Comment on ``Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions"

Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a weakly-interacting Bose-Einstein condensate. In addition to other interesting results, using the method of the pair correlation function, they questioned the validity of the mean-field picture of the formation of vortices and stated that the vortices are generated at the center of the cloud. This is in apparent contradiction to the Gross-Pitaevskii approach, which predicts that the vortices successively enter the cloud from its outer parts as L/N (where N is the number of atoms in the trap and hbar(L) is the angular momentum of the system) increases. We have managed to reproduce the results of Liu et al. however a more careful analysis presented below confirms the validity of the mean-field approach.Comment: 1 page, RevTex, 2 figure

A taxonomy of informality: exploring block types in five informal settlements in East Africa

Approximately 13% of the world population lives in informal settlements, characterized by limited state control, inadequate infrastructure provision, and lack of planning. While the relevance of studies of informal settlements is widely acknowledged, the urban morphology of such areas is understudied, compromising the development of effective planning and policy targeting such areas. In this paper, we present a taxonomic study at a fine level of spatial granularity of the urban form of five informal settlements, located in major cities of Sub-Saharan Africa. More specifically, a k-means clustering is applied to eight indicators of urban form computed at block level, for each of the settlements under examination. The best clustering identified ten different block types associated with distinctive features, such as blocks on public spaces (small, densely built, abundant public open space), fringe blocks (medium-sized, sparsely built, low local connectivity), blocks in the making (large, sparsely built, high levels of through movement at settlement level). We argue that this taxonomy provides detailed information about the case studies under examination, which can potentially inform design strategies aimed at their upgrading. Finally, it presents some of the first attempts at establishing replicable quantitative data driven descriptions of the urban form of informal settlements

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Difference between stable and exotic nuclei: medium polarization effects

The bare NN-potential, parametrized so as to reproduce the nuclear phase shifts leads to a sizable Cooper pair binding energy in nuclei along the stability valley. It is a much debated matter whether this value accounts for the "empirical" value of the pairing gap or whether a similarly important contribution arises from the exchange of collective vibrations between Cooper pair partners. In keeping with the fact that two-particle transfer reactions are the specific probe of pairing in nuclei, and that exotic halo nuclei like 11Li are extremely polarizable, we find that the recent studied reaction, namely 11Li+p -> 9Li+t, provides direct evidence of phonon mediated pairing in nuclei

Shape Deformations in Atomic Nuclei

The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.Comment: 20 pages, 10 figures, submitted to scholarpedi