6 papers
Extended pseudo-spectral physics-informed neural networks for phase-field models
Callum Marsh, Radek Erban, Andreas Munch
Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pat…
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…
On the role of fractional Brownian motion in models of chemotaxis and stochastic gradient ascent
Gustavo Cornejo-Olea, Lucas Buvinic, Jerome Darbon +3
Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical co…
Neural networks for learning macroscopic chemotactic sensitivity from microscopic models
Radek Erban
The macroscopic (population-level) dynamics of chemotactic cell movement -- arising from underlying microscopic (individual-based) models -- are often described by parabolic partia…
From Brownian dynamics to Poisson-Nernst-Planck equations: multi-resolution simulations of ions
Jinyuan Zhang, Radek Erban
Starting with a microscopic (individual-based) Brownian dynamics model of charged particles (ions), its macroscopic description is derived as a system of partial differential equat…
Planar chemical reaction systems with algebraic and non-algebraic limit cycles
Gheorghe Craciun, Radek Erban
The Hilbert number is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing…