arXiv subjects

Côme Fontaine

Publications and source records attributed to Côme Fontaine.

2 recordsLinked to original sources

arXiv2023

The unpredicted scaling of the one-dimensional Kardar-Parisi-Zhang equation

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree. Yet recent numerical simulations in the tensionless (or inviscid) limit of the KPZ equation [Phil. Trans. Roy. Soc. A 380, 20210090 (2022); Phys. Rev. E 106, 024802 (2022)] unveiled a new scaling, with a critical dynamical exponent $z=1$ different from the KPZ one $z=3/2$. In this Letter, we show that this scaling is controlled by a fixed point which had been missed so far and which corresponds to an infinite non-linear coupling. Using the functional renormalization group (FRG), we demonstrate the existence of this fixed point and show that it yields $z=1$. We calculate the correlation function and associated scaling function at this fixed point, providing both a numerical solution of the FRG equations within a reliable approximation, and an exact asymptotic form obtained in the limit of large wavenumbers. Both scaling functions accurately match the one from the numerical simulations.

cond-mat.stat-mech↗

arXiv2023

Functional renormalisation group approach to shell models of turbulence

Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (RG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.

physics.flu-dyn↗