# Linear and non-linear flow coefficients from transport theory

- Institution: CERN
- Department: Conferences
- Speaker: Urs Wiedemann
- Year: 2021
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3018941)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

The observation of fluid-like behavior in nucleus-nucleus (AA), proton-nucleus (pA) and high-multiplicity proton-proton (pp) collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed numerical methods to solve the ultra-relativistic Boltzmann equation for systems of arbitrary size and transverse geometry. Here, we apply these techniques for the first time to the study of azimuthal flow coefficients $v_n$ including non-linear mode-mode coupling and to an initial condition with realistic event-by-event fluctuations. We show how both linear and non-linear response coefficients extracted from $v_n$ develop as a function of opacity from free streaming to perfect fluidity. We note in particular that away from the fluid-dynamic limit, the signal strength of linear and non-linear response coefficients does not reduce uniformly, but that their hierarchy and relative size shows characteristic differences..

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## Lectures

1. [Linear and non-linear flow coefficients from transport theory](https://invisiblenetwork.ai/learn/cern/3018941/da9ce5105f63), 23 min (CERN's player)