Showing papers on "Maxwell's equations published in 2015"
TL;DR: The present work solves Maxwell equations and demonstrates the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors.
Abstract: We derive in the present work topological photonic states purely based on conventional dielectric material by deforming a honeycomb lattice of cylinders into a triangular lattice of cylinder hexagons. The photonic topology is associated with a pseudo-time-reversal (TR) symmetry constituted by the TR symmetry supported in general by Maxwell equations and the C_{6} crystal symmetry upon design, which renders the Kramers doubling in the present photonic system. It is shown explicitly for the transverse magnetic mode that the role of pseudospin is played by the angular momentum of the wave function of the out-of-plane electric field. We solve Maxwell equations and demonstrate the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors.
1,151 citations
TL;DR: In this paper, a numerical scheme for the time-harmonic Maxwell equations by using weak Galerkin (WG) finite element methods is introduced, which is based on two operators: discrete weak curl and discrete weak gradient, with appropriately defined stabilizations that enforce a weak continuity of the approximating functions.
Abstract: This paper introduces a numerical scheme for the time-harmonic Maxwell equations by using weak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete weak curl and discrete weak gradient, with appropriately defined stabilizations that enforce a weak continuity of the approximating functions. This WG method is highly flexible by allowing the use of discontinuous approximating functions on arbitrary shape of polyhedra and, at the same time, is parameter free. Optimal-order of convergence is established for the WG approximations in various discrete norms which are either $$H^1$$H1-like or $$L^2$$L2 and $$L^2$$L2-like. An effective implementation of the WG method is developed through variable reduction by following a Schur-complement approach, yielding a system of linear equations involving unknowns associated with element boundaries only. Numerical results are presented to confirm the theory of convergence.
165 citations
TL;DR: In this article, an extensible multi-fluid moment model is proposed for collisionless magnetic reconnection, which evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma.
Abstract: We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.
107 citations
TL;DR: In this paper, the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone was investigated.
Abstract: We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.
94 citations
TL;DR: In this paper, the authors consider the exterior of a slowly rotating Kerr black hole and prove the boundedness of a positive definite energy on each hypersurface of constant t. They also prove the convergence of each solution to a stationary Coulomb solution.
Abstract: We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant t. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localized energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell–Ipser equation for one component. To treat the Fackerell–Ipser equation, we use a Fourier transform in t. For the Fackerell–Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.
93 citations
TL;DR: A multiplicative regularized CSI-EPT method (contrast source inversion-electric properties tomography) where the electric tissue properties are retrieved in an iterative fashion based on a contrast source inversions approach is introduced.
Abstract: Electric properties tomography (EPT) is an imaging modality to reconstruct the electric conductivity and permittivity inside the human body based on $B_{1}^{+}$ maps acquired by a magnetic resonance imaging (MRI) system. Current implementations of EPT are based on the local Maxwell equations and assume piecewise constant media. The accuracy of the reconstructed maps may therefore be sensitive to noise and reconstruction errors occur near tissue boundaries. In this paper, we introduce a multiplicative regularized CSI-EPT method (contrast source inversion—electric properties tomography) where the electric tissue properties are retrieved in an iterative fashion based on a contrast source inversion approach. The method takes the integral representations for the electromagnetic field as a starting point and the tissue parameters are obtained by iteratively minimizing an objective function which measures the discrepancy between measured and modeled data and the discrepancy in satisfying a consistency equation known as the object equation. Furthermore, the objective function consists of a multiplicative Total Variation factor for noise suppression during the reconstruction process. Finally, the presented implementation is able to simultaneously include more than one $B_{1}^{+}$ data set acquired by complementary RF excitation settings. We have performed in vivo simulations using a female pelvis model to compute the $B_{1}^{+}$ fields. Three different RF excitation settings were used to acquire complementary $B_{1}^{+}$ fields for an improved overall reconstruction. Numerical results illustrate the improved reconstruction near tissue boundaries and the ability of CSI-EPT to reconstruct small tissue structures.
92 citations
TL;DR: In this paper, it was shown that a solution to the classical Maxwell equations at finite chiral conductivity is unstable due to the soft modes of the chiral magnetic effect that grow exponentially with time.
Abstract: Time evolution of an electromagnetic field created in heavy-ion collisions strongly depends on the electromagnetic response of the quark-gluon plasma, which can be described by the Ohmic and chiral conductivities. The latter is intimately related to the chiral magnetic effect. I argue that a solution to the classical Maxwell equations at finite chiral conductivity is unstable due to the soft modes $kl{\ensuremath{\sigma}}_{\ensuremath{\chi}}$ that grow exponentially with time. In the kinematical region relevant for the relativistic heavy-ion collisions, I derive analytical expressions for the magnetic field of a point charge. I show that finite chiral conductivity causes oscillations of magnetic field at early times.
89 citations
TL;DR: In this article, an explicit high-order non-canonical symplectic particle-in-cell algorithm for classical particle-field systems governed by the Vlasov-Maxwell equations is developed.
Abstract: Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.
88 citations
TL;DR: In this article, the authors studied the dynamical evolution of the chiral magnetic effect in an electromagnetic conductor and derived a quantum conservation law of the total helicity of the system.
Abstract: We study the dynamical evolution of the so-called chiral magnetic effect in an electromagnetic conductor. To this end, we consider the coupled set of corresponding Maxwell and chiral anomaly equations, and we prove that these can be derived from chiral kinetic theory. After integrating the chiral anomaly equation over space in a closed volume, it leads to a quantum conservation law of the total helicity of the system. A change in the magnetic helicity density comes together with a modification of the chiral fermion density. We study in Fourier space the coupled set of anomalous equations and we obtain the dynamical evolution of the magnetic fields, magnetic helicity density, and chiral fermion imbalance. Depending on the initial conditions we observe how the helicity might be transferred from the fermions to the magnetic fields, or vice versa, and find that the rate of this transfer also depends on the scale of wavelengths of the gauge fields in consideration. We then focus our attention on the quark-gluon plasma phase, and analyze the dynamical evolution of the chiral magnetic effect in a very simple toy model. We conclude that an existing chiral fermion imbalance in peripheral heavy ion collisions would affect the magnetic field dynamics, and consequently, the charge dependent correlations measured in these experiments.
85 citations
TL;DR: This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition and satisfies Poisson's equation without explicitly solving it.
TL;DR: In this article, a 3D analytical model for axial-flux eddy-current couplings and brakes is presented, leading to closed-form expressions for the torque and the axial force.
Abstract: This paper presents a 3-D analytical model for axial-flux eddy-current couplings and brakes, leading to closed-form expressions for the torque and the axial force. The proposed model is valid under a steady-state condition (constant speed operation). It takes into account the reaction field due to induced currents in the moving conducting part. In order to simplify the analysis, we adopt the assumption of linearization at the mean radius, and the problem is then solved in 3-D Cartesian coordinates (curvature effects are neglected). The solution is obtained by solving the Maxwell equations with a magnetic scalar potential formulation in the nonconductive regions (magnets and air gap) and a magnetic field strength formulation in the conductive region (copper). Magnetic field distribution, axial force, and torque computed with the 3-D analytical model are compared with those obtained from the 3-D finite-element simulations and experimental results.
01 Jan 2015
TL;DR: In this article, the authors proposed a multiplicative regularized CSI-EPT method, where the electric tissue properties are retrieved in an iterative fashion based on a con- trast source inversion approach.
Abstract: Electric properties tomography (EPT) is an imaging modality to reconstruct the electric conductivity and permittivity inside the human body based on maps acquired by a mag- netic resonance imaging (MRI) system. Current implementations of EPT are based on the local Maxwell equations and assume piecewise constant media. The accuracy of the reconstructed maps may therefore be sensitive to noise and reconstruction er- rors occur near tissue boundaries. In this paper, we introduce a multiplicative regularized CSI-EPT method (contrast source in- version—electric properties tomography) where the electric tissue properties are retrieved in an iterative fashion based on a con- trast source inversion approach. The method takes the integral representations for the electromagnetic field as a starting point and the tissue parameters are obtained by iteratively minimizing an objective function which measures the discrepancy between measured and modeled data and the discrepancy in satisfying a consistency equation known as the object equation. Furthermore, the objective function consists of a multiplicative Total Variation factor for noise suppression during the reconstruction process. Finally, the presented implementation is able to simultaneously include more than one data set acquired by complementary RF excitation settings. We have performed in vivo simulations using a female pelvis model to compute the fields. Three different RF excitation settings were used to acquire comple- mentary fields for an improved overall reconstruction. Nu- merical results illustrate the improved reconstruction near tissue boundaries and the ability of CSI-EPT to reconstruct small tissue structures.
TL;DR: For a bounded domain Ω⊂R3Ω⋅R3⋈R3 with Lipschitz boundary Γ and some relatively open subset Γ ∈ ∅Γt≠∅∅ of Γ ǫ, the existence of some c>0c>0, such that (0.1) may be viewed as a natural common generalization of Korn's first and Poincare's inequality.
TL;DR: It is shown that all transmission conditions proposed so far in the literature can be written and optimized in the common framework of optimized Schwarz methods, independently of the first or second order formulation one uses, and the performance of the corresponding algorithms is identical.
TL;DR: In this article, a Hamiltonian time integrator for the Vlasov-Maxwell equations is developed by splitting the Hamiltonian functional into five parts, which produces five exactly solvable subsystems.
Abstract: Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.
TL;DR: It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form and can be drastically reduced and a significant gain in performance can be obtained.
TL;DR: The coupling between angular momentum and the temporal degrees of freedom of ultrashort pulses is discovered by generalizing the X-wave solution of the Maxwell equation and the spatial twist of propagation invariant light pulse turns out to be directly related to the number of optical cycles.
Abstract: We introduce a new class of nondiffracting optical pulses possessing orbital angular momentum. By generalizing the X-wave solution of the Maxwell equation, we discover the coupling between angular momentum and the temporal degrees of freedom of ultrashort pulses. The spatial twist of propagation invariant light pulse turns out to be directly related to the number of optical cycles. Our results may trigger the development of novel multilevel classical and quantum transmission channels free of dispersion and diffraction. They may also find application in the manipulation of nanostructured objects by ultrashort pulses and for novel approaches to the spatiotemporal measurements in ultrafast photonics.
TL;DR: In this paper, the authors further developed the study of topologically non-trivial solutions of vacuum electrodynamics and discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables.
Abstract: In this paper we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to obtain a wide class of solutions from the basic configuration, such as constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of SU(2) gauge theory. We have computed the corresponding Chern–Simons charge in a class of solutions and the charge takes integer values.
TL;DR: In this paper, a discontinuous Galerkin time-domain (DGTD) algorithm with a resistive boundary condition (RBC) was proposed to characterize the electromagnetic features of graphene.
Abstract: In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin time-domain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using an RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is first approximated by rational basis functions using the fast-relaxation vector-fitting (FRVF) method in the Laplace domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant–Friedrichs–Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
TL;DR: A new generalisation of the Helmholtz decomposition theorem for both fractional time and space is proposed, which leads to four equations generalising the Maxwell equations that emerge as particular case.
TL;DR: A new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal, whose improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Magnetic-to-Electric operator.
TL;DR: In this paper, the authors presented a simple and accurate analytical expression to compute the torque of axial-field magnetic couplings by solving the three-dimensional (3-D) Maxwell equations by the method of separation of variables.
Abstract: In this paper, we present a simple and accurate analytical expression to compute the torque of axial-field magnetic couplings. The torque expression is obtained by solving the three-dimensional (3-D) Maxwell equations by the method of separation of variables. Here, we adopt the assumption of linearization at the mean radius, the problem is then solved in 3-D Cartesian coordinate (we neglect the curvature effects). To show the accuracy of the torque formula, the results are compared with those obtained from 3-D finite-element simulations and from experimental tests. As the proposed formula needs very low computational time and depends directly on the geometrical parameters, it is used for a design optimization using multiobjective genetic algorithms.
TL;DR: A new discontinuous Galerkin spectral element time-domain (DG-SETD) method for Maxwell's equations based on the field variables E and B is proposed to analyze three-dimensional transient electromagnetic phenomena to reduce the number of unknowns and computation load.
Abstract: A new discontinuous Galerkin spectral element time-domain (DG-SETD) method for Maxwell’s equations based on the field variables $\mathbf{E}$ and $\mathbf{B}$ is proposed to analyze three-dimensional (3-D) transient electromagnetic phenomena. Compared to the previous SETD method based on the field variables $\mathbf{E}$ and $\mathbf{H}$ (the $\mathbf{EH}$ scheme), in which different orders of interpolation polynomials for electric and magnetic field intensities are required, the newly proposed method can eliminate spurious modes using basis functions with the same order interpolation for electric field intensity and magnetic flux density (the $\mathbf{EB}$ scheme). Consequently, it can reduce the number of unknowns and computation load. Domain decomposition for the $\mathbf{EB}$ scheme SETD method is completed via the DG method. In addition, the $\mathbf{EB}$ scheme SETD method is extended to the well-posed time-domain perfectly matched layer (PML) to truncate the computation domain when solving open-region problems. The effectiveness and advantages of the new DG-SETD method are validated by eigenvalue analysis and numerical results.
TL;DR: An exact transparent boundary condition is developed to reformulate the open cavity scattering problem in an unbounded domain into an initial-boundary value problem in a bounded domain.
Abstract: This paper is concerned with the mathematical analysis of the time-domain Maxwell equations in a three-dimensional open cavity. An exact transparent boundary condition is developed to reformulate the open cavity scattering problem in an unbounded domain, equivalently, into an initial-boundary value problem in a bounded domain. The well-posedness and stability are studied for the reduced problem. Moreover, an a priori estimate is established for the electric field with a minimum regularity requirement for the data. (The PDF has been changed.)
TL;DR: In this article, fractional-order operators for physical lattice models based on the Grunwald-Letnikov fractional differences are suggested, where fractional order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions.
Abstract: Fractional-order operators for physical lattice models based on the Grunwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grunwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions. Continuum limits of these fractional-order difference equations are also suggested.
TL;DR: In this paper, a method of generating topologically non-trivial solutions of vacuum electrodynamics was proposed by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables.
Abstract: In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of the Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of $SU(2)$ gauge theory. We have computed the corresponding CS charge in a class of solutions and it takes integer values.
TL;DR: In this paper, the authors considered a periodic problem for compressible Euler-Maxwell equations arising in the modeling of magnetized plasmas and proved that smooth solutions exist globally in time and converge toward non-constant equilibrium states as the time goes to infinity.
27 Mar 2015
TL;DR: This paper deals with a neural network approach to model magnetic hysteresis at macro-magnetic scale and a suitable partitioning of the neural system, described in the paper, makes the computing process rather fast.
Abstract: This paper deals with a neural network approach to model magnetic hysteresis at macro-magnetic scale. Such approach to the problem seems promising in order to couple the numerical treatment of magnetic hysteresis to FEM numerical solvers of the Maxwell's equations in time domain, as in case of the non-linear dynamic analysis of electrical machines, and other similar devices, making possible a full computer simulation in a reasonable time. The neural system proposed consists of four inputs representing the magnetic field and the magnetic inductions components at each time step and it is trained by 2-d measurements performed on the magnetic material to be modeled. The magnetic induction B is assumed as entry point and the output of the neural system returns the predicted value of the field H at the same time step. A suitable partitioning of the neural system, described in the paper, makes the computing process rather fast. Validations with experimental tests and simulations for non-symmetric and minor loops are presented.