An Engel condition for orderable groups

Let m,n be positive integers, v a multilinear commutator word and w=v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v=x the group G is nilpotent (rather than merely locally nilpotent)

Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally-relevant particle models. We illustrate the method through the determination of the cholesteric behaviour of hard, structurally-resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of $45^\circ$. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold

Small satellites beyond boundaries

It is a great pleasure for me to present this special issue of the CEAS Space Journal devoted to Small Satellites Beyond Boundaries. This brings together some of the most interesting presentations delivered throughout several conferences held in the last couple of years in the area of Small Satellites and CubeSats. Small satellites (and, more recently, CubeSats) were initially developed for educational purposes, however their capabilities have opened a new design space for exploration that includes stand-alone spacecraft, constellations, and mother–daughter systems that collaborate. In light of recent advances in science instruments and spacecraft miniaturization technologies that have emerged in just the past few years, small spacecraft can now be considered for use in planetary exploration, either as adjuncts to larger missions on which they could “catch a ride” to the most remote and challenging destinations in the solar system, or in some cases, as stand-alone missions of their own. The first ever experience of an interplanetary mission carried out using CubeSats is the Mars Cube One (MarCO) mission to Mars, flown as a companion to the InSight mission to Mars. Next, a spectacular set of 13 CubeSats will be delivered in 2021 to a high lunar orbit within the frame of NASA’s Artemis-1 mission—the first launch of their new space launch system (SLS) rocket

Unsupervised Learning via Mixtures of Skewed Distributions with Hypercube Contours

Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have two unique features: they include a multivariate weight function, and the marginal distributions are also asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could equally well be used in the supervised or semi-supervised paradigms. The expectation-maximization algorithm is used for parameter estimation and the Bayesian information criterion is used for model selection. Simulated and real data sets are used to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components

Colour and stellar population gradients in galaxies

We discuss the colour, age and metallicity gradients in a wide sample of local SDSS early- and late-type galaxies. From the fitting of stellar population models we find that metallicity is the main driver of colour gradients and the age in the central regions is a dominant parameter which rules the scatter in both metallicity and age gradients. We find a consistency with independent observations and a set of simulations. From the comparison with simulations and theoretical considerations we are able to depict a general picture of a formation scenario.Comment: 4 pages, 4 figures. Proceedings of 54th Congresso Nazionale della SAIt, Napoli 4-7 May 201

Evolution of central dark matter of early-type galaxies up to z ~ 0.8

We investigate the evolution of dark and luminous matter in the central regions of early-type galaxies (ETGs) up to z ~ 0.8. We use a spectroscopically selected sample of 154 cluster and field galaxies from the EDisCS survey, covering a wide range in redshifts (z ~ 0.4-0.8), stellar masses ($\log M_{\star}/ M_{\odot}$ ~ 10.5-11.5 dex) and velocity dispersions ($\sigma_{\star}$ ~ 100-300 \, km/s). We obtain central dark matter (DM) fractions by determining the dynamical masses from Jeans modelling of galaxy aperture velocity dispersions and the $M_{\star}$ from galaxy colours, and compare the results with local samples. We discuss how the correlations of central DM with galaxy size (i.e. the effective radius, $R_{\rm e}$), $M_{\star}$ and $\sigma_{\star}$ evolve as a function of redshift, finding clear indications that local galaxies are, on average, more DM dominated than their counterparts at larger redshift. This DM fraction evolution with $z$ can be only partially interpreted as a consequence of the size-redshift evolution. We discuss our results within galaxy formation scenarios, and conclude that the growth in size and DM content which we measure within the last 7 Gyr is incompatible with passive evolution, while it is well reproduced in the multiple minor merger scenario. We also discuss the impact of the IMF on our DM inferences and argue that this can be non-universal with the lookback time. In particular, we find the Salpeter IMF can be better accommodated by low redshift systems, while producing stellar masses at high-$z$ which are unphysically larger than the estimated dynamical masses (particularly for lower-$\sigma_{\star}$ systems).Comment: 14 pages, 6 figures, 3 tables, MNRAS in pres

Nanosatellite-class dynamic attitude simulator for hands-on aerospace control education

Due to their low size, mass, development cost and time, nanosatellites have become an increasingly popular tool at universities for providing students with hands-on experience in aerospace education. Among spacecraft subsystems, the attitude determination and control one surely represents a fruitful resource for practicing aerospace control applications. To enable on-ground verification of spacecraft attitude control hardware and software, however, the biggest challenge to overcome is that of providing a representative testing environment. Towards this end, at the µ3S laboratory at the University of Bologna a dynamic hardware in the loop facility has been developed, which allows for testing attitude control subsystems of nanosatellites in the range of 1U to 3U, according to the CubeSat form factor. This paper describes the educational impact that the facility has been having, during both its development and commissioning phases, as well as its early use as a testbed for CubeSats attitude control, which is currently focused on magnetic-based actuation