38 research outputs found
Quantum hydrodynamics for supersolid crystals and quasicrystals
Supersolids are theoretically predicted quantum states that break the
continuous rotational and translational symmetries of liquids while preserving
superfluid transport properties. Over the last decade, much progress has been
made in understanding and characterizing supersolid phases through numerical
simulations for specific interaction potentials. The formulation of an
analytically tractable framework for generic interactions still poses
theoretical challenges. By going beyond the usually considered quadratic
truncations, we derive a systematic higher-order generalization of the
Gross-Pitaevskii mean field model in conceptual similarity with the
Swift-Hohenberg theory of pattern formation. We demonstrate the tractability of
this broadly applicable approach by determining the ground state phase diagram
and the dispersion relations for the supersolid lattice vibrations in terms of
the potential parameters. Our analytical predictions agree well with numerical
results from direct hydrodynamic simulations and earlier quantum Monte-Carlo
studies. The underlying framework is universal and can be extended to
anisotropic pair potentials with complex Fourier-space structure.Comment: 18 pages, 10 figures; supplementary information available on reques
Vortex line entanglement in active Beltrami flows
Over the last decade, substantial progress has been made in understanding the
topology of quasi-2D non-equilibrium fluid flows driven by ATP-powered
microtubules and microorganisms. By contrast, the topology of 3D active fluid
flows still poses interesting open questions. Here, we study the topology of a
spherically confined active flow using 3D direct numerical simulations of
generalized Navier-Stokes (GNS) equations at the scale of typical microfluidic
experiments. Consistent with earlier results for unbounded periodic domains,
our simulations confirm the formation of Beltrami-like bulk flows with
spontaneously broken chiral symmetry in this model. Furthermore, by leveraging
fast methods to compute linking numbers, we explicitly connect this chiral
symmetry breaking to the entanglement statistics of vortex lines. We observe
that the mean of linking number distribution converges to the global helicity,
consistent with the asymptotic result by Arnold. Additionally, we characterize
the rate of convergence of this measure with respect to the number and length
of observed vortex lines, and examine higher moments of the distribution. We
find that the full distribution is well described by a k-Gamma distribution, in
agreement with an entropic argument.Comment: 18 pages, 8 figure
Linearly forced fluid flow on a rotating sphere
We investigate generalized Navier-Stokes (GNS) equations that couple
nonlinear advection with a generic linear instability. This analytically
tractable minimal model for fluid flows driven by internal active stresses has
recently been shown to permit exact solutions on a stationary two-dimensional
sphere. Here, we extend the analysis to linearly driven flows on rotating
spheres. We derive exact solutions of the GNS equations corresponding to
time-independent zonal jets and superposed westward-propagating Rossby waves,
qualitatively similar to those seen in planetary atmospheres. Direct numerical
simulations with large rotation rates obtain statistically stationary states
close to these exact solutions. The measured phase speeds of waves in the GNS
simulations agree with analytical predictions for Rossby waves.Comment: 13 pages, 6 figure
Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames
It has been proposed that mixing induced by convective overshoot can disrupt
the inward propagation of carbon deflagrations in super-asymptotic giant branch
stars. To test this theory, we study an idealized model of convectively bounded
carbon flames with 3D hydrodynamic simulations of the Boussinesq equations
using the pseudospectral code Dedalus. Because the flame propagation timescale
is much longer than the convection timescale, we approximate the flame as fixed
in space, and only consider its effects on the buoyancy of the fluid. By
evolving a passive scalar field, we derive a {\it turbulent} chemical
diffusivity produced by the convection as a function of height, .
Convection can stall a flame if the chemical mixing timescale, set by the
turbulent chemical diffusivity, , is shorter than the flame
propagation timescale, set by the thermal diffusivity, , i.e., when
. However, we find for most of the flame
because convective plumes are not dense enough to penetrate into the flame.
Extrapolating to realistic stellar conditions, this implies that convective
mixing cannot stall a carbon flame and that "hybrid carbon-oxygen-neon" white
dwarfs are not a typical product of stellar evolution.Comment: Accepted to Ap