Sources partially diffuse

A diffuse source of radius is situated distance/from a fiber, as shown in Fig. 4-7(a). Each point on the surface of the source emits light in all possible directions. When these rays reach the plane of the fiber endface z = 0, the range of ray directions at each point on this plane is clearly reduced. In other words the diffuse source of finite area in Fig. 4-7(a) can be replaced by a partially diffuse source of irfinite extent which abuts the fiber in Fig. 4-7(6). 

Fig. 4-7 A diffuse source of finite radius distance/from the fiber in (a) is equivalent to a partially diffuse source of infinite extent abutting the fiber in (b).

Fig. 4-8 On-axis lens is focused onto the fiber endface and abuts a diffuse or partially diffuse source.

In the last five sections we have shown how a lens, on the one hand can increase source efficiency for collimated beam illumination of a fiber, while, on the other hand, it is ineffective at increasing the efficiency of the diffuse source. If we couple these facts with the description of the diffuse source as a superposition of collimated beams, it is evident that the efficiency of a partially diffuse source can be increased by a lens. The situation is illustrated in Fig. 4—8. We assume the step-profile fiber is weakly guiding so that 9 1, and the focal length satisfies... 

The partially diffuse source in Fig. 20-6(a) is modelled as a superposition of (coherent) beams, one of which is shown in Fig. 20-6(b). There is a random relative phase between adjacent beams, and consequently, the total power radiated by the source is found by summing the power in each beam. Assuming that the source is axisymmetric we have... 

The partially diffuse source of Fig. 20-6(a) illuminates a single-mode fiber. We showed in Sections 20-7 and 20-12 that the fundamental mode is most efficiently excited by on-axis beams. Thus, it is intuitive that the more diffuse the source, i.e. the larger 0 , the lower the efficiency of the source in exciting the fundamental mode. To demonstrate this behavior quantitatively, we consider a source with a Gaussian intensity... 

To evaluate fission product release in a reactor, it is necessary to supply the appropriate particle geometry, diffusion coefficients, and distribution coefficients. This is a formidable task. To approach this problem, postirradiation fission product release has been studied as a function of temperature. The results of these studies are complex and require considerable interpretation. The SLIDER code without a source term has proved to be of considerable value in this interpretation. Parametric studies have been made of the integrated release of fission products, initially wholly in the fueled region, as a function of the diffusion coefficients and the distribution coefficients. These studies have led to observations of critical features in describing integrated fission product releases. From experimental values associated with these critical features, it is possible to evaluate at least partially diffusion coefficients and distribution coefficients. These experimental values may then be put back into SLIDER with appropriate birth and decay rates to evaluate inreactor particle fission product releases. Figure 11 is a representation of SLIDER simulation of a simplified postirradiation fission product release experiment. Calculations have been made with the following pertinent input data ... 

Another source of error involves cases in which both the anodic and cathodic reactions are not charge transfer controlled processes, as required for the derivation of Eq 25. Modifications to Eq 25 exist for cases in which pure activation control is not maintained, such as in the case of partial diffusion control or passivation [35]. Other researchers have attempted to calibrate the polarization resist2ince method with gravimetrically determined mass loss [36], In fact, polarization resistance data for a number of alloy-electroljrte systems have been compared to the observed average corrosion currents determined from meiss loss via Faraday s law [28], A linear correspondence was obtained over six orders of magnitude in corrosion rates. 

Hydrocarbon vapor migration within the carbon canister is a significant factoi during the real time diurnal test procedure. The phenomenon occurs after the canister has been partially charged with fuel vapors. Initially the hydrocarbons will reside primarily in the activated carbon that is closest to the fuel vapor source. Over time, the hydrocarbons will diffuse to areas in the carbon bed with lower HC concentration. Premature break through caused by vapor migration for twc different canisters is shown in Fig. 17. The canister with the L/D ratio of 5.0 shows substantially lower bleed emissions than the canister with an L/D ratio of 3.0. 

Figure 3. Chloride reactant ion decay curves obtained by the PHPMS ion source shown in Figure 2 for the n2 nucleophilic displacement reaction, CP + CHjBr CH3CI + Br", in methane buffer gas at a pressure of 62 torr and a temperature of 125 °C. Cl" is made by electron attachment to CCI4 (partial pressure = 0.06 mtorr). For curve A, no CH3Br was present so that the loss of Cl" was determined only by the physical processes, diffusion and/or ion-ion recombination. For curves B and C, the concentration of CH3Br was 1.1 x 10 and 2.1 x 10 moiecules/cm, respectively.

From this simplified scheme, it follows that the diffusional process is reversible, whereas the enzymatic carbon fixation is irreversible. The two-step model of carbon fixation clearly suggests that isotope fractionation is dependent on the partial pressure of CO2, i.e. PCO2 of the system. With an unlimited amount of CO2 available to a plant, the enzymatic fractionation will determine the isotopic difference between the inorganic carbon source and the final bioproduct. Under these conditions, C fractionations may vary from -17 to —40%o (O Leary 1981). When the concentration of CO2 is the limiting factor, the diffusion of CO2 into the plant is the slow step in the reaction and carbon isotope fractionation of the plant decreases. 

The damping factors take into account 1) the mean free path k(k) of the photoelectron the exponential factor selects the contributions due to those photoelectron waves which make the round trip from the central atom to the scatterer and back without energy losses 2) the mean square value of the relative displacements of the central atom and of the scatterer. This is called Debye-Waller like term since it is not referred to the laboratory frame, but it is a relative value, and it is temperature dependent, of course It is important to remember the peculiar way of probing the matter that EXAFS does the source of the probe is the excited atom which sends off a photoelectron spherical wave, the detector of the distribution of the scattering centres in the environment is again the same central atom that receives the back-diffused photoelectron amplitude. This is a unique feature since all other crystallographic probes are totally (source and detector) or partially (source or detector) external probes , i.e. the measured quantities are referred to the laboratory reference system. 

When the diffusion profile is time-dependent, the solutions to Eq. 4.18 require considerably more effort and familiarity with applied mathematical methods for solving partial-differential equations. We first discuss some fundamental-source solutions that can be used to build up solutions to more complicated situations by means of superposition. 

Here, cr is the condensation rate constant, Aw is the partial pressure of water vapor, A at is the saturation pressure, Mh2o is the molecular weight of the water vapor. A corresponding source term has to be added to water vapor conservation equation and pressure correction equation (mass source). The liquid water velocity is assumed to be same as the gas velocity inside the gas channel. However, inside the porous region, the convection term is replaced by capillary diffusion term and the equation becomes... 

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