arXiv subjects

Guillaume Costa

Publications and source records attributed to Guillaume Costa.

5 recordsLinked to original sources

arXiv2026

Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates

When driven out of equilibrium, a Bose-Einstein condensate develops nonlinearly interacting density waves that trigger a turbulent cascade, transferring energy toward small scales. In this Letter, we investigate the nonstationary evolution of solutions to the two-dimensional Gross-Pitaevskii equation (GPE). Through numerical simulations of both the GPE and the corresponding Wave Kinetic Equation (WKE), we identify self-similar solutions relevant to turbulence in atomic and polariton Bose-Einstein Condensates. These solutions correspond to a new type of non-thermal fixed point and exhibit characteristics of both first and second kind self-similarity. In particular, we show that the dynamics of the propagating front is universal, governed by a dimensionless universal constant $β$, which we determine numerically.

cond-mat.quant-gas↗

arXiv2026

Stability of stationary solutions in Acoustic wave turbulence

We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and 3D equilibrium Rayleigh-Jeans and non-equilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.

nlin.CD↗

arXiv2025

Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices

Using the recent concept of fluids projected onto Log-Lattices, we investigate the validity of the Gallavotti-Cohen Fluctuation Theorem (GCFT) in the context of fluid mechanics. The dynamics of viscous flows are inherently irreversible, which violates a fundamental assumption of the fluctuation theorem. To address this issue, Gallavotti introduced a new model, the Reversible Navier-Stokes Equation (RNS), which recovers the time-reversal symmetry of the Navier-Stokes (NS) equations while retaining the core characteristics of the latter. We show that for fluids on Log-Lattices, the GCFT holds for the RNS system. Furthermore, we show that this result can be extended, under certain assumptions, to the traditional, irreversible Navier-Stokes equations. Additionally, we show that the phase space contraction rate satisfies a large deviation relation which rate function can be estimated.

cond-mat.stat-mech↗

arXiv2025

Behind the mirror: the hidden dissipative singular solutions of ideal reversible fluids on log-lattices

Empirical observations show that turbulence exhibits a broad range of scaling exponents, characterizing how the velocity gradients diverge in the inviscid limit. These exponents are thought to be linked to singular solutions of the Euler equations. In this work, we propose a dynamic approach to construct concept of these solutions directly from the fluid equations, using a reversible framework and introducing the efficiency $\cal{E}$, a non-dimensional number that quantifies the amount of energy stored within the flow due to an applied force. To circumvent the computational burden of tracking singularities at finer and finer scale, we test this approach on fluids on log-lattices, which allow for high effective resolutions at a moderate cost, while preserving the same symmetries and global conservation laws as ordinary fluids. We observe a phase transition at a given efficiency, separating regular, viscous solutions (hydrodynamic phase), from singular, inviscid solutions (singular phase). The singular solutions experience self-similar blow-ups with exponents corresponding to non-dissipative solutions. By applying a stochastic regularization, we are able to go past the blow-up, and show that the resulting solutions converge to power-law solutions with exponents characterizing dissipative solutions. Overall, the range of scaling exponents observed for log-lattice solutions is comparable to those of ordinary fluids.

nlin.CD↗

arXiv2023

Tracking complex singularities of fluids on log-lattices

In 1981, Frisch and Morf [1] postulated the existence of complex singularities in solutions of Navier-Stokes equations. Present progress on this conjecture is hindered by the computational burden involved in simulations of the Euler equations or the Navier-Stokes equations at high Reynolds numbers. We investigate this conjecture in the case of fluid dynamics on log-lattices, where the computational burden is logarithmic concerning ordinary fluid simulations. We analyze properties of potential complex singularities in both 1D and 3D models for lattices of different spacings. Dominant complex singularities are tracked using the singularity strip method to obtain new scalings regarding the approach to the real axis and the influence of normal, hypo and hyper dissipation.

math.AP↗