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Interacting Particles

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Ellipsoidal Interaction Potential
Double Mill

Interacting Particles

Interacting particles are used in many different applications. Our research mostly considers swarming phenomena as birds or fishes, moving pedestrians or groups of pedestrians, sheep, fibers, and bubbles. In all cases the movement of the individual particles is described by an ODE or an SDE model. To cover the interaction between these individuals, we use different potentials. Depending on this potential the particles are attracted or repulsed by each other, where the strength of this behavior mostly depends on the distance between the particles. If the number of particles grows, the ODE/SDE system gets quite large. For infinitively many particles one can derive the mean field equation, describing a distribution function for the particles. With the help of closures one can also derive some hydrodynamic or diffusive limit equations.
Our research group is interested in deriving these different models and comparing them numerically. For a more detailed information on the different applications see