Folding frequency

Figure 3.11. (A) Correctly chosen spectral width. (B) Spectral width chosen is too narrow, so that the peaks lying beyond the Nyquist frequency fold over and give rise to erroneous signals marked a .

The negligible effect of frequency on dielectric constant and power factor from 60 to 10 Hz is particular interest. It should, however, be noted that at 10 Hz the power factor may increase about four-fold. 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

There is also inside-outside (transverse) asymmetry of the phospholipids. The choline-containing phospholipids (phosphatidylcholine and sphingomyelin) are located mainly in the outer molecular layer the aminophospholipids (phosphatidylserine and phos-phatidylethanolamine) are preferentially located in the inner leaflet. Obviously, if this asymmetry is to exist at all, there must be limited transverse mobility (flip-flop) of the membrane phospholipids. In fact, phospholipids in synthetic bilayers exhibit an extraordinarily slow rate of flip-flop the half-life of the asymmetry can be measured in several weeks. However, when certain membrane proteins such as the erythrocyte protein gly-cophorin are inserted artificially into synthetic bilayers, the frequency of phospholipid flip-flop may increase as much as 100-fold. 

Figure 1.33 The underlying principle of the Redfield technique. Complex Fourier transformation and single-channel detection gives spectrum (a), which contains both positive and negative frequencies. These are shown separately in (b), corresponding to the positive and negative single-quantum coherences. The overlap disappears when the receiver rotates at a frequency that corresponds to half the sweep width (SW) in the rotating frame, as shown in (c). After a real Fourier transformation (involving folding about n = 0), the spectrum (d) obtained contains only the positive frequencies.

Figure 1.34 (a) Reduced S/N ratio resulting from noise folding. If the Rf carrier frequency is placed outside the spectral width, then the noise lying beyond the carrier frequency can fold over, (b) Better S/N ratio is achieved by quadrature detection. The Rf carrier frequency in quadrature detection is placed in the center of the spectrum. Due to the reduced spectral width, noise cannot fold back on to the spectrum. 

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