Localization and the invariant probability measure for a structural dynamic system

Kissel, Glen J.

doi:10.1117/12.817760

Cited by 3 publications

(2 citation statements)

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“…As already demonstrated through earlier applications of the Anderson localization theory to a variety of periodic dynamic systems (see, for example, [3]- [5]), this average exponential decay has been shown to provide for an accurate quantitative measure of the disorder-induced degradation of the response attributes of the periodic structure. In earlier studies, we have demonstrated how this technique can be used to analyze the effects of statistical material/geometric disorder in the electromagnetic properties of transmission-line-based metamaterial structures, where lumped circuit elements and transmission-line-based structures suffice for their modeling [6].…”

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confidence: 89%

Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides

Ochoa

Cangellaris

2012

IEEE Trans. Microwave Theory Techn.

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A methodology is presented for the fast electromagnetic analysis of the impact of statistical disorder on the transmission properties of periodic waveguides. The proposed methodology makes use of ideas from the Anderson localization theory to derive closed-form expressions for the calculation of an effective exponential decay ratio that quantifies the impact of periodicity disorder on the transmission properties of the waveguide. With regard to the quantification of the statistics of periodicity disorder from data obtained from a limited number of manufactured devices, a nonparametric probability density estimation process is examined and found to be satisfactory for our purposes. The computational efficiency of the proposed method over brute-force MonteCarlo-based alternatives is demonstrated through specific examples involving a periodically loaded parallel-plate waveguide. Furthermore, this numerical study is used to examine the accuracy of calculating the overall change in the propagation constant of the structure due to several sources of disorder as the sum of the changes calculated with each one of the sources of disorder considered individually.

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confidence: 89%

Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides

Ochoa

Cangellaris

2012

IEEE Trans. Microwave Theory Techn.

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“…This approach, which makes use of the Anderson localization theory [2], leads to the computationally-efficient calculation of an average exponential decay per unit cell for the transmitted wave, which is also known in the solid state physics literature as localization factor. As demonstrated through its application to a variety of periodic dynamic systems (see, for example, [3], [4], and [5] for applications in the structural dynamics community), this average exponential decay has been shown to provide for an accurate quantitative measure of the disorder-induced degradation of the response attributes of the periodic structure.…”

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confidence: 99%

A methodology for expedient analysis of the impact of disorder in periodic waveguides

Ochoa¹,

Cangellaris²

2012

2012 IEEE/MTT-S International Microwave Symposium Digest

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An expedient methodology is presented for the predictive analysis of the impact of statistical disorder on the electromagnetic attributes of periodic waveguides. The proposed methodology makes use of ideas from the Anderson localization theory to derive closed-form expressions for the calculation of an effective exponential decay ratio that quantifies the impact of periodicity disorder on the transmission properties of the waveguide. The computational efficiency of the proposed method over Monte Carlo based alternatives is demonstrated through a specific example involving a periodically-loaded parallel plate waveguide.

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Fast analysis of the impact of interconnect routing variability on signal degradation

Ochoa

Cangellaris

2012

2012 IEEE 21st Conference on Electrical Performance of Electronic Packaging and Systems

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Localization and the invariant probability measure for a structural dynamic system

Cited by 3 publications

References 20 publications

Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides

Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides

A methodology for expedient analysis of the impact of disorder in periodic waveguides

Fast analysis of the impact of interconnect routing variability on signal degradation

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