Stability program density

Equations (2.302) and (2.303) enable us to explicitly calculate the temperatures t U at time = t0 + At from the initial temperature distribution .. These can then be used to calculate the temperature of the next time level etc. This difference method is relatively simple to program. It is also suitable for a temperature dependent thermal power density W(d), because WU is calculated for the already known temperature The disadvantage of this explicit difference method lies in its limited stability, cf. 2.4.1.2. The stability condition, from which none of the coefficients on the right hand side of (2.302) are allowed to be negative, limits the time step... 

Numerical experiments provided the critical EPR density Acr 2.5. No stagnation is formed if A < Acr the profiles U(z) in the EPR bottom tend to a constant slop, and r0 = r(0) = const + 0. Stagnation begins at a certain distance Xs (Fig. 3.8) if A > Acr and then ranges to infinity. At this distance, the shear on the wall reaches the value r(Xs, 0) 0, and the computing program loses its stability. 

There is at present considerable controversy " 9 -i03 on the occurrence and the extent of stabilization that is achieved by the back-donation of electron density into vacant d-orbitals in phosphorus. The CNDO/2 calculations show some interesting trends in this respect, in particular concerning the effect on the relative stability of the various isomers of a given molecule. The method of the calculation is first illustrated for PFs. Table 10 is an extract from the density matrix of the program. The diagonal elements correspond to electron densities of the described orbital. The sum of these elements, 3 8890, is equal to the total valence shell electron density for the phosphorus. Of this, 1 3671 units of electron charge, or about 35%, reside in the five d-orbitals of the phosphorus. 

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