Time average contribution

Proton-transfer processes in solution are generally characterized by a low interconversion barrier. Measurements at laboratory temperature typically fall into a fast-exchange regime. Under these conditions, the experimentally observed NMR parameters represent the time-averaged contributions of the individual forms. Exact knowledge of the NMR parameters of the individual components is essential for determining... 

Very recently, a low-temperature NMR study of tautomerism in purine derivatives has been conducted. The temperature dependences of the H NMR spectra were studied in DMF- /j solution. Two sets of signals were observed in the NMR spectra of the two purine derivatives at 213 K, whereas at laboratory temperature, there was only a single set of signals, reflecting the time-averaged contribution of the two components. Based on the characteristic values of the and N chemical shifts and the three-bond scalar coupling constants, the two components were determined to be the N -H and N -H tautomers. The NMR parameters obtained for the two tautomers of 6-methoxy purine are shown in Fig. 12. 

Example 3-7 Consider the steady-state continuity equation for an incompressible fluid in cylindrical coordinates. Using the turbulence representations for the velocities, determine the time-average contributions to this representation. 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

The focus of RANS simulations is on the time-averaged flow behavior of turbulent flows. Yet, all turbulent eddies do contribute to redistributing momentum within the flow domain and by doing so make up the inherently transient character of a turbulent-flow field. In RANS, these effects of the full range of eddies are made visible via the so-called Reynolds decomposition of the NS equations (see, e.g., Tennekes and Lumley, 1972, or Rodi, 1984) of the flow variables into mean and fluctuating components. To this end, a clear distinction is required between the temporal and spatial scales of the mean flow on the one hand and those associated with the turbulent fluctuations on the other hand. 

The second contribution in eq. [8] is the square-electric-field (SEF) effect, where (E2) is the time-averaged square of the electric field E (76) ... 

To perform a PO analysis of nonadiabatic quantum dynamics, we employ a quasi-classical approximation that expresses time-dependent quantities of a vibronically coupled system in terms of the vibronic POs of the system [123]. Considering the quasi-classical expression (16) for the time-dependent expectation value of an observable A, this approximation assumes that the integrable islands in phase space represent the most significant contributions to the dynamics of the observables considered [236]. As a consequence, the short-time dynamics of the system is determined by its shortest POs and can be approximated by a time average over these orbits. Denoting the A th PO with period 7 by qk t),Pk t) we obtain [123]... 

If r j is assumed to be constant, i.e., the directly bonded protons provide the dominant contribution, and 0j j(t) is only time dependent, the time averaged local field is given by... 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

In this paper we have shown that there is no simple answer to the question posed in the title of this paper. Primary carbon particles dominate the carbonaceous aerosol under certain conditions while substantial secondary carbon may be present at other times. However, the importance of secondary carbon contributions is much less obvious when 24-h samples are examined. With shorter time averaged samples (e.g. 6-h or less) the increase in secondary carbon formation can be more easily detected. Secondary carbon appears to be more important in the summer rather than winter, in the afternoon father than the early morning, and in LA rather than St. Louis. It should be noted that these conditions of increased secondary carbon aerosol formation are also more favorable conditions for photochemical reactions. Our detailed emission inventory Indicates that much more primary carbon exists in the urban aerosol than was thought previously. This is in agreement with the data. Our analysis shows that even on the very smoggy days in the ACHEX study there were times when primary carbon dominated the carbonaceous aerosol. 

The equation of motion and the equation of energy balance can also be time averaged according to the procedure indicated above (SI, pp. 336 et seq. G7, pp. 191 et seq. pp. 646 et seq.). In this averaging process there arises in the equation of motion an additional component to the stress tensor t(,) which may be written formally in terms of a turbulent (eddy) coefficient of viscosity m(I) and in the equation of energy balance there appears an additional contribution to the energy flux q(1), which may be written formally in terms of the turbulent (eddy) coefficient of thermal conductivity Hence for an incompressible fluid, the x components of the fluxes may be written... 

In paramagnetic systems, there can be non-negligible contributions to the CSA of NH nuclei from their dipolar coupling with the time-averaged magnetic moment of the electron (see Section 3.6). As a consequence, it cannot be predicted a priori which will be the sharpest component for each NH peak in a heterocorrelated experiment, and TROSY is less useful, unless four different TROSY spectra are acquired by selecting a different component each time [27]. 

---