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

Galaxy evolution within the Kilo-Degree Survey

The ESO Public Kilo-Degree Survey (KiDS) is an optical wide-field imaging survey carried out with the VLT Survey Telescope and the OmegaCAM camera. KiDS will scan 1500 square degrees in four optical filters (u, g, r, i). Designed to be a weak lensing survey, it is ideal for galaxy evolution studies, thanks to the high spatial resolution of VST, the good seeing and the photometric depth. The surface photometry have provided with structural parameters (e.g. size and S\'ersic index), aperture and total magnitudes have been used to derive photometric redshifts from Machine learning methods and stellar masses/luminositites from stellar population synthesis. Our project aimed at investigating the evolution of the colour and structural properties of galaxies with mass and environment up to redshift $z \sim 0.5$ and more, to put constraints on galaxy evolution processes, as galaxy mergers.Comment: 4 pages, 2 figures, to appear on the refereed Proceeding of the "The Universe of Digital Sky Surveys" conference held at the INAF--OAC, Naples, on 25th-28th november 2014, to be published on Astrophysics and Space Science Proceedings, edited by Longo, Napolitano, Marconi, Paolillo, Iodic

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