Distance geometry time dependence

Next, whenever diffusion is considered to proceed simultaneously along with a non-steady state loading history, such as if slow strain rate tests were simulated, the stress-field is obviously time dependent, and so, the stress dependent element matrices do, too. Besides, when large geometry changes occur, the deformed distances become the diffusion paths of interest, so that coordinates x must be continuously updated with deformation displacements, and thus, they also become time dependent. As a result, all the element matrices in equations (13) must be updated throughout the simulation histories, i.e., they... 

Fig. 19. L Comparison between calculated and expierimentally observed weld pool geometry (sheet edge). Right Calculated temperatrne vs. time dependence at different distances from the welding seam (upper and lower side, x = L/2).

The general treatment of the time-dependent response of a reactor to a local change in reactivity is quite complicated and involves explicitly the geometry of the reactor. 12 if the reactivity change is distributed uniformly over the reactor volume, only the fxmdamental space mode of the reactor is involved (i.e., the initial space distribution of neutron flux is preserved, and the only reactor characteristics needed to describe the response are the neutron lifetime and the delayed neutron characteristics. The same is true for a localized reactivity variation if the time rate of change is low enough and if the response is measured at some distance from the location of the reactivity change. 

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