13 papers
Gradient Flow Structure of the Spontaneous Aggregation Model
Jan Haskovec
We identify a previously unnoticed gradient-flow structure of the Fokker--Planck equation arising in the spontaneous particle aggregation model. For an exponential response functio…
Memory Stabilizes Spontaneous Particle Aggregation: A Linearized Vlasov--Fokker--Planck Analysis
Jan Haskovec
We perform a linearized stability analysis of the Vlasov--Fokker--Planck equation obtained as the mean-field description of a stochastic spontaneous aggregation model with memory.…
A duality approach to the dense graph limit for biological transportation networks
Nuno J. Alves, Jan Haskovec
We develop a duality-based formulation of the dense graph limit for a variational model of biological transportation networks, where edge conductivities balance pumping power again…
Consensus and flocking with transmission and reaction delays
Elisa Continelli, Jan Haskovec, Cristina Pignotti
We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delays: a transmission delay accounting for information exchange be…
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…
Measure-based approach to mesoscopic modeling of optimal transportation networks
Jan Haskovec, Peter Markowich, Simone Portaro
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the…
Numerical approach to centrality of optimal transportation networks
Jan Haskovec
We study hierarchical properties of optimal transportation networks with biological background. The networks are obtained as minimizers of an energy functional which involves a met…
Robust network formation with biological applications
Jan Haskovec, Jan Vybiral
We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metab…
Particle systems and kinetic equations modeling interacting agents in high dimension
Massimo Fornasier, Jan Haskovec, Jan Vybiral
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain d…