Bl Bas Michielsen

A statistical characterization of resonant electromagnetic interactions with thin wires : variance and kurtosis analysis

A statistical characterization of random electromagnetic interactions affected by resonances is presented. It hinges on the analysis of the variance and the kurtosis to assess the intensity of the resonances. The method is illustrated by the study of a randomly varying thin wire modeled by a Pocklington integral equation.

Experimental validation of the stochastic model of a randomly fluctuating transmission-line

A modeling method is proposed to quantify uncertainties affecting electromagnetic interactions. This method considers the uncertainties as random and measures them thanks to probability theory. A practical application is considered through the case of a transmission-line of varying geometry, illuminated by a fixed electromagnetic field. The results of the stochastic numerical model are compared to the measurements performed on the transmission-line setup.

Estimates in first order approximations to electromagnetic boundary integral equations on stochastic surfaces

In this paper, we address the problem of computing estimates of the variability of “observables.” Observables are measurable quantities which are defined as the integral of an appropriately chosen electromagnetic field against a (current-) distribution. The latter is obtained by solving a boundary value problem. In the case of an uncertain boundary geometry, the current distribution underlying the observable computation is a stochastic distribution whereas the field evaluated on this distribution to define the observable remains deterministic. The result is a stochastic observable of which the variance provides an interesting measure of the spreading of its values. Here, we develop a technique for explicitly computing the covariance operator of the stochastic distribution corresponding to the boundary value problem with uncertain geometry. The variance of observables can be computed directly from this operator as a bilinear form evaluated on the field defining the observable.

Semi-intrusive quantification of uncertainties in stochastic electromagnetic interactions: Analysis of a spectral formulation

A stochastic approach is presented to statistically characterise uncertainties in electromagnetic interactions. A spectral definition of the observables allows for the assessment of the effect of a randomly deformed device independent of the incident field.