TY - JOUR A1 - Burger, Martin T1 - Network structured kinetic models of social interactions N2 - The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, which we treat by an appropriate mesoscopic description, and a different role of interacting agents. The latter differs from interactions treated in classical statistical mechanics in the sense that the agents do not have symmetric roles, but there is rather an active and a passive agent. We will demonstrate how a certain form of kinetic equations can be obtained to describe such interactions at a mesoscopic level and moreover obtain macroscopic models from monokinetics solutions of those. The derivation naturally leads to systems of nonlocal reaction-diffusion equations (or in a suitable limit local versions thereof), which can explain spatial phase separation phenomena found to emerge from the microscopic interactions. We will highlight the approach in three examples, namely the evolution and coarsening of dialects in human language, the construction of social norms, and the spread of an epidemic. Y1 - 2021 U6 - https://doi.org/10.1007/s10013-021-00505-8 ET - Vietnam Journal of Mathematics ER - TY - INPR A1 - Burger, Martin A1 - Humpert, Ina A1 - Pietschmann, Jan T1 - Dynamic optimal transport on networks N2 - In this paper we study a dynamical optimal transport problem on a network that allows for transport of mass between different edges if a penalty κ is paid. We show existence of minimisers using duality and discuss the relationships of the distance-functional to other metrics such as the Fisher-Rao and the classical Wasserstein metric and analyse the resulting distance functional in the limiting case κ → ∞. Y1 - 2021 ER -