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The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of invertibility. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.
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Anomalous power-law behavior in the electrical impedance of endothelial cellular networks
In this paper, we report on the electrical impedance measurement of human endothelial cellular networks and show the existence of emergent power law behavior in its admittance. In particular, we find that the admittance scales with the frequency ω as ωα, with the exponent that varies with the degree of the disruption caused by the inflammation in the endothelial cellular network. We demonstrate that the power law of the measured electrical admittance can be understood by a simple percolation model of a large R–C (resistor–capacitor) network, which allows us to relate quantitatively and the intensity of inflammation. Our results suggest that the electrical properties of heterogeneous biomaterials, like living tissues, behave as a complex microstructural network.
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- PAR ID:
- 10594004
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 136
- Issue:
- 14
- ISSN:
- 0021-8979
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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