The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter

We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are exacerbated by thermal instability when cooling is present, forming post--shock `stripes'. These are orthogonal to the classic post--shock 'ringing' fluctuations. The resulting post--shock `striping' substantially modifies the flow. We discuss three different methods to resolve this problem. These include (1) a method based on artificial viscosity; (2) grid--jittering and (3) a new localized oscillation filter that acts on specific grid cells in the shock front. These methods are tested using a radiative wall shock problem with an embedded shear layer. The artificial viscosity method is unsatisfactory since, while it does reduce post--shock ringing, it does not eliminate the stripes and the excessive shock broadening renders the calculation of cooling inaccurate, resulting in an incorrect shock location. Grid--jittering effectively counteracts striping. However, elsewhere on the grid, the shear layer is unphysically diffused and this is highlighted in an extreme case. The oscillation filter method removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. It also has the advantage of only acting on a small fraction of the cells in a two or three dimensional simulation and does not significantly impair performance.Comment: 20 pages, 6 figures, revised version submitted to ApJ Supplement Serie

Lipase inhibition attenuates the acute inhibitory effects of oral fat on food intake in healthy subjects

The lipase inhibitor, orlistat, is used in the treatment of obesity and reduces fat absorption by about 30%. However, the mean weight loss induced by orlistat is less than expected for the degree of fat malabsorption. It was hypothesised that lipase inhibition with orlistat attenuates the suppressive effects of oral fat on subsequent energy intake in normal-weight subjects. Fourteen healthy, lean subjects (nine males, five females; aged 25 +/- 1.3 years) were studied twice, in a double-blind fashion. The subjects received a high-fat yoghurt 'preload' (males 400 g (2562 kJ); females 300 g (1923 kJ)), containing orlistat (120 mg) on one study day (and no orlistat on the other 'control' day), 30 min before ad libitum access to food and drinks; energy intake was assessed during the following 8 h. Blood samples were taken at regular intervals for the measurement of plasma cholecystokinin (CCK). Each subject performed a 3 d faecal fat collection following each study. Energy intake during the day was greater following orlistat (10,220 (SEM 928) kJ) v. control (9405 (SEM 824) kJ) (P=0.02). On both days plasma CCK increased (P<0.05) after the preload. Plasma CCK 20 min following ingestion of the preload was less after orlistat (4.1 (SEM 0.9) pmol/l) v. control (5.3 (SEM 0.9) pmol/l (P=0.028); however there was no difference in the area under the curve 0-510 min between the two study days. Fat excretion was greater following orlistat (1017 (SEM 168) kJ) v. control (484 (SEM 90) kJ) (P=0.004). In conclusion, in healthy, lean subjects the acute inhibitory effect of fat on subsequent energy intake is attenuated by orlistat and the increase in energy intake approximates the energy lost due to fat malabsorption.Deirdre O’Donovan, Christine Feinle-Bisset, Judith Wishart and Michael Horowit

Depletion and fluctuations of a trapped dipolar Bose-Einstein condensate in the roton regime

We consider the non-condensate density and density fluctuations of a trapped dipolar Bose-Einstein condensate, focusing on the regime where a roton-like excitation spectrum develops. Our results show that a characteristic peak in the non-condensate density occurs at trap center due to the rotons. In this regime we also find that the anomalous density becomes positive and peaked, giving rise to enhanced density fluctuations. We calculate the non-condensate density in momentum space and show that a small momentum halo is associated with the roton excitations.Comment: 8 pages, 5 figure

Finite-temperature trapped dipolar Bose gas

We develop a finite temperature Hartree theory for the trapped dipolar Bose gas. We use this theory to study thermal effects on the mechanical stability of the system and density oscillating condensate states. We present results for the stability phase diagram as a function of temperature and aspect ratio. In oblate traps above the critical temperature for condensation we find that the Hartree theory predicts significant stability enhancement over the semiclassical result. Below the critical temperature we find that thermal effects are well described by accounting for the thermal depletion of the condensate. Our results also show that density oscillating condensate states occur over a range of interaction strengths that broadens with increasing temperature.Comment: 10 pages, 7 figure

Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.Comment: 10 pages, 8 figure