Implementation of the Numerical Laplace Transform: A Review Task Force on Frequency Domain Methods for EMT Studies, Working Group on Modeling and Analysis of System Transients Using Digital Simulation, General Systems Subcommittee, IEEE Power Engineering Society

Moreno, P.; Ramirez, Abner

doi:10.1109/tpwrd.2008.923404

Cited by 161 publications

(27 citation statements)

References 22 publications

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“…In this situation, the Laplace transform is the optimal method to explore the complex spectrum [19]. We essentially identify three distinct regimes on the basis of symmetric spatial modes participating in the field spectrum.…”

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confidence: 99%

Locally parity-time-symmetric and globally parity-symmetric systems

et al. 2016

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We introduce a new class of systems holding Parity Time (PT)-symmetry locally whereas being globally Psymmetric. The potential is globally symmetric, U=U(|r|), and fulfills PT-symmetry with respect to periodically distributed points r 0 : U(|r 0 +r|)=U*(|r 0 -r|) being r 0 ∫ 0. We show that such systems hold novel properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, r=0, when the coupling of outward to inward propagating waves is favored. We explore such general potentials in 1D and 2D, which could have actual realizations in different fields, in particular in optics, combining gain/loss and index modulations in nanophotonic structures. As a direct application, we show how to render a broad aperture VCSEL into a bright and narrow beam source.PACS numbers: 78.20. Bh, 42.25.Bs PT-symmetric systems, introduced as a curiosity in quantum mechanics [1,2], are recently being explored in the field of optics, acoustics, plasmonics or Bose-Einstein condensates [3][4][5][6][7][8]. A necessary condition for a system to be PT-symmetric is that the complex potential fulfills U(r)=U* (-r). Such complex systems with real spectra may support novel unexpected properties [9][10][11].Most PT-symmetric systems can be regarded as belonging to two limiting situations of complex periodic potentials. On one extreme, there are purely real-valued potentials holding real periodic modulations in space; which potential, in the simplest harmonic modulation case, reads: U(r) = n Re cos(qx), being q the spatial period of the modulation and n Re its amplitude. On the other extreme, we find purely imaginary potentials only exhibiting gain-loss modulations, which in the simplest harmonic case may be expressed as: U(r) = n Im cos(qx). Both limits lead to a symmetric coupling of resonant modes, i.e. the two counter-propagating modes with wavevector |k|, exp( ) ikx  and exp( ), ikx are coupled symmetrically at resonance, for 2 q k  . The most peculiar situation arises when both the real and imaginary parts of the potential are simultaneously modulated, with a / 2   phase shift: U(r) = n Re cos(qx) + n Im sin(qx). When both modulations are balanced, n Re = n Im , the complex potential can be simply expressed as: U(r) = n exp(±iqx), which evidences that the coupling becomes strongly unidirectional. E.g. for such a complex modulation the left-propagating mode exp(, is efficiently coupled to the right propagating mode, exp( ), ikx  but not vice versa. The point n Re = n Im is precisely the so-called phase transition, separating two extreme situations. Mathematically, the coupling between left/right propagating modes is conveniently described via linear coupling matrices, M = {{0,n Re +n Im },{n Re -n Im ,0}} which at the PT-phase transition point degenerate to M ={{0,2n},{0,0}}. Generally, in the presence of several modes (or mode continuum) the situation becomes more engaged, however the phase transition separating the two extreme limits of ...

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confidence: 99%

Locally parity-time-symmetric and globally parity-symmetric systems

et al. 2016

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“…the minimum value among Eqs. (15)- (17). Then decide that the unknown appliance X1 belongs to group G A , G B or G C accordingly under the acceptance that the min J ı indicates the minimum distance of the unknown appliance X1 from the candidate group.…”

Section: Identification Proceduresmentioning

confidence: 99%

Development of distinct load signatures for higher efficiency of NILM algorithms

Bouhouras

Milioudis

Labridis

2014

Electric Power Systems Research

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“…To get e d (r,t) the scattered field in time domain (or the local field inside the object), one needs to compute the inverse [20]. At the cost of introducing manageable truncation and discretization errors, f (t) can now be computed efficiently via inverse fast Fourier transform (FFT).…”

Section: B Dda In Time Domainmentioning

confidence: 99%

“…Finding this β max is not easy and remains an empirical process. Wilcox [20,21] proposed the following value:…”

Section: B Dda In Time Domainmentioning

confidence: 99%