Chain Models of Physical Behavior for Engineering Analysis and Design

The relationship between geometry (form) and physical behavior (function) dominates many engineering activities. The lack of uniform and rigorous computational models for this relationship has resulted in a plethora of inconsistent (and thus usually incompatible) computer aided design (CAD) tools and systems, causing unreasonable overhead in time, effort, and cost, and limiting the extent to which CAD tools are used in practice. It seems clear that formalization of the relationship between form and function is a prerequisite to taking full advantage of computers in automating design and analysis of engineering systems. We present a unified computational model of physical behavior that explicitly links geometric and physical representations. The proposed approach characterizes physical systems in terms of their algebraic-topological properties: cell complexes, chains, and operations on them