ANALYSIS OF FDTD TO UPML FOR MAXWELL EQUATIONS IN POLAR COORDINATES

An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.

Physical interpretation of Planck's constant based on the Maxwell theory

The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,however,has not been well understood.It was originally suggested as a fitting constant to explain the black-body radiation.Although Planck had proposed a theoretical justification of h,he was never satisfied with that.To solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet.We find that the energy of the wave packet is indeed proportional to its oscillation frequency.This allows us to derive the value of Planck＇s constant.Furthermore,we show that the emission and transmission of a photon follows the all-or-none principle.The ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse axis.We reason that ζ should have a fixed cut-off value for all photons.Our results suggest that a wave packet can behave like a particle.This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.

Relating Maxwell's demon and quantitative analysis of information leakage for practical imperative programs

Shannon observed the relation between information entropy and Maxwell demon experiment to come up with information entropy formula. After that, Shannon＇s entropy formula is widely used to measure information leakage in imperative programs. But in the present work, our aim is to go in a reverse direction and try to find possible Maxwell＇s demon experimental setup for contemporary practical imperative programs in which variations of Shannon＇s entropy formula has been applied to measure the information leakage. To establish the relation between the second principle of thermodynamics and quantitative analysis of information leakage, present work models contemporary variations of imperative programs in terms of Maxwell＇s demon experimental setup. In the present work five contemporary variations of imperative program related to information quantification are identified. They are： （i） information leakage in imperative program, （ii） imperative multi- threaded program, （iii） point to point leakage in the imperative program, （iv） imperative program with infinite observation, and （v） imperative program in the SOA-based environment. For these variations, minimal work required by an attacker to gain the secret is also calculated using historical Maxwell＇s demon experiment. To model the experimental setup of Maxwell＇s demon, non-interference security policy is used. In the present work, imperative programs with one-bit secret information have been considered to avoid the complexity. The findings of the present work from the history of physics can be utilized in many areas related to information flow of physical computing, nano-computing, quantum computing, biological computing, energy dissipation in computing, and computing power analysis.

Characterization of barrier-tunable radio-frequency-SQUID for Maxwell's demon experiment

We present the design, fabrication, and characterization of a barrier-tunable superconducting quantum interference device（SQUID） qubit for the study of Maxwell＇s demon experiment. In this work, a compound Josephson junction（CJJ）radio-frequency（RF）-SQUID qubit with an overdamped resistively shunted direct-current（DC）-SQUID magnetometer is used to continuously monitor the state of the qubit. The circuit is successfully fabricated with the standard Nb/Al-Al Ox/Nb trilayer process of our laboratory and characterized in a low noise measurement system, which is capable of measuring coherent dynamics of superconducting qubits, in an Oxford dilution refrigerator. All circuit parameters are determined accurately by fitting experimental data to theoretical analysis and simulation, which allows us to make a quantitative comparison between the results of the experiment and theory.

Stochastic-periodic Homogenization of Maxwell＇s Equations with Linear and Periodic Conductivity

Stochastic-periodic homogenization is studied for the Maxwell equations with the linear ＂and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions to a class of highly oscillatory problems converges to the solution of a homogenized Maxwell equation.

Complex Maxwell's equations

A unified complex model of Maxwell＇s equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell＇s equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac＇s quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell＇s equations to include longitudinal waves.A formal analogy between this formulation and Dirac＇s equation is also discussed.

Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out： they represent the tangent surface and the normal surface fluxes of a tensor, reslpetivcly. The definitions of the divergence and the curl of a 2D surface flux of a tensor arc obtained. Maxwell＇s equations, namely, the constraction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law （ mass or fluid flux quantity and so on） and the feature of central field （or its composition）. By the feature of central field （or its composition）, the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory （ a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces） axe presented： magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell＇s equations.

A DIAGONAL SPLIT-CELL MODEL FOR THE OVERLAPPING YEE FDTD METHOD

In this paper, we present a nonorthogonal overlapping Yee method for solv- ing Maxwell＇s equations using the diagonal split-cell model. When material interface is presented, the diagonal split-cell model does not require permittivity averaging so that better accuracy can be achieved. Our numerical results on optical force computation show that the standard FDTD method converges linearly, while the proposed method achieves quadratic convergence and better accuracy.

ANALYSIS OF TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING BY A PERFECTLY CONDUCTING OBSTACLE IN A HOMOGENEOUS CHIRAL ENVIRONMENT

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved.

Analysis of the Linear Sampling Method for Boundary Reconstruction of Chiral Obstacle in Electromagnetic Scattering Problems

In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.

Well-posedness of the time-varying linear electromagnetic initial-boundary value proble

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss＇s formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES

A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.

RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS:A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS

We review time-domain formulations of radiation boundary conditions for Maxwell＇s equations, focusing on methods which can deliver arbitrary accuracy at acceptable compu-tational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.

UNIFIED ANALYSIS OF TIME DOMAIN MIXED FINITE ELEMENT METHODS FOR MAXWELL'S EQUATIONS IN DISPERSIVE MEDIA

In this paper, we consider the time dependent Maxwell＇s equations when dispersive media are involved. The Crank-Nicolson mixed finite element methods are developed for three most popular dispersive medium models： the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for all three models solved by the Raviart-Thomas-Ndd@lec spaces. Extensions to multiple pole dispersive media are presented also.

OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS

In this paper, we obtain optimal error estimates in both L^2-norm and H（curl）-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell＇s equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec＇s second type elements, we present an optimal convergence estimate which improves the best results available in the literature.

NON SPURIOUS SPECTRAL-LIKE ELEMENT METHODS FOR MAXWELL'S EQUATIONS

In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell＇s equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods （DGM） are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.

A Second Order Nonconforming Rectangular Finite Element Method for Approximating Maxwell's Equations

Abstract The main objective of this paper is to present a new rectangular nonconforming finite element scheme with the second order convergence behavior for approximation of Maxwell＇s equations. Then the corresponding optimal error estimates are derived. The difficulty in construction of this finite element scheme is how to choose a compatible pair of degrees of freedom and shape function space so as to make the consistency error due to the nonconformity of the element being of order O（h^3）, properly one order higher than that of its interpolation error O（h^2） in the broken energy norm, where h is the subdivision parameter tending to zero.

A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.

NUMERICAL RECONSTRUCTION OF SMALL PERTURBATIONS IN THE ELECTROMAGNETIC COEFFICIENTS OF A DIELECTRIC MATERIAL

The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.

AN ADAPTIVE FINITE ELEMENT METHOD FOR THE WAVE SCATTERING BY A PERIODIC CHIRAL STRUCTURE

The electromagnetic wave propagation in the chiral medium is governed by Maxwell＇s equations together with the Drude-Born-Fedorov （constitutive） equations. The problem is simplified to a two-dimensional scattering problem, and is formulated in a bounded domain by introducing two pairs of transparent boundary conditions. An a posteriori error estimate associated with the truncation of the nonlocal boundary operators is established. Based on the a posteriori error control, a finite element adaptive strategy is presented for computing the diffraction problem. The truncation parameter is determined through sharp a posteriori error estimate. Numerical experiments are included to illustrate the robustness and effectiveness of our error estimate and the proposed adaptive algorithm.