arXiv subjects

Liubov Gosteva

Publications and source records attributed to Liubov Gosteva.

5 recordsLinked to original sources

arXiv2026

Scaling regimes of the Kuramoto-Sivashinsky equation from the functional renormalization group

We revisit the renormalization group (RG) approach to the one-dimensional stochastic Kuramoto-Sivashinsky (KS) equation and show that previous approaches based on perturbative Wilsonian RG with a sharp cutoff are not valid, even though they yield a qualitatively correct picture. The reason is that taking momentum derivatives while using the sharp cutoff is not well-defined in some cases and leads to intrinsic divergencies. This is a well-known problem of Wilsonian RG, which can be simply cured by using a smooth cutoff, and employing the functional renormalization group (FRG) framework. We establish the flow equations for the KS model within the FRG, and demonstrate that it flows to the Kardar-Parisi-Zhang (KPZ) fixed point at large scales. We then calculate the full two-point correlation function over a wide range of momenta and frequencies. We show that it exhibits three universal scaling regimes that we characterize: the KPZ regime (with dynamical exponent $z=3/2$), the Edwards-Wilkinson regime (with $z=2$) and the recently discovered inviscid regime (with $z=1$). The latter develops over an extended range of large wavenumbers and originates from the vanishing of the effective viscosity. Lastly, we investigate the large-scale behavior of the deterministic KS equation by studying the limit of vanishing noise and we determine the scales where the KPZ regime can emerge in the deterministic case.

cond-mat.stat-mech↗

arXiv2026

Inviscid scaling in the Kuramoto-Sivashinsky equation from functional renormalization group and direct numerical simulations

We show that the one-dimensional Kuramoto-Sivashinsky (KS) equation features a scaling regime characterized by the dynamical exponent $z=1$ at intermediate scales between the large-scale Kardar-Parisi-Zhang (KPZ) scaling with $z=3/2$ and the small-scale non-universal behavior. This scaling regime is intrinsic to the KS dynamics since it arises from the vanishing of the effective viscosity when evolving from its microscopic negative KS value, to its macroscopic effective positive KPZ value. This vanishing of the viscosity deeply imprints the behavior of correlations at intermediate scales, which exhibit a universal $z=1$ scaling. This behavior pertains to the inviscid-Burgers universality class, which corresponds to the zero-viscosity fixed point of the KPZ equation. We evidence and characterize this so-far-overlooked scaling regime using both functional renormalization group and direct numerical simulations.

cond-mat.stat-mech↗

arXiv2025

Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise

In this work, we investigate the Navier-Stokes equation in the presence of thermal noise, both at finite viscosity (revisiting the seminal work by Forster-Nelson-Stephen) and in the inviscid limit, which has not yet been explored. We determine the space-time velocity correlations in this dynamics, using functional renormalisation group and direct numerical simulations. While spectrally truncated three-dimensional Euler flows reach a stationary equilibrium state, they exhibit non-trivial temporal correlations. We show that these non-trivial correlations persist for small but finite viscosity, yielding an emergent $τ\sim k^{-1}$ dynamical scaling, where $τ$ is the decorrelation time. We characterise the crossover from the scaling $τ\sim 1/(νk^2)$, expected at large viscosity, to the scaling $τ\sim 1/(u_{\rm rms}k)$ found in the inviscid limit.

physics.flu-dyn↗

arXiv2025

Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported in recent numerical simulations. This new regime is characterised by a dynamical exponent $z=1$, markedly different from the expected one $z=3/2$ for the KPZ universality class, and it emerges when approaching the inviscid limit. The origin of this scaling has been traced down to the existence of a new fixed point, termed the inviscid Burgers (IB) fixed point, which was uncovered using the functional renormalisation group (FRG). The FRG equations can be solved analytically in the asymptotic regime of vanishing viscosity and large momenta, showing that indeed $z=1$ exactly at the IB fixed point. In this work, we set up an advanced method to numerically solve the full FRG flow equations in a certain approximation, which allows us to determine in a unified way the correlation function over the whole range of momenta, not restricted to some particular regime. We analyse the crossover between the different fixed points, and quantitatively determine the extent of the IB regime.

cond-mat.stat-mech↗

arXiv2024

The inviscid fixed point of the multi-dimensional Burgers-KPZ equation

A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing from the well-known KPZ one $z=3/2$, was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated. It was shown to be controlled by a yet unpredicted fixed point of the one-dimensional Burgers-KPZ equation, termed inviscid Burgers (IB) fixed point. The associated universal properties, including the scaling function, were calculated. All these findings were restricted to $d=1$, and it raises the intriguing question of the fate of this new IB fixed point in higher dimensions. In this work, we address this issue and analyze the multi-dimensional Burgers-KPZ equation using functional renormalization group. We show that the IB fixed point exists in all dimensions $d\geq 0$, and that it controls the large momentum behavior of the correlation functions in the inviscid limit. It turns out that it yields in all $d$ the same super-universal value $z=1$ for the dynamical exponent.

cond-mat.stat-mech↗