The role of complexity for digital twins of cities.

We argue that theories and methods drawn from complexity science are urgently needed to guide the development and use of digital twins for cities. The theoretical framework from complexity science takes into account both the short-term and the long-term dynamics of cities and their interactions. This is the foundation for a new approach that treats cities not as large machines or logistic systems but as mutually interwoven self-organizing phenomena, which evolve, to an extent, like living systems.

Anomalous roughening of Hele-Shaw flows with quenched disorder.

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.

Interface depinning in the absence of an external driving force.

We study the pinning-depinning phase transition of interfaces in the quenched Kardar-Parisi-Zhang model as the external driving force F goes towards zero. For a fixed value of the driving force, we induce depinning by increasing the nonlinear term coefficient lambda, which is related to lateral growth, up to a critical threshold. We focus on the case in which there is no external force applied (F=0) and find that, contrary to a simple scaling prediction, there is a finite value of lambda that makes the interface to become depinned. The critical exponents at the transition are consistent with directed percolation depinning.