Density functional theory modeling of vortex shedding in superfluid He-4

Formation of vortex rings around moving spherical objects in superfluid He-4 at 0 K is modeled by time-dependent density functional theory. The simulations provide detailed information of the microscopic events that lead to vortex ring emission through characteristic observables such as liquid current circulation, drag force, and hydrodynamic mass. A series of simulations were performed to determine velocity thresholds for the onset of dissipation as a function of the sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The threshold was observed to decrease with the sphere radius and increase with pressure thus showing that the onset of dissipation does not involve roton emission events (Landau critical velocity), but rather vortex emission (Feynman critical velocity), which is also confirmed by the observed periodic response of the hydrodynamic observables as well as visualization of the liquid current circulation. An empirical model, which considers the ratio between the boundary layer kinetic and vortex ring formation energies, is presented for extrapolating the current results to larger length scales. The calculated critical velocity value at zero pressure for a sphere that mimics an electron bubble is in good agreement with the previous experimental observations at low temperatures. The stability of the system against symmetry breaking was linked to its ability to excite quantized Kelvin waves around the vortex rings during the vortex shedding process. At high vortex ring emission rates, the downstream dynamics showed complex vortex ring fission and reconnection events that appear similar to those seen in previous Gross-Pitaevskii theory-based calculations, and which mark the onset of turbulent behavior.Comment: 23 pages, 7 figure

On the swelling of rolled up vortex surfaces and the breakdown of the vortex core for slender wings

Simplified models of the vortex distribution over cylindrical surfaces are developed. The effect of a change of vortex strength was analyzed quantitatively by menas of potential theory. The considerable bulging of the cylindrical vortex sheet as a consequence of the change of the vortex strength is discussed. The coiling-up of the vortices rotation in opposite directions over the cylindrical surface renders the condition for instability and the subsequent large spreading of the vortex core. These processes occur without a positive pressure gradient being necessary in the field of flow surrounding the coiled up vortex sheet

ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic

A Semi-Analytical Model of Visible-Wavelength Phase Curves of Exoplanets and Applications to Kepler-7 b and Kepler-10 b

Kepler has detected numerous exoplanet transits by precise measurements of stellar light in a single visible-wavelength band. In addition to detection, the precise photometry provides phase curves of exoplanets, which can be used to study the dynamic processes on these planets. However, the interpretation of these observations can be complicated by the fact that visible-wavelength phase curves can represent both thermal emission and scattering from the planets. Here we present a semi-analytical model framework that can be applied to study Kepler and future visible-wavelength phase curve observations of exoplanets. The model efficiently computes reflection and thermal emission components for both rocky and gaseous planets, considering both homogeneous and inhomogeneous surfaces or atmospheres. We analyze the phase curves of the gaseous planet Kepler-7 b and the rocky planet Kepler-10 b using the model. In general, we find that a hot exoplanet's visible-wavelength phase curve having a significant phase offset can usually be explained by two classes of solutions: one class requires a thermal hot spot shifted to one side of the substellar point, and the other class requires reflective clouds concentrated on the same side of the substellar point. The two solutions would require very different Bond albedos to fit the same phase curve; atmospheric circulation models or eclipse observations at longer wavelengths can effectively rule out one class of solutions, and thus pinpoint the albedo of the planet, allowing decomposition of the reflection and the thermal emission components in the phase curve. Particularly for Kepler-7 b, reflective clouds located on the west side of the substellar point can best explain its phase curve. We further derive that the reflectivity of the clear part of the atmosphere should be less than 7% and that of the cloudy part should be greater than 80% (abridged)Comment: 16 pages, 7 figures, accepted for publication in Ap

Theoretical Transit Spectra for GJ 1214b and Other "Super-Earths"

We present new calculations of transit spectra of super-Earths that allow for atmospheres with arbitrary proportions of common molecular species and haze. We test this method with generic spectra, reproducing the expected systematics and absorption features, then apply it to the nearby super-Earth GJ 1214b, which has produced conflicting observational data, leaving the questions of a hydrogen-rich versus hydrogen-poor atmosphere and the water content of the atmosphere ambiguous. We present representative transit spectra for a range of classes of atmosphere models for GJ 1214b. Our analysis supports a hydrogen-rich atmosphere with a cloud or haze layer, although a hydrogen-poor model with less than 10% water is not ruled out. Several classes of models are ruled out, however, including hydrogen-rich atmospheres with no haze, hydrogen-rich atmospheres with a haze of about 0.01-micron tholin particles, and hydrogen-poor atmospheres with major sources of absorption other than water. We propose an observational test to distinguish hydrogen-rich from hydrogen-poor atmospheres. Finally, we provide a library of theoretical transit spectra for super-Earths with a broad range of parameters to facilitate future comparison with anticipated data.Comment: 33 pages, 21 figures, 3 table