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Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mechanical balances. Second, we present a new microscopic modelling method to describe the interaction among pedestrians in conflicting situations. A local navigation based on a continuous density estimator is adopted for the configuration of pedestrians’ temporary route choices on the tactical level. On the operational level, a balancing mechanism is installed to ensure correct execution of the planned position transitions of the pedestrians. A comparison of the test results of our simulation with a real-world video clip is provided.

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In this paper we describe the formal Lagrange-technique to optimize the production process of solid state crystals from a mixture crystal melt. After the construction of the adjoint equation system of the Boussinesq equation of the crystal melt the forward and backward problems (KKT-system) are discretized by a conservative finite volume method.