Time integrated flux

A second recent development has been the application 46 of the initial value representation 47 to semiclassically calculate A3.8.13 (and/or the equivalent time integral of the flux-flux correlation fiinction). While this approach has to date only been applied to problems with simplified hannonic baths, it shows considerable promise for applications to realistic systems, particularly those in which the real solvent bath may be adequately treated by a fiirther classical or quasiclassical approximation. 

Fig. 4. Physical zones of ablators. Typical time-integrated heat flux, J/m, (a) 500, (b) 5000, (c) <50 maximum instantaneous heat flux, MW/m, (a) 0.5,...

The neutron dose to graphite due to irradiation is commonly reported as a time integrated flux of neutrons per unit area (or fluence) referenced to a particular neutron energy. Neutron energies greater that 50 keV, 0.1 MeV, 0.18 MeV, and 1 MeV were adopted in the past and can be readily foimd in the literature. In the U.K., irradiation data are frequently reported in fluences referenced to a standard flux spectrum at a particular point in the DIDO reactor, for which the displacement rate was measured by the nickel activation [ Ni(np) t o] reaction [equivalent DIDO nickel (EDN)]. Early on, neutron irradiation doses to the graphite moderator were reported in terms of the bum-up (energy extracted) from imit mass of the adjacent nuclear fuel, i.e., MW days per adjacent tonne of fuel, or MWd/Ate. 

Figure 49. The time-integrated fluxes at t = 3.5 ps as a function of fico for v = 4. Taken from...

Figure 50. Time variation of the time-integrated fluxes 7,(t) for v = 4. Taken from Ref. [126].

Whereas the heat flux DSC measures the temperature difference between the sample and the reference sample, power-compensated DSCs are based on compensation of the heat to be measured by electrical energy. Here the sample and the reference are contained in separate micro-furnaces, as shown in Figure 10.6(b). The time integral over the compensating heating power is proportional to the enthalpy absorbed by or released from the sample. 

The bioaccumulated amount, time integral of the uptake flux ... 

McCarthy, J.F. Southworth, G.R. Palmer, J.A. Ham, K.D. 2000, Time-integrated, flux-based monitoring using semipermeable membrane devices to estimate the contribution of industrial facilities to regional polychlorinated biphenyl budgets. Environ. Toxicol. Chem. 19 352-359. 

For acute exposure in a specific airway, the average rate of flux to the epithelial tissue or mucus layer may be the critical quantity and is measured in micrograms per square centimeter per second (in the steady state the unit is micrograms per square centimeter per breath). Chronic effects are probably related to the time integral over the period of exposure. When sensory receptors are involved in the acute response, the local flux to the small surface areas containing the receptor sites may be crucial. 

Figure 22 displays the time-integrated mean of mass flux as function of standard volume flux of primary air for all the three wood fuels, respectively. As indicated by Figure 22, the time-integrated mean of mass flux of conversion gas exhibits a hyperbolic relationship with the volume flux of primary air. In the low range of volume fluxes the conversion gas rate increases up to a maximum. After the maximum point is passed, the mass flux of conversion gas decreases due to convective cooling of the conversion reaction. 

Figure 22 The time-integrated mean of mass flux of conversion gas...

Now let us assume that a monochromatic source of flux is placed in the plane of the entrance slit so that there is no constant phase relationship between the fields at any two given points in the slit. This, in itself, is a contradiction, because a perfect source monochromaticity implies both spatial and temporal coherence. By definition of coherence, a constant phase relationship would result. To eliminate the possibility of such a relationship, we must require the source spectrum to have finite breadth. Let us modify the assumption accordingly but specify the source spectrum breadth narrow enough so that its spatial extent when dispersed is negligible compared with the breadth of the slits, diffraction pattern, and so on. Whenever time integrals are required to obtain observable signals from superimposed fields, we evaluate them over time periods that are long compared with the reciprocal of the frequency difference between the fields. We shall call the assumed source a quasi-monochromatic source. 

To find Zw, the total flux of molecules passing through the plane (the total number per unit area per unit time), integrate to obtain the contributions from the molecules in all possible velocity ranges ... 

For a quantum mechanical system in thermal equilibrium a transport coefficient Aab may be determined from the time integral of a flux-flux correlation function [64]. 

We see that the rate constant may be determined as the time integral of the canonical averaged flux autocorrelation function for the flux across the dividing surface between reactants and products. It is also clear that we only need to calculate the flux correlation function for trajectories starting on the dividing surface, for otherwise F(p(0), q(0)) = 0 and there will be no contributions to the product formation. 

In Section 5.2, we have seen how the rate constant for a chemical reaction may be determined as a time integral of the auto-time-correlation function of the flux operator... 

In these equations fi is the coluirm mass of dry air, V is the velocity (u, v, w), and (jf) is a scalar mixing ratio. These equations are discretized in a finite volume formulation, and as a result the model exactly (to machine roundoff) conserves mass and scalar mass. The discrete model transport is also consistent (the discrete scalar conservation equation collapses to the mass conservation equation when = 1) and preserves tracer correlations (c.f. Lin and Rood (1996)). The ARW model uses a spatially 5th order evaluation of the horizontal flux divergence (advection) in the scalar conservation equation and a 3rd order evaluation of the vertical flux divergence coupled with the 3rd order Runge-Kutta time integration scheme. The time integration scheme and the advection scheme is described in Wicker and Skamarock (2002). Skamarock et al. (2005) also modified the advection to allow for positive definite transport. 

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