Explore the physics of functional networks in this comprehensive lecture from the Workshop on Topology: Identifying Order in Complex Systems. Delve into optimal network topology, sound control in mechanical networks, and physical response optimization. Investigate the growth and remodeling of vascular networks, minimizing dissipation through growth, and optimal trade-offs in plant leaves. Examine structural networks in biology, focusing on leaf venation, and learn about making networks rigid through constrained optimization and simulated annealing. Discover the design principles for resilient grids, optimal noise-canceling networks, and the connection between engineering and biology. Analyze AC power grids as coupled phase oscillators and explore the formation and prediction of loops in network structures. Compare topological findings to real leaf networks and gain insights into the complex world of functional network physics.
Overview
Syllabus
Intro
Optimal network topology for form and function
Can we control sound in mechanical networks?
Physical response optimization to control sound
Can we switch the gap on and off?
Tuning realistic materials
Vascular networks grow and remodel themselves
Minimizing dissipation through growth
Networks and fluctuations
Optimal trade-offs in plant leaves
Structural Networks in Biology: Leaf venation
Making Networks Rigid
Constrained Optimization: Simulated Annealing
Optimal Elastic Networks
3D Printed Leaf Networks
Designing resilient networks
AC power grids are coupled phase oscillators
Fluctuations in input cause fluctuations in output
Design principles for resilient grids
Optimal noise-canceling networks
Connecting engineering and biology
Where do loops come from?
Where will the next loop form?
Topological comparison to real leaf networks
Taught by
Institute for Advanced Study
