Search results for "Maxwell's equation"
showing 10 items of 40 documents
Transmission line meshes for computational simulation of electromagnetic modes in the Earth's atmosphere
2007
PurposeTwo transmission line meshes to simulate electromagnetic waves in the Earth's atmosphere are developed, one with the link transmission lines connected in parallel and the other with connections in series.Design/methodology/approachThe equations describing propagation of waves through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in a spherical cavity with lossy dielectric material between the external conducting surfaces, respectively.FindingsThe transmission line meshes are used for a numerical study of the natural electromagnetic noise due to lightning discharges in the Earth‐ionosphere cavity.Originality/valueThe numerical algorithm f…
On new ways of group methods for reduction of evolution-type equations
2005
AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.
Partial data inverse problems for Maxwell equations via Carleman estimates
2015
In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.
Symmetries and Covariance of the Maxwell Equations
2012
Already within a given, fixed division of four-dimensional spacetime into the space where experiments are performed, and the laboratory time variable, Maxwell’s equations show interesting transformation properties under continuous and discrete space-time transformations. However, only the action of the whole Lorentz group on them reveals their full symmetry structure. A good example that illustrates the covariance of Maxwell’s equations is provided by the electromagnetic fields of a point charge uniformly moving along a straight line.
On the Theory of Domain Structure of Disordered Ferroelectrics
2009
We present a comprehensive analysis of domain structure formation in ferroelectric phase of incipient ferroelectrics with off-center dipole impurities like KTaO 3 :Li, Nb,Na. Our analysis is carried out on the base of effective free energy of disordered ferroelectrics, derived by us earlier. This free energy permits to apply the standard approach to domain structure calculation. Using coupled system of Maxwell equations with those obtained by minimization of above free energy, we calculate the physical characteristics of domain structure as functions of impurity dipoles concentration n. Our theory can be easily generalized for arbitrary temperature and crystal shape including thin films.
On the use of a meshless solver for PDEs governing electromagnetic transients
2009
In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
2006
AbstractIn this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of elec…
Quantitative prediction of effective material properties of heterogeneous media
1999
Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…
Automated Stress Separation Along Stress Trajectories
2007
A procedure for the separation of principal stresses in automated photoelasticity is presented. It is based on the integration of indefinite equations of equilibrium along stress trajectories, also known as Lame-Maxwell equations. A new algorithm for precise and reliable stress trajectory calculation, which is an essential feature of the procedure, has also been developed. Automated stress separation is carried out along stress trajectories starting from free boundaries. Experimental tests were performed on a disc in diametral compression and on a ring with internally applied pressure. Full-field principal stress values were obtained and results were compared with those from the theory of e…
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.