Swift-Hohenberg equation with broken reflection symmetry

The bistable Swift-Hohenberg equation possesses a variety of time-independent spatially localized solutions organized in the so-called snakes-and-ladders structure. This structure is a consequence of a phenomenon known as homoclinic snaking, and is in turn a consequence of spatial reversibility of the equation. We examine here the consequences of breaking spatial reversibility on the snakes-and-ladders structure. We find that the localized states now drift, and show that the snakes-and-ladders structure breaks up into a stack of isolas. We explore the evolution of this new structure with increasing reversibility breaking and study the dynamics of the system outside of the snaking region using a combination of numerical and analytical techniques

Solidification in soft-core fluids: disordered solids from fast solidification fronts

Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. For the one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.Comment: 18 pages, 14 fig

Buoyancy driven rotating boundary currents

The structure of boundary currents formed from intermediately dense water introduced into a rotating, stably stratified, two-layer environment is investigated in a series of laboratory experiments, performed for Froude numbers ranging from 0.01 to 1. The thickness and streamwise velocity profiles in quasi-steady currents are measured using a pH activated tracer (thymol blue) and found to compare favorably to simplified analytic solutions and numerical models. Currents flowing along sloping boundaries in a stratified background exhibit robust stability at all experimental Froude numbers. Such stability is in sharp contrast to the unequivocal instability of such currents flowing against vertical boundaries, or of currents flowing along slopes in a uniform background. The presence of a variety of wave mechanisms in the ambient medium might account for the slower and wider observed structures and the stability of the currents, by effecting the damping of disturbances through wave radiation.Comment: 9 pages with 2 figures to appear in Ann NYAS "Long range effects in physics and astrophysics

On the degenerated soft-mode instability

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general equation of motion the full amplitude equation is derived systematically and formulas for the dependence of the coefficients on the system parameters are obtained. We emphasise the importance of nonlinear derivative terms in the amplitude equation for the behaviour in the vicinity of the bifurcation point. Especially the numerical values of the corresponding coefficients determine the region of coexistence between the stable trivial solution and stable spatially periodic patterns. Our approach clearly shows that similar considerations fail for the case of oscillatory instabilities.Comment: 16 pages, uses iop style files, manuscript also available at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/jpa_97/ or at http://athene.fkp.physik.th-darmstadt.de/public/wolfram_publ.html. J. Phys. A in pres

Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow

Hollerbach and Rudiger have reported a new type of magnetorotational instability (MRI) in magnetized Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields. The salient advantage of this "helical'' MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize than standard MRI (axial field only). We confirm their results, calculate HMRI growth rates, and show that in the resistive limit, HMRI is a weakly destabilized inertial oscillation propagating in a unique direction along the axis. But we report other features of HMRI that make it less attractive for experiments and for resistive astrophysical disks. Growth rates are small and require large axial currents. More fundamentally, instability of highly resistive flow is peculiar to infinitely long or periodic cylinders: finite cylinders with insulating endcaps are shown to be stable in this limit. Also, keplerian rotation profiles are stable in the resistive limit regardless of axial boundary conditions. Nevertheless, the addition of toroidal field lowers thresholds for instability even in finite cylinders.Comment: 16 pages, 2 figures, 1 table, submitted to PR

The Stability of Magnetized Rotating Plasmas with Superthermal Fields

During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper, we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a non-trivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfven speeds exceeding the geometric mean of the sound speed and the rotational speed. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.Comment: 24 pages, 12 figures. Accepted for publication in ApJ. Sections 2 and 5 substantially expanded, added Appendix A and 3 figures with respect to previous version. Animations are available at http://www.physics.arizona.edu/~mpessah/research

Localized transverse bursts in inclined layer convection

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wavenumber, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems.Comment: 4 pages, 8 figure

Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula

Gravitational instability of a vertically thin, dusty sheet near the midplane of a protoplanetary disk has long been proposed as a way of forming planetesimals. Before Roche densities can be achieved, however, the dust-rich layer, sandwiched from above and below by more slowly rotating dust-poor gas, threatens to overturn and mix by the Kelvin-Helmholtz instability (KHI). Whether such a threat is real has never been demonstrated: the Richardson criterion for the KHI is derived for 2-D Cartesian shear flow and does not account for rotational forces. Here we present 3-D numerical simulations of gas-dust mixtures in a shearing box, accounting for the full suite of disk-related forces: the Coriolis and centrifugal forces, and radial tidal gravity. Dust particles are assumed small enough to be perfectly entrained in gas; the two fluids share the same velocity field but obey separate continuity equations. We find that the Richardson number Ri does not alone determine stability. The critical value of Ri below which the dust layer overturns and mixes depends on the height-integrated metallicity Z (surface density ratio of dust to gas). Nevertheless, for Z between one and five times solar, the critical Ri is nearly constant at 0.1. Keplerian radial shear stabilizes those modes that would otherwise disrupt the layer at large Ri. If Z is at least 5 times greater than the solar value of 0.01, then midplane dust densities can approach Roche densities. Such an environment might be expected to produce gas giant planets having similarly super-solar metallicities.Comment: ApJ, in press. Connections made to baroclinic instability. Movies available at http://astro.berkeley.edu/~echiang/im/im.htm