Lorentzian spectrum

This is a direct generalization of the Hubbard relation (2.27) to the case ft) 0. It is actually an algorithm for extraction of a wide spectral component which forms the pedestal. Bi-Lorentzian spectrum (2.54) may serve as an example of the above algorithm realization. Using its correlation function (2.53) in (2.72), we find TV in addition to G(. 

Brownian motion of a single molecular species results in a Lorentzian spectrum defined by the relationship ... 

The single relaxation time approximation corresponds to a stochastic model in which the fluctuating force on a molecule has a Lorentzian spectrum. Thus if the fluctuating force is a Gaussian-Markov process, it follows that the memory function must have this simple form.64 Of course it would be naive to assume that this exponential memory will accurately account for the dynamical behavior on liquids. It should be regarded as a simple model which has certain qualitative features that we expect real memory functions to have. It decays to zero and, moreover, is of a sufficiently simple mathematical form that the velocity autocorrelation function,... 

The single relaxation time approximation can be applied to the angular momentum memory function in a Completely analogous way.68 Kj(t) can be interpreted as the time-correlation function of the random torque acting on the molecule. If this random torque has a Lorentzian spectrum or, more restrictively, is a Gaussian-Markov process, Kj(t) is exponential. 

We detected the saturated fluorescence emitted by a beam of 23S metastable atoms as they cross at right angle the slave laser light. A 1015 atoms/s.sterad flux of metastable helium atoms was produced by electronic collisions in a DC discharge of a helium atomic beam, similar to that described in [15]. To improve the precision of the linecenter determination, we increased the signal-to-noise ratio S/N by means of standard frequency modulation the third harmonic demodulated lineshape is shown in Fig. 4. The function expected for a Lorentzian spectrum was fit and linecenters were calculated with an uncertainty ranging between 10 kHz and 20 kHz, that is consistent with the observed S/N, mainly limited by the stability of the reference frequency and of the metastable helium beam. The reproducibility was two or three times worse than the uncertainty,... 

D2. BeUdc, Exact analytical expressions for any Lorentzian spectrum in the fast Fade transform (FPT), J. Comp. Meth. Sci. Eng. 3 (2003) 109. 

The excitation transfer of an atom with like atoms (Case 1) can affect the spectrum. If either an upper or a lower state is connected to the ground state by optically allowed transitions and these excited atoms are surrounded by ground state like-atoms, the Lorentzian spectrum half-line width (w) of the transition is expressed in terms of k (1, 5) as... 

A model membrane system that also shows reproducible and clear 1/f behavior was described by Bezrukov and Brutyan (76). Fluctuations of current through lipid bilayers with one-sided application of three different polyene antibiotics of very close chemical structure (i.e., amphotericin B, nystatin, and mycoheptin) were studied. For one-sided application these antibiotics form channels that are weakly bound to the membrane as compared with the channels of the two-sided action. All three compounds produced pronounced noise component with spectral distribution of 1/f type (Figure 8). It was found that the noise intensity scales as the ratio of single channel conductances for amphotericin B, nystatin, and mycoheptin namely, hA hN hM = 10 5 1. For mycoheptin the spectrum is described by the function 1/f0-86 over the whole frequency range used. With two-sided application of these antibiotics, channels are more stable and strongly bound to the bilayer. In this case, significantly lower noise intensities were found the spectrum for amphotericin B was described by a single Lorentzian spectrum of relatively small amplitude (63). 

Yet another attractive approach is to artificially broaden the resonance width T, by using the Lorentzian spectrum (17)... 

At both wavebands, EPR PAni-TSA demonstrates Lorentzian spectrum with Dyson contribution due to the appearance of skin-layer on its surface (Figure 1.17). The temperature dependences of the linewidth of the vacuum-processed PAni-TSA sample determined at both 3 cm and 2 mm wavebands EPR are also presented in Figure 1.17. 

Standard deviation, whereas Dj and F represent the height and width of the Lorentzian spectrum, respectively. The quantity 4> is the error function. It has been assumed for simplicity that all spectral widths are identical, i.e., yj=yj+i= y and rj=Fj+ i=F similar but more complex expressions are obtained when this is not the case. 

This equation was used to calculate the absorption spectra as a function of the parameters a=Cl /fi= l/z and D=a where is the relaxation time of the ensemble average of and (jx y=k T ntCl. Examines of spectral shapes computed in this way are shown in Figure 6.12 for a fixed value of D and a range of values of ot. From Equation (6.17) it can be seen that for very smaD values of a, a Lorentzian spectrum of linewidth F+2k D, as expected for a freely diffusing particle, is obtained. For large a (a/F=QV F> 1)... 

The variance of the recorded fluctuations is equal to the integral of the power spectrum over the recording bandwidth and it is measured with much greater accuracy than the spectral distribution However, undesired noise contributions cannot be easily subtracted from the total variance without the help of the spectral analysis. Furthermore, the measured variance is an underestimation of the actual variance, due to bandwidth limitations (the integral of Lorentzian spectrum up to its cut-off frequency yields only 50% of the variance). 

In squid giant axons potassium and sodium current noise spectra were simply fitted with the sum of a Lorentzian spectrum plus a 1/f component (13) and their analysis was confined to the verification that the cut-off frequencies of the Lorentzians were in qualitative agreement with what expected from a simple HH kinetics. 

At wavelengths about 10.6 pm and at temperatures of 295 K the knee frequency reached 100 MHz [385]. Ini-xAlxSb and Hgi xCdxTe detectors were investigated and in both types a strong correlation was established with their dark current. At temperatures below 100 K only g-r component appeared, at about 140 K noise with Lorentzian spectrum appeared, typical for excess noise due to g-r processes at... 

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