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Spiral density waves can arise in galactic disks as linear instabilities of the underlying stellar distribution function. Such an instability grows exponentially in amplitude at some fixed growth rate $\beta$ before saturating nonlinearly.…
In several space dimensions, scalar shock waves between two constant states u $\pm$ are not necessarily planar. We describe them in detail. Then we prove their asymptotic stability, assuming that they are uniformly non-characteristic. Our…
Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence…
Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to…
A cylindrical elastomer tube can stay in an everted state without any applied external forces. If the thickness of the tube is small, the everted tube, except for the regions close to the two ends of the tube, is cylindrical, if the…
We report experimental study of the secondary modulational instability of a one-dimensional non-linear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatio-temporal defects are…
We present the first realistic 3D simulations of flame front instabilities during type I X-ray bursts. The unperturbed front is characterised by the balance between the pressure gradient and the Coriolis force of a spinning neutron star…
The effect of nonlinearity on plasma wake wave excited by a relativistic cylindrical charged bunch is investigated. It is shown that owing to the nonlinearity the amplitude of wake wave gets modulated in the longitudinal direction. The…
A core-collapse supernova might produce large amplitude gravitational waves if, through the collapse process, the inner core can aquire enough rotational energy to become dynamically unstable. In this report I present the results of 3-D…
Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…
We perform a laboratory-scale experiment of submarine avalanches on a rough inclined plane. A sediment layer is prepared and thereafter tilted up to an angle lower than the spontaneous avalanche angle. The sediment is scrapped until an…
The problem of convective instability onset in a horizontal porous channel is explored. The channel's impermeable walls are heated with asymmetric thermal conditions modelled through unequal, but uniform, wall heat fluxes. A stationary…
We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We study from the numerical point of view, instabilities developed in a fluid layer with a free surface, in a cylindrical container which is non-homogeneously heated from below. In particular we consider the case in which the applied heat…
We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and…
This paper investigates the nature of the MHD turbulence excited by the streaming of accelerated cosmic rays in a shock wave precursor. The two recognised regimes (non-resonant and resonant) of the streaming instability are taken into…
We study line driven stellar winds using time-dependent radiation hydrodynamics where the continuum radiation couples to the gas via either a scattering or absorption opacity and there is an additional radiation force due to spectral lines…
The nonlinear dynamics of thermal and electromagnetic perturbations in the vortex state of type II superconductors is analyzed with account of dissipation and dispersion effects. A theoretical analysis shows that nonlinear thermal and…
The stability theory of the skin layer plasma of the inductive discharge is developed for the case when the electron quiver velocity in RF wave is of the order of or is larger than the electron thermal velocity. This theory is grounded on…