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Saddle-node bifurcation during the relaminarization of turbulent puffs in pipe
Basheer Ahmad Khan, Shai Arogeti, Oriel Shoshani, Alexander Yakhot
https://arxiv.org/abs/2508.08862

Saddle-node bifurcation during the relaminarization of turbulent puffs in pipe
Turbulent puffs in a pipe persist for a long time before abruptly transitioning to laminar flow through viscous exponential decay. Direct numerical simulation results reveal a saddle-node bifurcation sequence governing the final relaminarization stage. Specifically, a universal square-root scaling law in the annihilation of critical points that is indicative of a saddle-node bifurcation. The Riccati equation has been proposed as a straightforward approach to modeling these bifurcations.

Critical demand in a stochastic model of flows in supply networks
Yannick Feld, Marc Barthelemy
https://arxiv.org/abs/2505.24813 https://

Critical demand in a stochastic model of flows in supply networks
Supply networks are essential for modern production, yet their critical properties remain understudied. We present a stochastic model with random production capacities to analyze material flow to a root node, focusing on topology and buffer stocks. The critical demand, where unsatisfied demand diverges, is examined mostly through numerical simulations. Without stocks, minimal production dictates behavior, making topology irrelevant. With stocks, memory effects arise, making topology crucial. In…