5 papers
Area and water-capacity statistics for upper hulls of Dyck paths
Aleksander L. Owczarek, Thomas Prellberg
We study Dyck paths refined simultaneously by proper area and water capacity, where water capacity is measured above the path and below its lattice-path upper hull. The finite-heig…
Random sampling of self-avoiding theta-graphs
Nicholas R. Beaton, Aleksander L. Owczarek
Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a comb…
Self-avoiding walks pulled at an angle
C J Bradly, N R Beaton, A L Owczarek
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle to the surface. We use the canonical sel…
Compressed self-avoiding walks in two and three dimensions
C J Bradly, N R Beaton, A L Owczarek
We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the res…
Exact solution of asymmetric gelation between three walks on the square lattice
Aleksander L Owczarek, Andrew Rechnitzer
We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different…