Extreme Filtering of Rapid Energy Deposition and Its Multiscale Implications

The present paper focuses on rapid energy deposition processes, where there is extremely strong filtering of spatial and temporal structure within the associated diffusion pattern. This strong filtering tends to establish conditions where reconstruction of detailed features of the energy source using data-driven inverse analysis is not well posed. These strong filtering conditions imply that information that is available concerning the coupling of energy into a spatial region of interest from the site of surface deposition will be difficult to correlate with experimental observations of the associated energy diffusion pattern. The analysis and simulations imply that rapid energy deposition should be characterized by two distinctly separate scales for both spatial and temporal structures. Accordingly, the inverse rapid energy deposition problem requires a formulation with respect to system parameterization that is in terms of two separate sets of parameters. One represents the energy source characteristics on spatial and temporal scales commensurate with that of thermal diffusivity within the material, and the other represents energy source characteristics on spatial and temporal scales commensurate with those of surface phenomena.