Modified spectral density

Let us consider again the transitions between 5, (0) to Sq (fiJj, —0)f) at an energy h(0. The modified spectral density of the radiative decay rate is... 

The modified spectral density is obtained (as for the free-space case)... 

We shall modify in the present section the general definition of the spectral density (1), according to... 

Noise correlation function, 22 113 Noise equivalent power (NEP), 19 133 Noise spectral density, 19 134-135 Nomarski, Georges, 16 480 Nomarski-modified Wollaston prism, 16 481... 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

Bertini and co-workers 119) and Kruk et al. 96) formulated a theory of electron spin relaxation in slowly-rotating systems valid for arbitrary relation between the static ZFS and the Zeeman interaction. The unperturbed, static Hamiltonian was allowed to contain both these interactions. Such an unperturbed Hamiltonian, Hq, depends on the relative orientation of the molecule-fixed P frame and the laboratory frame. For cylindrically symmetric ZFS, we need only one angle, p, to specify the orientation of the two frames. The eigenstates of Hq(P) were used to define the basis set in which the relaxation superoperator Rzpsi ) expressed. The superoperator M, the projection vectors and the electron-spin spectral densities cf. Eqs. (62-64)), all become dependent on the angle p. The expression in Eq. (61) needs to be modified in two ways first, we need to include the crossterms electron-spin spectral densities, and These terms can be... 

Fig. 3 Absorption spectra of one sample of B850 calculated with different methods for an Ohmic spectral density with / = 3.37 and usc = 0.027 eV. Left Methods with Markov approximation, i.e. Redfield theory with and without secular approximation and TL method. Right TL with and without Markov approximation, TNL and modified Redfield method. (Reproduced from Ref. [37]. Copyright 2006, American Institute of Physics.)...

Interestingly, due to the linearity of the generalized Langevin equation (22), the same effective temperature T,eff(( ) can consistently be used in the modified Nyquist formula linking the noise spectral density C/ /- ([Pg.313]

Figure 1. The agreement of the spectral density of voltage fluctuations from valinomycin-modified phospholipid bilayers at equilibrium conditions (13, 14) with the Nyquist relation 1. An aqueous 0.01-M KCl solution at 33 °C was used in the experiments. Bilayer direct current resistances and valinomycin solution concentrations were 0.52-Mfl and 1.5 X 10 8 M (l), 0.19 Mfl and 5 X 10 8 M (2), and 0.055 Mi2 and 1.5 X 10 7 M (3). Solid lines are drawn in accordance with relation 1 for the impedance of a parallel resistance-capacitance (RC) circuit using foregoing resistance values and a value of membrane geometrical capacitance.

Nonequilibrium noise generated by carrier-mediated ion transport was studied in lipid bilayers modified by tetranactin (41). As expected, deviations of measured spectral density from the values calculated from the Nyquist formula 1 were found. The instantaneous membrane current was described as the superposition of a steady-state current and a fluctuating current, and for the complex admittance in the Nyquist formula only a small-signal part of the total admittance was taken. The justification of this procedure is occasionally discussed in the literature (see, for example, Tyagai (42) and references cited therein), but is unclear. 

This frequency response functions enter the modified Priestley s formulation of Sec. 2, resulting in evolutionary output power spectral density functions for deflection and moments, respectively. We... 

A Computer-oriented algorithm for nonstationary random vibrations of polygonal Kirchhoff-plates has been developed. A fast and accurate BEM for calculation of undamped frequency response function has been used. Light hysteretic damping has been introduced subsequently, and the modified spectral Priestley-formulation has been applied in order to calculate evolutionary output power spectral density functions. It is hoped that this solution strategy will be of interest for workers in the field of probabilistic structural dynamics. 

Note that the damping rate [r q )] has been modified by the contribution of translational diflFusion D) from the form of Eq. (6.21) under the one-constant approximation. The reduced spectral density ji j (a ) due to director fiuctuations is obtained by Foirrier transformation of q (t)... 

Brochard [6.6] and Blinc et al. [6.37] extended the one-constant approximation to include the set of anisotropic elastic constants and viscosity coefficients. Suppose that the different elastic constants and viscosities are retained while effects of magnetic field and translational diffusion are not included in Eqs. (6.21)-(6.22). The reduced spectral density [Eq. (6.30)] is modified by using an ellipsoidal volume over the q space with two high-frequency cutoffs Qzc and q c [6.38],... 

Fig. 2 Envelope curves of acceleration noise power spectral density (in units of dB relative to 1 (m/s ) / Hz) as a function of noise period (according to Peterson 1993). They define the new global high (NHNM) and low noise models (NLNM) which are currently the accepted standard curves for generally expected limits of microseismic noise depending on period. No single station site, however, meets in the whole period range the NLNM or NHNM. However, some exceptional seasonal, diurnal, or local site noise conditions may exceed these limits. Also shown are for the NLNM the related curves calculated for the displacement and velocity power spectral density P,j and Py in units of dB relative to 1 (m/s) /Hz and 1 m /Hz (Modified version of Fig. 2 from P. Bormann 1998 Springer with kind permission from Springer Science + Business Media)...

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