Related papers: The nonlinear development of the relativistic two-…

We here present two simplified models aimed at describing the long-term, irregular behaviours observed in the rheological response of certain complex fluids, such as periodic oscillations or chaotic-like variations. Both models exploit the…

The nonlinear evolution of the quantum two-stream instability in a plasma with counter-streaming electron beams is studied. It is shown that in the long-wave limit the nonlinear stage of the instability can be described by the elliptic…

Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to…

We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

Theoretical and numerical analysis of the relativistic effects on the Richtmyer-Meshkov (RM) instability reveals new and potentially very useful effects. We find that, in contrast with the non- relativistic case, the growth rate of the RM…

In this paper we argue that differential rotation can possibly sustain hydrodynamic turbulence in the absence of magnetic field. We explain why the non-linearities of the hydrodynamic equations (i.e. turbulent diffusion) should not be…

Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations…

The Rayleigh-Taylor instability is a key process in many fields of Physics ranging from astrophysics to inertial confinement fusion. It is usually analyzed deriving the linearized fluid equations, but the physics behind the instability is…

We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and…

In this note, we propose a new idea by analyzing the basic disturbance equations, and give starting equations for understanding the instability phenomena of laminar flows and transition to turbulence. It is considered that there is an…

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 stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed…

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…

We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…

The evolution of an instability at the interface of active and passive media is considered. An asymptotic form of a collision integral is found and the limitations of hydrodynamic approach are determined. A growth increment of small…

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…

We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard…

We examine the hydrodynamics of a granular gas using numerical simulation. We demonstrate the appearance of shearing and clustering instabilities predicted by linear stability analysis, and show that their appearance is directly related to…