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4 papers
Local-order fluctuations in Kob-Andersen-type glass formers
John Çamkıran, Fabian Parsch, Glenn D. Hibbard
Notwithstanding decades of work, we still lack a satisfactory understanding of the structural relaxation that takes place as a liquid is rapidly cooled to form a glass. The present…
Geodesic Nets: Some Examples and Open Problems
Alexander Nabutovsky, Fabian Parsch
Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general propertie…
An example for a nontrivial irreducible geodesic net in the plane
Fabian Parsch
We construct a geodesic net in the plane with four unbalanced (boundary) vertices that has 16 balanced vertices and does not contain proper geodesic subnets. This is the first exam…
Geodesic nets with three boundary vertices
Fabian Parsch
We prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for t…