional bipolar pulses in an array of semiconductor carbon nanotubes. The heterogeneity of the pulse field along the axis of the nanotubes is accounted for the first time. The evolution of the electromagnetic field and the charge density of the sample are described by Maxwell's equations supplemented by the continuity equation. Our analysis reveals for the first time the possibility of propagation of three-dimensional electromagnetic breathers in CNTs arrays. Specifically, we found that the propagation of short electromagnetic pulse induces a redistribution of the electron density in the sample.

Development of a 2-D Analytical Model for the Electromagnetic Computation of Axial-Field Magnetic Gears

Abstract: This paper describes a two-dimensional (2-D) analytical model to predict the magnetic field distribution in axial-field magnetic gears by using the sub-domain method The sub-domain method consists in solving the partial differential equations linked to the Maxwell's equations in each rectangular region (magnets, air gaps, and slots) by the separation of variables method The proposed model is based on a two-dimensional approximation for the magnetic field distribution (mean radius model) ie the problem is solved in 2-D Cartesian coordinates One of the main contributions of the paper concerns the analytic solution of the magnetic field in a slot open on the two sides (space between the ferromagnetic pole-pieces) Moreover, it is shown that the analytical model and the 3-D finite elements simulations follow the same trends in the determination of the optimum values for the geometrical parameters As the analytical model takes less computational time than 3-D numerical model, it can be used as an effective tool for the first step of design optimization

Maxwell’s Equations on Cantor Sets: A Local Fractional Approach

Abstract: Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell’s equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.

Electromagnetic rogue waves in beam–plasma interactions

Abstract: The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid Maxwell equations describing weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schr?dinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered as potential candidates for the modeling of rogue waves (freak waves) in beam?plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov?Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-)frequency and the plasma frequency.

Analytical Armature Reaction Field Prediction in Field-Excited Flux-Switching Machines Using an Exact Relative Permeance Function

Abstract: In this paper, an analytical approach for the prediction of the armature reaction field of field-excited flux-switching (FE-FS) machines is presented. The analytical method is based on the magnetomotive force (MMF)-permeance theory. The doubly-salient air-gap permeance, developed here, is derived from an exact solution of the slot permeance. Indeed, the relative slot permeance is obtained by solving Maxwell's equations in a subdomain model and applying boundary and continuity conditions. In addition, during a no-load study, we found that, regarding the stator-rotor teeth combination, phase distributions were modified. Hence, in this paper, phase MMF distributions, for q phases, several stator-rotor combinations and also phase winding distribution (single- or double-layers) are proposed. We compare extensively magnetic field distributions calculated by the analytical model with those obtained from finite-element analyses. Futhermore, the model is used to predict the machine inductances. Once again, FE results validate the analytical prediction, showing that the developed model can be advantageously used as a design tool of FE-FS machine.

Electromagnetism on anisotropic fractal media

Abstract: Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green–Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampere laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell’s electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Discontinuous Galerkin Methods for the Vlasov-Maxwell Equations

Abstract: Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Maxwell system. The proposed scheme employs discontinuous Galerkin discretizations for both the Vlasov and the Maxwell equations, resulting in a consistent description of the distribution function and electromagnetic fields. It is proven, up to some boundary effects, that charge is conserved and the total energy can be preserved with suitable choices of the numerical flux for the Maxwell equations and the underlying approximation spaces. Error estimates are established for several flux choices. The scheme is tested on the streaming Weibel instability: the order of accuracy and conservation properties of the proposed method are verified.

Efficient algorithms for electrostatic interactions including dielectric contrasts

Abstract: Coarse-grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need to compute exact electrostatic interactions between charges in those systems is computationally demanding. We review here several algorithms developed by us that perform exactly this task. For planar dielectric surfaces in partial periodic boundary conditions, the arising image charges can be either treated with the MMM2D algorithm in a very efficient and accurate way or with the electrostatic layer correction term, which enables the user to use his favorite 3D periodic Coulomb solver. Arbitrarily-shaped interfaces can be dealt with using induced surface charges with the induced charge calculation (ICC*) algorithm. Finally, the local electrostatics algorithm, MEMD(Maxwell Equations Molecular Dynamics), even allows one to employ a smoothly varying dielectric constant in the systems. We introduce the concepts of these three algorithms and an extension for the inclusion of boundaries that are to be held fixed at a constant potential (metal conditions). For each method, we present a showcase application to highlight the importance of dielectric interfaces.

A study of alfvén wave propagation and heating the chromosphere

Abstract: Alfven wave propagation, reflection, and heating of the chromosphere are studied for a one-dimensional solar atmosphere by self-consistently solving plasma, neutral fluid, and Maxwell's equations with incorporation of the Hall effect and strong electron-neutral, electron-ion, and ion-neutral collisions. We have developed a numerical model based on an implicit backward difference formula of second-order accuracy both in time and space to solve stiff governing equations resulting from strong inter-species collisions. A non-reflecting boundary condition is applied to the top boundary so that the wave reflection within the simulation domain can be unambiguously determined. It is shown that due to the density gradient the Alfven waves are partially reflected throughout the chromosphere and more strongly at higher altitudes with the strongest reflection at the transition region. The waves are damped in the lower chromosphere dominantly through Joule dissipation, producing heating strong enough to balance the radiative loss for the quiet chromosphere without invoking anomalous processes or turbulences. The heating rates are larger for weaker background magnetic fields below ~500 km with higher-frequency waves subject to heavier damping. There is an upper cutoff frequency, depending on the background magnetic field, above which the waves are completely damped. At the frequencies below which the waves are not strongly damped, the interaction of reflected waves with the upward propagating waves produces power at their double frequencies, which leads to more damping. The wave energy flux transmitted to the corona is one order of magnitude smaller than that of the driving source.

Maxwell boundary condition and velocity dependent accommodation coefficient

Abstract: A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.

Modeling Backward Wave Propagation in Metamaterials by the Finite Element Time-Domain Method

Abstract: In this paper we develop a leap-frog-type finite element method for modeling the electromagnetic wave propagation in metamaterials. The metamaterial model equations are represented by integrodifferential Maxwell's equations, which are quite challenging to analyze and solve in that we have to solve a coupled problem with different partial differential equations given in different material regions. Our method is based on a mixed finite element method using edge elements, which can easily handle the tangential continuity of the electric field. Stability analysis and optimal error estimate are carried out for the proposed scheme. The scheme is implemented and confirmed to obey the proved optimal convergence rate by using a smooth analytical solution. Then the scheme is extended to model wave propagation in heterogeneous media composed of metamaterials and free space, and extensive numerical results (using a rectangular edge element, a triangular edge element, and mixed edge elements) demonstrate the effective...

A smoothed particle hydrodynamics study on the electrohydrodynamic deformation of a droplet suspended in a neutrally buoyant Newtonian fluid

Abstract: In this paper, we have presented a 2D Lagrangian two-phase numerical model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of viscous, surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so-called leaky dielectric model. All governing equations and the pertinent jump and boundary conditions are discretized in space using the incompressible Smoothed Particle Hydrodynamics method with improved interface and boundary treatments. Upon imposing constant electrical potentials to upper and lower horizontal boundaries, the droplet starts acquiring either prolate or oblate shape, and shows rather different flow patterns within itself and in its vicinity depending on the ratios of the electrical permittivities and conductivities of the constituent phases. The effects of the strength of the applied electric field, permittivity, surface tension, and the initial droplet radius on the droplet deformation parameter have been investigated in detail. Numerical results are validated by two highly credential analytical results which have been frequently cited in the literature. The numerically and analytically calculated droplet deformation parameters show good agreement for small oblate and prolate deformations. However, for some higher values of the droplet deformation parameter, numerical results overestimate the droplet deformation parameter. This situation was also reported in literature and is due to the assumption made in both theories, which is that the droplet deformation is rather small, and hence the droplet remains almost circular. Moreover, the flow circulations and their corresponding velocities in the inner and outer fluids are in agreement with theories.

Efficient Modeling and Simulation of Graphene Devices With the LOD-FDTD Method

Abstract: The intraband term of the graphene electronic model is incorporated into Maxwell equations, and then the locally one-dimensional finite difference time domain (LOD-FDTD) method is applied to simulate graphene devices efficiently. Numerical results of the approach are compared with the explicit FDTD method. At Courant Friedrich Levy number (CFLN) equal to 100, the proposed approach is approximately 60% faster in terms of simulation time and with reasonable accuracy as compared to the FDTD method.

Spacecraft Formation Flying Dynamics and Control Using the Geomagnetic Lorentz Force

Abstract: The motion of a charged satellite subjected to the Earth’s magnetic field is considered. The Lorentz force, which acts on a charged particle when it is moving through a magnetic field, provides a new concept of propellantless electromagnetic propulsion. A dynamic model of a charged satellite, including the effect of the Lorentz force in the vicinity of a circular or an elliptic orbit, is derived and its application to formation flying is considered. Based on Hill–Clohessy–Wiltshire equations and Tschauner–Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on the linearized equations shows the controllability of the system by stepwise charge control. The sequential quadratic programming method is applied to solve the orbital transfer problem of the original nonlinear equations in which the analytical solutions cannot be obtained. A strategy to reduce the charge amount using sequential quadratic programming is also developed.