Fig. 7: Experimental vs. simulations with ideal/nonideal components. | Nature Communications

Fig. 7: Experimental vs. simulations with ideal/nonideal components.

From: Imaging nodal knots in momentum space through topolectrical circuits

Fig. 7

a Simulated impedance map for N = 9 with ideal components specified by Supplementary Table 1 with no parasitic resistance or uncertainty, with an elevated drumhead region clearly visible. White regions denote impedance values above 600 Ω. b Contour plot of simulated impedance map for the same scenario as in (a), but with parasitic resistance RpL = 0.11 Ω, RpC = 0.03 Ω and random variation in inductor and capacitor values u [−0.01, 0.01], Zsim., and Experimentally measured impedance \({Z}_{\exp .}\) (colored crosses), see Supplementary Table 3. b Normalized error of measured points, \({\mathrm{Normalized}}\,{\mathrm{Error}}={(| {Z}_{{\mathrm{exp}} .}-{Z}_{{\mathrm{sim}}.}| /{Z}_{{\mathrm{sim}}.})}^{2}\). c Plot of the Log of expected simulated impedance, Log(Zsim.), vs. the Log of experimentally measured impedance, \({\rm{Log}}({Z}_{\exp}{.})\) (blue and red dots). The blue dots represent points in the low-lying regions, while the red dots are located near the drumhead region. The gray dashed line is the line computed by least squares regression. Gray crosses represent the mean of the simulated impedance within a 0.03 radius in k space surrounding a particular kykz point, while error bars represent the standard deviation of impedance within the 0.03 k radius of that particular kykz point, which is shown in Supplementary Tables 414. For kykz points in regions with very high local standard deviation, the gray cross may not coincide with the blue/red dots. The correlation coefficient between Log(Zsim) and \({\rm{Log}}({{\rm{Z}}}_{\exp .})\) is 0.743, and increases to 0.863 when the three borderline points with largest variance are excluded.

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