Related papers: The deceiving delta: on the equilibrium dependent …
The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the…
Recent simulation and experimental results suggest that the magnetic island and flow on resonant surface often do not satisfy the "no-slip" condition in the steady state. A new theory model on nonlinear plasma response to external magnetic…
The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable $\Delta' > 0$…
The magnetic Rayleigh-Taylor instability has been shown to play a key role in many astrophysical systems. The equation for the growth rate of this instability in the incompressible limit, and the most-unstable mode that can be derived from…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
The nonlinear dynamo effect of tearing modes is derived with the resistive MHD equations. The dynamo effect is divided into two parts, parallel and perpendicular to the magnetic field. Firstly, the force-free plasma is considered. It is…
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model,…
Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic \beta parameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model's differential rotation yields stability in the absence of a magnetic field, but if a…
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state…
The tearing mode instability and the associated magnetic islands can lead to a degradation of tokamak plasma performance and eventually to a disruption. A crucial issue for the extension of advanced tokamak scenarios to long pulse operation…
The uniform states of a model for one-dimensional chains of thin magnetic islands on a nonmagnetic substrate coupled via dipolar interactions are described here. Magnetic islands oriented with their long axes perpendicular to the chain…
The dynamics of a propagating magnetic island interacting with a resistive wall or a static external magnetic perturbation is investigated using two-fluid, drift-MHD theory in slab geometry. In both cases, the island equation of motion is…
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…