Complex

Our work with x-ray micro-CT images of complex porous materials has required the development of topologically valid and efficient algorithms for studying and quantifying their intricate structure. As an example, simulations of two-phase fluid displacements in a porous rock depend on network models that accurately reflect the connectivity and geometry of the pore space. These network models are usually derived from curve skeletons and watershed basins. Existing algorithms compute these separately and may give inconsistent results.

No Abstract

Using the methods of numerical algebraic geometry, one can compute a
numerical irreducible decomposition of the solution set of polynomial
systems. This decomposition describes the enitre solution set and
its breakup into irreducible pieces over complex Euclidean space.
However, in engineering or science, it is common that only the real
solutions are of interest. A single complex component may contain
multiple real components, some possibly having lower dimension in the