Position error coefficient

The Cottrell equation assumes that planar diffusion is the only contribution to the overall current. However, purely planar diffusion is only achievable with very large electrodes or with shielded electrodes. The current measured with small, unshielded electrodes can exhibit appreciable edge effects, resulting in positive deviations from the Cottrell equation and thus positive errors in the diffusion coefficient. Edge effects are normally manifested at long times (i.e., small values of The presence of convection at long times will also be evidenced by a positive deviation of the current. For these reasons, only those data points from the linear portion of the i vs. t curve should be used for the analysis of D. 

Unfortunately, due to a fundamental design difference, the RBMK design was inherently less safe than Western reactors. All Western reactors are required to have a negative core power feedback coefficient. This means fliat if an unexpected error occurs in core functioning, all automatic feedback mechanisms will tend to reduce core power and deescalate the situation. Thus, any unexpected occurrence will tend to decrease the chances of an accident happening. The RBMK reactor, however, had a positive feedback coefficient under certain circumstances. 

These small positive and negative errors partially cancel each other. The result is that capital cost targets predicted by the methods described in this chapter are usually within 5 percent of the final design, providing heat transfer coefficients vary by less than one order of magnitude. If heat transfer coefficients vary by more than one order of magnitude, then a more sophisticated approach can sometimes be justified. ... 

As can be seen in Figure 5-17, some search fields (e.g., POW [= Power]) do not need any input in the search mask this means that all entries with any content of those Helds are retrieved. However, other fields always demand an input. In case the input is omitted (for example for the decadic logarithm of the partition coefficient), a corresponding error message results. Since the PCB are more soluble in the organic phase, the input of that Field is restricted to positive values. 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

The described method can generate a first-order backward or a first-order forward difference scheme depending whether 0 = 0 or 0 = 1 is used. For 9 = 0.5, the method yields a second order accurate central difference scheme, however, other considerations such as the stability of numerical calculations should be taken into account. Stability analysis for this class of time stepping methods can only be carried out for simple cases where the coefficient matrix in Equation (2.106) is symmetric and positive-definite (i.e. self-adjoint problems Zienkiewicz and Taylor, 1994). Obviously, this will not be the case in most types of engineering flow problems. In practice, therefore, selection of appropriate values of 6 and time increment At is usually based on trial and error. Factors such as the nature of non-linearity of physical parameters and the type of elements used in the spatial discretization usually influence the selection of the values of 0 and At in a problem. 

Fig. 4.41 Angular positional control system. = Error detector gain (V/rad) K2 = Amplifier gain (A/V) Kj = Motor constant (Nm/A) n = Gear ratio Hi = Tachogenerator constant (Vs/rad) H = Load moment of inertia (kg m ) Q = Load damping coefficient (Nms/rad).

In aqueous solution at room temperature the coefficient B is positive for the majority of electrolytes. For some, however, it is negative in such a case the viscosity at moderate concentrations, where the B term is predominant, is less than that of pure water, while at lower concentrations, where the A s/c term becomes predominant, the value of the viscosity rises above that of pure water. An example of this is shown in Fig. 51, where abcissas are /c. The straight line is a plot of A s/c with A = +0.0052, while the lower curve is a plot of Be with B = —0.033. On adding the ordinates of these two curves the middle curve is obtained, which reproduces, within the experimental error, the values of 17/770 obtained for KC1 in aqueous solution at 18°C. 

A kinetic study of dedeuteration at 25 °C yield the following rate coefficients for [2H]-C6H4R578> 579 (R = )4-Me, 1,900 2-Me, 530 3-Me, 2.7 4-Ph, 1,400 2-Ph, 260 3-Ph, < 0.2 2,3-benzo(l position of naphthalene) 20,000-30,000 and 3,4-benzo (2 position of naphthalene) 500. Rather surprisingly, the rates of dedeuteration were little different from the rates of deuteration and it should be noted that quoted partial rate factors in this work were obtained by dividing these rates for dedeuteration at 25 °C by the rates of deuteration of benzene at 20 °C and errors of a factor of 2 or more may be introduced by this. 

It follows that ri2 = 1 implies also that r34 = 1. Usually, rs4 >rj2 e.g., when rj2 = 0, rs4 is positive and higher the smaller the interval (Ti, T2). For example, for T]/T2 =. 9 and Si = S2, we get the surprisingly high coefficient T34 =. 9986. This extreme case is worth a diagram (Figures 9 and 10). There is shown a completely artificial correlation due not to experimental errors-which can be arbitrarily small-but to the inhomogeneity of the reaction series. 

It can easily be shown that for the upwind scheme all coefficients a appearing in Eq. (37) are positive [81]. Thus, no unphysical oscillatory solutions are foimd and stability problems with iterative equation solvers are usually avoided. The disadvantage of the upwind scheme is its low approximation order. The convective fluxes at the cell faces are only approximated up to corrections of order h, which leaves room for large errors on course grids. 

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