Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.

A new strategy taken from statistical and nuclear physics enables a qualitative and macroscopic approach to combinatorial optimization. For this purpose the mean field approximation is interpreted in a fuzzy manner and the strategy is tested at some NP complete layout problems. The described applications concerning graph partitioning, linear ordering and two dimensional assignment show performance comparable with simulated annealing, but much faster. Especially a new fuzzy net model can treat hypergraphs without splitting multi pin nets into two point nets.