Thread by @sfiscience

"From undirected to directed networks of dynamical agents"

Today's SFI Seminar from @robinus88 (@UCSantaBarbara), streaming now:


(Follow this 🧵 for highlights and select slides)

"[This is] the main question when we talk about power grids...it could be water, it could be gas, it could be opinions transmitted over social media:"

- @robinus88 (@UCSantaBarbara), streaming now:

"We want to keep the right-hand side of this equation as close to zero as possible. What happens if you produce too much, the frequency increases, which we don't want for a variety of reasons."

- @robinus88 (@UCSantaBarbara), streaming now:

#electricity

"What happens if we turn on the accelerator at @CERN *and* many people turn on their lights at the same time? All the turbines slow down and the kinetic #energy is taken from the turbines...after a few seconds, a new power source is commissioned."

- @robinus88 (@UCSantaBarbara):

In undirected systems, flow is not conserved and average velocity is state-/time-dependent.
/
In a directed network of dynamical agents, consider directed incidence matrices:

@robinus88 (@UCSantaBarbara) on #synchronization #oscillation #systems

"We have no guarantee that the Eigenvalues are real anymore..."

- @robinus88 (@UCSantaBarbara):

On calculating winding numbers and winding vectors (partitioning the state space)

"The reason this is important to me is that this partition is naturally induced by the...underlying network structure of the system."

- @robinus88 (@UCSantaBarbara):

In summary...

Watch the entire talk:


@robinus88 (@UCSantaBarbara)

#synchronization #networks #systems #grid #energy #diffusion #graphs #physics #flows