Concentration, integral

Equimolar Counterdiffusion in Binary Cases. If the flux of A is balanced by an equal flux of B in the opposite direction (frequently encountered in binary distillation columns), there is no net flow through the film and like is directly given by Fick s law. In an ideal gas, where the diffusivity can be shown to be independent of concentration, integration of Fick s law leads to a linear concentration profile through the film and to the following expression where (P/RT)y is substituted for... 

Maximum concentrations, integrated exposure values, inhaled dose values... 

It was not until the late 1970s that the importance of the nitrate radical was recognized when it was first reported by Noxon and co-workers (1978) in terms of its total column abundance, i.e., the concentration integrated through a column extending through the atmosphere from the earth s surface (see Chapter ll.A.4a). N03 was subsequently confirmed to be in the troposphere by Noxon et al. (1980) and by Platt and coworkers (1980, 1984) in polluted atmospheres and rural continental air. 

The use of the sun or moon as the light source allows one to measure the total column abundance, i.e., the concentration integrated through a column in the atmosphere. This approach has been used for a number of years (e.g., see Noxon (1975) for NOz measurements) and provided the first measurements of the nitrate radical in the atmosphere (Noxon et al., 1978). As discussed later in this chapter, such measurements made as a function of solar zenith angle also provide information on the vertical distributions of absorbing species. Cloud-free conditions are usually used for such measurements as discussed by Erie et al. (1995), the presence of tropospheric clouds can dramatically increase the effective path length (by an order of... 

The determination of the distribution of the LVRPA requires the use of some type of radiative transfer model. In the case of transparent pollutants, it can be considered that Cl depends on Ti02 concentration (Qatai) only, and not on the concentration of the pollutant, since it is the former component which absorbs and scatters radiation. This allows imcoupling the radiation problem from the degradation kinetics when Equation (13) is solved that is, one can first evaluate and then, independently of the value of the pollutant concentration, integrate F2(Cl) over the reactor volume. Once this quantity has been calculated, its numerical value is taken as a constant in Equation (13), which can now be solved to obtain the evolution of Cp av... 

Within a limited range of oxidation, where E ( /[S,]) depends on neither the degree of ozonation nor the ozone concentration, integration of equation 22 yields... 

Concentration Integration Consecutive Acquisition Counts/ug/16 msec Integration... 

Concentration, Integration Peak Height, Peak Area, SNR... 

Figure 16. FACTS (Griffiths, 2000)/UDM (Hall et al., 2003) simulations of the release of a tracer over (a) flat terrain, (b) hilly terrain and (c) hilly terrain with buildings, all other conditions being equal. The contours are of dosage, i.e. tracer concentration integrated through time...

This equation is the same as Eq. (8.67) except that the time is now called fj instead of t. The limits on the two definite integrations must be done correctly. If the lower limit of the time integration is zero, the lower limit of the concentration integration must be the value of the concentration at zero time. The upper limit is similar. ... 

The deactivation model allows calculation of the rate of deactivation given the temperature and the activity of the catalyst (via site concentrations). Integration of the rate permits computation of the variation in activity with time. The model is incorporated into a reformer code by making the quasi-steady state assumption the rate of deactivation is slow so that the species and temperature profiles in the reformer are determined by the existing activity profile of the catalyst. 

For the measurements, about 100 crystals are placed in an optical vacuiun cuvette connected to a vacuum system consisting mainly of a gas reservoir, a pressure sensor, and a turbo-molecular pump. The system allows the sor-bate pressure in the cuvette to be changed rapidly (a step change initiating sorbate uptake or release) or to be maintained constant. The concentration integrals are measured of an individual crystal. 

Fig. 37 profile of methanol InEquilibrium intracrystalline concentration profile of methanol in a CrAPO-5 crystal. The color intensity is proportional to the integrals of local concentration in the y direction (a) and z direction (b). Darker regions correspond to larger concentration integrals. x,y, and z are the crystallographic directions (the channel direction is z)... 

Fig. 39 The mean concentration integrals I recorded by FTIR (diamonds) and interference microscopy (points) along the y direction for x values between 35 and 55 xm x, y, and z are the crystallographic directions...

Fig.40 Intracrystalline concentration profiles of water in CrAPO-5 (al-3) and SAPO-5 (bl-3) crystals integrated along the y direction under equilibrium with water vapor at 1 mbar (al, bl, a3, b3) and 20mbar (a2, b2). The profiles under the pressure of 1 mbar were recorded after the change of the water pressure from 0 to 1 mbar (al, bl) and from 20 to 1 mbar (a3, b3). The profiles are shown for only the crystal surface marked in c. The channels run along the z axis. Darker regions correspond to higher concentration integrals...

Figure 46b and c provide an overview of the observed evolution of the molecular concentration (integrated in the x direction) during molecular uptake, namely the evolution over the total y-z plane (c) as well as, for clarity, selected profiles in the z direction (b) and / direction (d) [88,90]. These latter two sets of profiles help us to understand that the time dependence of the observed integral concentrations may be easily explained by assuming a two-stage process, namely a first fast one during which the rooflike... 

Fig. 51 Transport diffusivity calculated from the profiles in the y and z directions [92], Analyzed concentration profiles are at 330, 350, and 370 s, where the concentration fronts propagating from opposite faces have not yet overlapped. The thin lines represent the analytical dependence of the diffusivities which yields excellent agreement with the measured concentration integrals (standard deviation a = 0.006)...

Since these catastrophic events were temporal and episodic, it was difficult to estimate the sediment transport due to individual wind storms. The calculation of SPM variation was, therefore, based on all grids and anchor stations investigations at stations E3 and B1 in the BH98 and BH99 cruises. The concentrations of resuspended SPM were estimated to be 1.97 4.48 mg/L at station E3 and 2.53 7.82 mg/L at station B1 by calculation of the variation of SPM concentrations integrated over the water depth. The phosphate and silicate loads at stations E3 and B1 were calculated by integrating phosphate and silicate concentrations over the water depth, which showed that released nutrients after resuspension could account for 1% for phosphate, 3% 6% for silicate, Q.2% 0.4% for nitrate and 4% 9% for ammonium at station E3, and 4% 52% for phosphate, 4% 83% for silicate, 2% 6% for nitrite, 0.6% 28% for nitrate and 2% 16% for ammonium at station Bl. The difference between stations E3 and Bl was due to the fact that the resuspension released nutrients at station E3 were from experiments at a constant solid-solution ratio, while those at station Bl were from the maximum release experiments at station Bl. It was clear that nutrient loads in the water colmnn were affected by resuspension of sediment, especially in shallow water areas. Resuspension... 

The area under a chromatographic peak, a spectroscopic band, or in thermal analysis is often directly proportional to the analyte concentration. Integration of signals is, therefore, important for quantitative data evaluation. 

An intrinsic semiconductor does not possess impurities. Each valence band electron that is excited enough to transfer to the conduction band leaves behind a hole carrying a positive charge as a result, the concentrations in electron n and in hole p are equal, which is expressed as n = p = u u is the intrinsic carrier concentration. Integrating [3.20] and [3.21] yields the following relations for electron and hole concentrations ... 

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