5 papers · 1 filter
High-friction limit for bipolar Euler-Riesz systems
Nuno J. Alves, Jan Haskovec
We consider a bipolar Euler-Riesz system and rigorously justify the high-friction limit of weak solutions towards a bipolar aggregation-diffusion system with Riesz interactions. Th…
Gradient Flows for the -Laplacian Arising from Biological Network Models: A Novel Dynamical Relaxation Approach
Jan Haskovec, Peter Markowich, Stefano Zampini
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral…
Impact of memory on clustering in spontaneous particle aggregation
Radek Erban, Jan Haskovec
The effect of short-term and long-term memory on spontaneous aggregation of organisms is investigated using a stochastic agent-based model. Each individual modulates the amplitude…
Rigorous dense graph limit of a model for biological transportation networks
Nuno J. Alves, Jan Haskovec
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with…
Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks
Jan Haskovec, Peter Markowich, Simone Portaro +1
We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of…