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March 29, 2023

Radiographic Pathology For Technologists Pdf 74

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We analyze each system as a whole rather than atom by atom, in order to focus on the Multi-body (M2/3) approximation. We show that the Galerkin-based energy functional produced by any of this past literature can be derived from a variational principle of the form shown in (20). This establishes the consistency of the Galerkin approximation for systems of arbitrary size. The key insight is that the energy is a quadratic form involving interconnections between boundary (forces) and bulk (micro strain) quantities, and is defined entirely in terms of such bulk quantities.

We continue by considering the most important instance of a bulk term for a system subjected to boundary loads. In this case, the bulk energy is defined by the micro strains induced in the system by the boundary loads, and the bulk term in is chosen to compare the boundary and bulk energies against one another. This leads to a set of boundary conditions for the boundary loads such that, when combined with our definition for the bulk energy, the boundary and bulk energies are equal to one another.

The boundary and bulk energies are defined in terms of,,, and, while forces are determined by combining and with to give a boundary condition. This results in the minimum-energy boundary condition for a system subjected to boundary loads.

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