4 papers
From PDEs on standard domains to self-similar particle systems on fractals
Georgi Medvedev, Emmanuel Trélat
We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems tha…
Kuramoto model on Sierpinski Gasket I: Harmonic maps
Georgi S. Medvedev, Matthew S. Mizuhara
Motivated by the study of attractors in the Kuramoto model (KM) on graphs approximating the Sierpinski gasket (SG), we revisit the problem of harmonic maps (HMs) from SG to the cir…
The Kuramoto model on the Sierpinski Gasket II: Twisted states
Georgi S. Medvedev, Matthew S. Mizuhara
We study the Kuramoto model (KM) of coupled phase oscillators on graphs approximating the Sierpinski gasket (SG). As the size of the graph tends to infinity, the limit points of th…
Metastability in the stochastic nearest-neighbor Kuramoto model of coupled phase oscillators
Nils Berglund, Georgi S. Medvedev, Gideon Simpson
The Kuramoto model (KM) of coupled phase-oscillators is analyzed in this work. The KM on a Cayley graph possesses a family of steady state solutions called twisted states. Topo…