Niklas Wellander

A Floquet--Bloch Decomposition of Maxwell's Equations Applied to Homogenization

Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.

Homogenization of the Maxwell Equations at Fixed Frequency

The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic, and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calder´on operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result on the correctors. (Less)

Experimental Investigation and Mathematical Modeling of Design Parameters for Efficient Stirrers in Mode-Stirred Reverberation Chambers

In this paper, we have investigated the design parameters for efficient stirring in reverberation chambers. We have measured the efficiency of the stirrer in terms of the lowest possible frequency for which it gives a certain number of uncorrelated samples. Rotating stirrers, when rotated about their axes, generate cylindrical volumes. The impact of a change of the stirrer diameter is approximately cubic compared with the change of the stirrer height. The efficiency of stirrers that are translated is proportional to the stepping increment and to the square root of the area of projection of the stirrer on a plane orthogonal to the direction of translation

Homogenization of the Maxwell equations: Case I. Linear theory

The Maxwell equations in a heterogeneous medium are studied. Nguetsengs method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.

The maximum value distribution in a reverberation chamber

The maximum over mean distribution of received power in the FOI reverberation chamber is analyzed. The experimental results are compared with the theoretical distribution for a chi squared distributed power. For the theoretical distribution the confidence intervals are given as functions of the number of independent measurements for the maximum over mean values. The minimum number of required samples to obtain an acceptable estimate of the maximum over mean is discussed. It turns out that the number of samples should be at least greater than 20. Further the relation between statistical independence and linear correlation coefficients of measured data are discussed and analyzed. The authors make a chi square goodness of fit test to reject data that are statistically dependent. These results are compared with linear correlation coefficient evaluations.

Stirrer Blade Separation experiment in reverberation chambers

It is often claimed that it is the volume swept by the stirrers in relation to the reverberation chamber volume that is of importance for the efficiency of the stirrers. The impact of a change of the stirrer diameter is however approximately cubic compared with the change of the stirrer height. In this paper it is shown that it is mainly the periphery of the stirrers that contribute in the tuning of reverberation chambers.

Derivation of the viscous Moore-Greitzer equation for aeroengine flow

The viscous Moore-Greitzer equation modeling the airflow through the compression system in turbomachines, such as a jet engine, is derived using a scaled Navier-Stokes equation. The method utilizes a separation of scale argument based on the different spatial scales in the engine and the different time scales in the flow. The pitch and size of the rotor-stator pair of blades provides a small parameter, which is the size of the local cell. The motion of the stator and rotor blades in the compressor produces a very turbulent flow on a fast time scale. The leading order equation, for the fast time and local scales, describes this turbulent flow. The next order equations produce an axisymmetric swirl and a flow pattern analogous to Rayleigh-Benard convection rolls in Rayleigh-Benard convection. On a much larger spatial scale and a slower time scale, there exist modulations of the flow including instabilities called surge and stall. A higher order equation, in the small parameter, describes these global flow m...

The two-scale Fourier transform approach to homogenization; periodic homogenization in Fourier space

A two-scale Fourier transform for periodic homogenization in Fourier space is introduced. The transform connects the various existing techniques for periodic homogenization, i.e., two-scale convergence, periodic unfolding and the Floquet– Bloch expansion approach to homogenization. It turns out that the two-scale compactness results are easily obtained by the use of the two-scale Fourier transform. Moreover, the Floquet–Bloch eigenvalue problems for differential operators is recovered in a natural and straight forward way by the use of this transform. The transform is generalized to the (N + 1)-scale case.

Design parameters for efficient stirring of reverberation chambers

We have investigated the design parameters for stirrers in reverberation chambers. The efficiency of a stirrer is defined as the lowest possible frequency for which the stirrer gives a certain number of uncorrelated samples. Rotating stirrers generates cylindrical volumes when rotated about its axis. The impact of a change of the stirrer diameter is cubic compared with a change of the stirrer height. Another principle for stirring is to translate the stirrer along a fixed direction in space. The efficiency of translated stirrers is proportional to the stepping increment and to the square root of the area of the projection of the stirrer on a plane orthogonal to the direction of translation.

Uncertainty quantification of radio propagation using polynomial chaos

In this paper we demonstrate how so-called polynomial chaos expansions can be used to create efficient algorithms for uncertainty quantification in some classes of problems related to wave propagation in stochastic environment. We provide an example from telecommunication.