Forward flux method

The simplest multiflux model can be developed for a one-dimensional planar medium or a one-dimensional axisymmetric cylindrical geometry by dividing the entire solid angle range (4k sr) into two components one in the forward and the other in the backward hemisphere. It is assumed that the incident radiation and flux are proportional to each other in each of these hemispheres. Then, the question is finding a closure condition, or, in other words, a proportionality factor between flux and integrated intensity in each half-sphere. This choice yields different two-flux methods, such as Schuster-Hamaker, Schuster-Schwarzchild or modified two-flux models [1,19, 51]. 

The forward flux sampling method (FFS) was conceived by Allen, Warren and ten Wolde [190-192] to deal with stochastic non-equilibrium systems in which the phase space distribution is not a priori known. Inspired by the TIS method, FFS employs the notion of a set of interfaces along a reaction coordinate (see Fig. 9), and even uses the same central reaction rate expression. 

Table 4-1 lists six combinations of rate constants for which an RCS can be defined and two others lacking one. A method has been presented for exploring the concept of the RCS by means of reactant fluxes.11 Consider the case k < (k- + k2), such that the steady-state approximation is valid. One defines an excess rate , for each step i as the difference between the forward rate of that step and the net forward rate v/. Thus, for Step 1,... 

As seen in equations (32)-(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, As, corresponding to the formation of M — Rcen following measurement of [M] and (M —Rceii. For example, a (Scatchard) plot of (M — RCeii /[M] versus (M — RCeii should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]). 

L. Deffet M. de Coster, Explosifs (Belgium) 5, 106-13(1952) Chim Ind (Paris) 69, 490(1953) CA 49, 6605-07 (1955) (Initiation to deton of solid expls by X-ray flashes. The method consisted of producing a flux of X-rays of an extremely short period, such as less than 1 microsecond, using detonators contg 0.45 g MF 0.75 g TNT. Radiographs taken at various times after beginning of deton, such as 7 to 24 microsecs, showed that expansion of deton gas occurs laterally and that the forward part of the detonator hardly moved. The deton of MF was slowed down by that of TNT. It has been shown that the form... 

A large number of explicit numerical advection algorithms were described and evaluated for the use in atmospheric transport and chemistry models by Rood [162], and Dabdub and Seinfeld [32]. A requirement in air pollution simulations is to calculate the transport of pollutants in a strictly conservative manner. For this purpose, the flux integral method has been a popular procedure for constructing an explicit single step forward in time conservative control volume update of the unsteady multidimensional convection-diffusion equation. The second order moments (SOM) [164, 148], Bott [14, 15], and UTOPIA (Uniformly Third-Order Polynomial Interpolation Algorithm) [112] schemes are all derived based on the flux integral concept. 

Figure 3 shows a test of the sensitivity of this method to two key factors, the size of Djj (determined by the number of concentration measurements, , and source layers, m) and the presence or absence of the near-field term in in the dispersion matrix D,j. Figure 3a shows the assumed concentration field, based on forward calculation of the concentration profile q (i = 1 to n) from a specified source profile using Eq. (17), with D j as in Figure 1, and with n = 20, m = 10. This concentration field is then used to reconstruct the source profile 4> z) with Eq. (30), and the flux f(z) from Eq. (20), under three scenarios (1) n,m) = (20,10), with DT" included (2) (n,m) = (10,5), with included and (3) (n,m) = (10,5), with omitted. Figures 3b and 3c respectively show the inferred profiles 0, and Fj at layers centered on heights... 

The first detailed investigation of [n, p) and [n, 2n) reactions with neutrons of 9 Mev and above, was made by Waffler. He measured the cross sections for the n, p) process for a number of elements irradiated by the neutrons emitted in the forward direction from Li and B, bombarded by 500 kev deuterons. In the forward direction the former reaction, in addition to producing many low energy neutrons, produces also neutrons of 10 and I3 Mev the latter reaction produces neutrons of 9 and 13-5 Mev. The flux of neutrons was determined by a photographic plate method. The cross sections were found by measuring the radioactivities of the product nuclei. Since the neutron sources produced a rather varied energy spectrum, Waffler s results represent average cross sections, and. a strict comparison with theoretical values is difficult. His results, however, show that the n, p) process is consistently more probable than theory will allow. 

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