Research
I am currently pursuing a Bachelor's degree in Mathematics in Business and Economics at TU Dresden.
Master of Science Physics, TU Dresden
Thesis, at Institute of Theoretical Physics, Chair for Network Dynamics: ''The non-Markovian Random Walks of Ridepooling''
Ridepooling services have become an increasingly attractive mobility option in urban areas.
As users issue requests for transport, ridepooling vehicles drive through the road network,
continually adjusting their routes to pick up and deliver users with similar trips in shared rides.
The quality of such services strongly depends on the dynamics of evolving vehicle routes,
which collectively emerge from the interactions of the vehicles, requests and the dispatching algorithm.
So far, theories of ridepooling services have focused on macroscopic and mean-field dynamics,
neglecting the underlying microscopic route evolution. In this thesis,
the structure and dynamics of these random routes in the limit of optimal service efficiency is analyzed.
An emerging random walk of a route that is specified not only by the current location of the vehicle, but also by the route planned ahead,
is described. This process is mapped to an ordinary Markov random walk on an abstract graph
whose nodes represent the shortest paths of the original street network.
Thereby emerging routing patterns are identified and with the help of event-based simulations
evaluated with respect to their implications for the ridepooling service.
In addition, the calculation of an already known scaling parameter, which includes the
topology of the street network, is formalized.
Bachelor of Science Physics, TU Dresden
Thesis, at Institute of Polymer Research Dresden:
''The Simulation of the Synthesis of Olympic Gels through Ring-opening Polymerization''
Olympic gels are purely topologically linked networks of polymer rings. There are several
methods for creating such a network. However, these methods are difficult to realize exper-
imentally. In my thesis, the possibility of the synthesis of Olympic gels through another
mechanism is analyzed and discussed. It uses the standard reaction of reversible ring-opening
polymerization, which is more convenient to use in experiment.
The method is implemented using the Bond Fluctuation Model (BFM) with a Metropolis
algorithm. A breaking energy and an attachment energy are introduced, which model the
transition probabilities from bound states to open states. The time dependence of various
properties regarding formation of polycatenanes and Olympic gels are analyzed and discussed.
In addition, simulation results regarding number and mass distributions of rings and chains
and therefore the ring-chain equilibrium, are compared to a set of rate equations that are
solved numerically.
The number of linked ring pairs per system is analyzed with the help of an algorithm using
the HOMFLY-polynomial. Percolation and the size of the biggest clusters is qualitatively
discussed. Formation of a gel is observed for a sample, which shows that very promising results
can be achieved.
