Damped shape oscillations of a viscous compound droplet suspended in a viscous host fluid

A study of small-amplitude shape oscillations of a viscous compound droplet suspended in a viscous host fluid is performed. A generalized eigenvalue problem is formulated and is solved by using the spectral method. The effects of the relevant non-dimensional parameters are examined for three cases, i.e. a liquid shell in a vacuum and a compound droplet in a vacuum or in a host fluid. The fundamental mode $l=2$ is found to be dominant. There exist two oscillatory modes: the in phase and the out of phase. In most situations, the interfaces oscillate in phase rather than out of phase. For the in-phase mode, in the absence of the host, as the viscosity of the core or the shell increases, the damping rate increases whereas the oscillation frequency decreases; when the viscosity exceeds a critical value, the mode becomes aperiodic with the damping rate bifurcating into two branches. In addition, when the tension of the inner interface becomes smaller than some value, the in-phase mode turns aperiodic. In the presence of the unbounded host fluid, there exists a continuous spectrum. The viscosity of the host may decrease or increase the damping rate of the in-phase mode. The mechanism behind it is discussed. The density contrasts between fluids affect oscillations of the droplet in a complicated way. Particularly, sufficiently large densities of the core or the host lead to the disappearance of the out-of-phase mode. The thin shell approximation predicts well the oscillation of the compound droplet when the shell is thin.

On the propagation of waves in the atmosphere

The leading-order equations governing the unsteady dynamics of large-scale atmospheric motions are derived, via a systematic asymptotic approach based on the thin-shell approximation applied to the ellipsoidal model of the Earth’s geoid. We present some solutions of this single set of equations that capture properties of specific atmospheric flows, using field data to choose models for the heat sources that drive the motion. In particular, we describe standing-waves solutions, waves propagating towards the Equator, equatorially trapped waves and we discuss the African Easterly Jet/Waves. This work aims to show the benefits of a systematic analysis based on the governing equations of fluid dynamics.

Accurate Magnetic Shell Approximations with Magnetostatic Finite Element Formulations by a Subdomain Approach

This paper presents a subproblem approach with h-conformal magnetostatic finite element formulations for treating the errors of magnetic shell approximation, by replacing volume thin regions by surfaces with interface conditions. These approximations seem to neglect the curvature effects in the vicinity of corners and edges. The process from the surface-to-volume correction problem is presented as a sequence of several subdomains, which can be composed to the full domain, including inductors and thin magnetic regions. Each step of the process will be separately performed on its own subdomain and submesh instead of solving the problem in the full domain. This allows reducing the size of matrix and time computation.

Robust Correction Procedure for Accurate Thin Shell Models via a Perturbation Technique

This research proposes a robust correction procedure to improve inaccuracies around edges and corners inherent to thin shell electromagnetic problems by means of perturbation technique. This proposal is developed with three processes: A classical thin shell approximation replaced with an impedance-type interface condition across a surface is first considered and then a volume correction is introduced to overcome the thin shell approximation. However, the volume correction is quite sensitive to cancellation errors, with dramatic effects in the calculation of the local fields near edges and corners. Therefore, a robust correction procedure is added to improve cancellation errors of the volume correction. Each step of the developed method is validated on the practical problem.

Radiative absorption enhancements by black carbon controlled by particle-to-particle heterogeneity in composition

Black carbon (BC) absorbs solar radiation, leading to a strong but uncertain warming effect on climate. A key challenge in modeling and quantifying BC’s radiative effect on climate is predicting enhancements in light absorption that result from internal mixing between BC and other aerosol components. Modeling and laboratory studies show that BC, when mixed with other aerosol components, absorbs more strongly than pure, uncoated BC; however, some ambient observations suggest more variable and weaker absorption enhancement. We show that the lower-than-expected enhancements in ambient measurements result from a combination of two factors. First, the often used spherical, concentric core-shell approximation generally overestimates the absorption by BC. Second, and more importantly, inadequate consideration of heterogeneity in particle-to-particle composition engenders substantial overestimation in absorption by the total particle population, with greater heterogeneity associated with larger model–measurement differences. We show that accounting for these two effects—variability in per-particle composition and deviations from the core-shell approximation—reconciles absorption enhancement predictions with laboratory and field observations and resolves the apparent discrepancy. Furthermore, our consistent model framework provides a path forward for improving predictions of BC’s radiative effect on climate.

The full evolution of supernova remnants in low- and high-density ambient media

ABSTRACT Supernova explosions and their remnants (SNRs) drive important feedback mechanisms that impact considerably the galaxies that host them. Then, the knowledge of the SNRs evolution is of paramount importance in the understanding of the structure of the interstellar medium and the formation and evolution of galaxies. Here, we study the evolution of SNRs in homogeneous ambient media from the initial, ejecta-dominated phase, to the final, momentum-dominated stage. The numerical model is based on the Thin-Shell approximation and takes into account the configuration of the ejected gas and radiative cooling. It accurately reproduces well-known analytic and numerical results and allows one to study the SNR evolution in ambient media with a wide range of densities n0. It is shown that in the high-density cases, strong radiative cooling alters noticeably the shock dynamics and inhibits the Sedov-Taylor stage, thus limiting significantly the feedback that SNRs provide to such environments. For n0 > 5 × 105 cm−3, the reverse shock does not reach the centre of the explosion due to the rapid fall of the thermal pressure in the shocked gas caused by strong radiative cooling.

GS242-03+37: a lucky survivor in the galactic gravitational field

Context. HI shells and supershells, found in discs of many galaxies including our own, are formed by the activity of young and massive stars (supernova explosions and stellar winds), but the formation of these structures may be linked to other energetic events, such as interactions of high-velocity clouds with the galactic disc. The larger structures in particular significantly influence their surroundings; their walls are often places where molecular clouds reside and where star formation happens. Aims. We explore the HI supershell GS242-03+37, a large structure in the outer Milky Way. Its size and position make it a good case for studying the effects of large shells on their surrounding. Methods. We perform numerical simulations of the structure with the simplified hydrodynamical code RING, which uses the thin-shell approximation. The best fit is found by a comparison with the HI data and then we compare our model with the distribution of star clusters near this supershell. Results. The best model of GS242-03+37 requires, contrary to previous estimates, a relatively low amount of energy, and it has an old age of ∼100 Myr. We also find that the distribution of young star clusters (with ages <120 Myr) is correlated with walls of the supershell, while the distribution of older clusters is not. Clusters that have the highest probability of being born in the wall of the supershell show an age sequence along the wall. Conclusions. GS242-03+37 is a relatively old structure, shaped by the differential rotation, and its wall is a birthplace of several star clusters. The star formation started at a time when the supershell was not already supersonically expanding; it was a result of the density increase due to the galactic shear and oscillations perpendicular to the disc of the Milky Way.