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physics.flu-dyn2026
An Optimal Seed Reveals the Dynamical Route to Spontaneous Splitting of Turbulent Puffs
Chihang Liu, Hao Ni, Jiashun Guan
The localized turbulence in pipe flow, known as puffs, is sustained by their proliferation. This process is crucial to the subcritical laminar-turbulent transition, a century-old f…
math.PR2026
The -bounds for Derivatives of Unitary Developments of Random Continuous Geometric Rough Paths
Chong Liu, Zijiu Lyu, Hao Ni
In this paper we derive an explicit formula for derivatives of unitary developments of random continuous geometric rough paths of all orders and establish proper -bounds for t…