Related papers: Landau Instability and soliton formation
We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
A free-energy minimization approach is used to address the secular & dynamical instabilities & the bifurcations along sequences of rotating, self-gravitating fluid and stellar systems. Our approach stems from the Landau-Ginzburg theory of…
In this work, the normal density $\rho_n$ and moment of inertia of a moving superfluid are investigated. We find that, even at zero temperature, there exists a finite normal density for the moving superfluid. When the velocity of superfluid…
We theoretically study the nonlinear dynamics of the instability of counter-superflow in two miscible Bose-Einstein condensates. The condensates become unstable when the relative velocity exceeds a critical value, which is called…
We study the superfluid dynamics of the outer core of neutron stars by means of a hydrodynamic model made of a neutronic superfluid and a protonic superconductor, coupled by both the dynamic entrainment and the Skyrme SLy4 nucleon-nucleon…
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to…
We show that the presence of soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficient enough to induce dynamical instability of the system. We also predict that for two-species condensates, two…
Over the last decade, an increasing body of evidence has emerged, supporting the existence of a metastable liquid-liquid critical point in supercooled water, whereby two distinct liquid phases of different densities coexist. Analysing long…
We study a holographic model of a relativistic quantum system with a global U(1) symmetry, at non-zero temperature and density. When the temperature falls below a critical value, we find a second-order superfluid phase transition with…
A new element is proposed to play a role in the evolution of extrasolar planetary systems: the tidal (or elliptical) instability. It comes from a parametric resonance and takes place in any rotating fluid whose streamlines are (even…
The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e. there are macroscopic evolution equations for homogeneous states. The stability…
The formation of velocity vortices and density clusters is an intriguing phenomenon of freely cooling granular flows. In this work, the critical length scale $L_c$ for the onset of instability is determined via stability analysis of the…
Understanding the interface dynamics in non-equilibrium quantum systems remains a challenge. We study the interface dynamics of strongly coupled immiscible binary superfluids by using holographic duality. The full nonlinear evolution of the…
There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity…
We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice…
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of…
The possible instabilities in a running superfluid has been a long-time historical problem since first studied by L. P. Landau. By constructing effective actions in terms of suitable order parameters, we revisit this outstanding open…
Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow…