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In this book, the following aspects related to the exploration of flow fields have been investigated. Firstly, a novel reconstruction method has been developed, which uses a physics-based filter operation to generate a velocity field that is consistent with the underlying flow model described by the Navier-Stokes equations. Interactive steering of this process is achieved by exploiting programmable graphics hardware for numerical computations and visualization of 2D flow fields. Secondly, a new focus for particle tracing, so called anchor lines, has been introduced to analyze local flow...

The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the...