Time scales defined

By convention, available solutes are defined as those that are in, or can equilibrate with, soil solution on a time scale defined in minutes this is es.sentially an arbitrary definition but it is intended to encompa.ss solution and exchangeable ions and to exclude every other solute form. The total concentration, C, of available ions in a given soil volume is then... 

To determine how the scalar time scale defined in Eq. (15) is related to the turbulence integral time scale given in Table I, we can introduce a normalized model scalar energy spectrum (Fox, 2003) as follows ... 

Passive puff or plume In addition to the restriction on plumes discussed above, there is an along-wind dispersion time scale given by td = 2Gjur where Gx is evaluated at the endpoint distance xe. The release can usually be considered a plume if ts > 2.5 fd, where ts is the source time scale defined above, and the release can be considered a puff if td > ts. For td< ts< 2.5 td, neither puff nor plume models are entirely appropriate the predicted concentration is considered the largest of the puff and plume predictions. 

This time scale is proportional to the turbulence integral time scale defined by... 

In a fully developed turbulent flow, the rate at which the size of a scalar eddy of length l,P decreases depends on its size relative to the turbulence integral scale L and the Kolmogorov scale ij. For scalar eddies in the inertial sub-range (ij < Ip, < Lu), the scalar mixing rate can be approximated by the inverse of the spectral transfer time scale defined in (2.68), p. 42 8... 

Krt < k scalar spectral transport time scale defined in terms of the velocity spectrum (e.g., rst). 

The requirement for equilibrium should be considered first. It is necessary that region C be truly at equilibrium. Unless this region is at equilibrium, the relationship between the sensor and its immediate environment is not uniquely defined. Hence, for sensor measurements to be definitive, equilibrium must exist in region C. For region A, in areal measurement situation, equilibrium is not required to be established. It is sufficient that the pw of the immediate environment (pA) be in a steady state relationship with the sample, unchanging on a time scale defined by the investigator. 

The motion of the R1 nitroxide in a protein has contributions from the overall tumbling of the protein, the internal motions of the side chain, and fluctuations in the backbone structure. For membrane proteins such as rhodopsin, the correlation time for molecular tumbling is slow on the EPR time scale defined above and can be ignored. The internal motion of the R1 side chain is due to torsional oscillations about the bonds that connect the nitroxide to the backbone, and the correlation times for these motions lie in the nanosecond regime where the EPR spectra are highly sensitive to changes in rate. 

C 0) (t) and Q0) (t) are plotted in Figs. 7.6.1a, b. It should be noted that neither of these two functions decay to zero as z —> oo. This is because there are always molecules for which u(f) has a time-invariant projection along the axis of rotation. These functions decay on the time scale defined by t0 = (IjknT)112, the average rotational period. 

This is exactly the Peclet number defined by Eq. (5.3.25), which measures the characteristic rotational Brownian diffusion time to the time scale defined by the reciprocal of the shear rate. It is the same measure found for dilute polymer solutions with the particle radius here replacing the Flory radius for the polymer. 

The shape of a nitroxide radical CW EPR spectram reveals high sensitivity to its rotational motion in liquid solutions. Thus, it can be used as a valuable tool for monitoring the local and global dynamics of NAs on time scales defined by the EPR frequency. 

Models for Transverse Relaxation. The simplest model to describe chain statistics from the NMR point of view is a chain of freely jointed segments of fixed length (12). Such a chain maybe rescaled in several hierarchical steps according to the time scale of the motions which takes place at different space scales, compared to the time scale defined by the NMR spin interactions. All intrachain motions are assumed to be fast enough to average elementary interactions, whereas junction average positions are static. 

Coordinated Universal Time (UTC) UTC, an atomic time scale, is the basis for civil time. It is occasionally adjusted by one-second increments to ensure that the difference between the uniform time scale, defined by atomic clocks, does not differ from the earth s rotation by more than 0.9 sec. Differential A technique used to improve radionavigation system accuracy by determining positioning error at a known location and subsequently transmitting the determined error, or corrective factors, to users of the same radionavigation system, operating in the same area. 

Adsorption processes which are slow on a time scale (defined as the time it takes to measure an impedance spectrum within a reasonable frequency interval) can be monitored by impedance analysis. In Figure 6.22 such spectra are shown for the adsorption of carbon monoxide (CO, 3.7) on activated carbon (AC) Norit R1 taken at T = 298 K for a gas pressure of p = 7.5 MPa, the initial state referring to vacuum (p < 1 Pa), [6.13, 6.33]. The time it took to monitor the real part of the capacitance (ReC(v)) within the frequency interval 0.1 MHz < V <1 MHz, At was about 20 minutes. The adsorption process itself, monitored simultaneously with a magnetic suspension balance, Cp. Sect. 3.2, lasted about 24 h. However, the impedance spectra of the system showed considerable changes for a much longer time and actually have been observed for 41 h, or 2460 minutes, or 123 At. 

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