Spectral functions function

McCain D 0 and Markley J L 1986 Rotational spectral density functions for aqueous sucrose ... 

The emissivity, S, is the ratio of the radiant emittance of a body to that of a blackbody at the same temperature. Kirchhoff s law requires that a = e for aH bodies at thermal equHibrium. For a blackbody, a = e = 1. Near room temperature, most clean metals have emissivities below 0.1, and most nonmetals have emissivities above 0.9. This description is of the spectraHy integrated (or total) absorptivity, reflectivity, transmissivity, and emissivity. These terms can also be defined as spectral properties, functions of wavelength or wavenumber, and the relations hold for the spectral properties as weH (71,74—76). 

We seek the poles of the spectral function g(E) given by (3.7). In the WKB approximation the path integral in (3.7) is dominated by the classical trajectories which give an extremum to the action functional... 

Here we shall describe how the periodic-orbit theory of section 3.4, relating the energy levels with the poles of the spectral function g E), can be extended to two dimensions. For simplicity we shall exemplify this extension by the simplest model in which the total PES is constructed of two paraboloids crossing at some dividing line. Each paraboloid is characterized by two eigenfrequen-cies, o + and [Pg.72]

The energy spectral density function (or power spectrum) P f) is given by the absolute square of P f) ... 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

If the resolving capacity of the instruments is ideal then vibrational-rotational absorption and Raman spectra make it possible in principle to divide and study separately vibrational and orientational relaxation of molecules in gases and liquids. First one transforms the observed spectrum of infrared absorption FIR and that of Raman scattering FR into spectral functions... 

In quantum theory as well as in classical theory, linear absorption of light at frequency co is described by a spectral function... 

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

We can consider EMS to be a direct probe for the energy-momentum spectral density function... 

Thus they were able to calculate the velocity intensity from the mass-transfer intensity and the spectral distribution function of mass-transfer fluctuations. By measuring and correlating mass-transfer fluctuations at strip electrodes in longitudinal and circumferential arrays, information was obtained about the structure of turbulent flow very close to the wall, where hot wire anemometer techniques become unreliable. A concise review of this work has been given by Hanratty (H2). 

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

The relevant contribute of relaxation measurements on the use of NMR spectroscopy in studying interactions can be argued by considering the relationship between relaxation rates and spectral density function being the latter related to the correlation time, which accounts for the molecular motion. Therefore, spin-lattice and spin-spin can be used to probe interactions between, in principle, every species bearing an active NMR nucleus. 

The modulation index is related to the transmission spectra of the gas-filled reference cell, TRef( ), the measurement cell, with its unknown gas concentration, Ty Ca,(/.), and the optical filter, F(/.), all of which are shown in Equation 1. If required, the source spectra can also be taken into account, by using additional spectral functions (although this will usually have little spectral variation over the linewidth of the gas band) ... 

With analogy to electric circuits, a transfer function of the antenna can be calculated and the response of the antenna to an incoming wave obtained. The output signal is usually expressed as antenna cross-section. It is defined as the ratio between the total energy absorbed by the antenna and the incident spectral density function of the incident wave. In the case of Nautilus antenna (2300 kg, 3 x 0.6 m) the cross-section is of the order of 10 25m2 Hz. 

While the assumption of an isotropic rotational motion is reasonable for low molecular weight chelates, macromolecules have anisotropic rotation involving internal motions. In the Lipari-Szabo approach, two kinds of motion are assumed to affect relaxation a rapid, local motion, which lies in the extreme narrowing limit and a slower, global motion (86,87). Provided they are statistically independent and the global motion is isotropic, the reduced spectral density function can be written as ... 

Transitions between superbarrier states (a > N, see Fig. 4.4) involve nondiagonal in cr elements of the density matrix which give, at AU > T, a small contribution to the spectral function for frequencies of the order a>h + 0cr - 0spectral function at frequencies near co, we can neglect this contribution. 

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