On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs) in the presence of a spatio-temporally varying external potential. The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrodinger equation (called the 'transverse equation') and a one-dimensional (1D) nonlinear Schrodinger equation (called the 'longitudinal equation'), constrained by a variational condition for the controlling potential. The latter corresponds to the requirement for the minimization of the control operation in the transverse plane. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. A consistency condition between the transverse and longitudinal solutions yields a relationship between the transverse and longitudinal restoring forces produced by the external trapping potential well through a 'controlling parameter' (i.e. the average, with respect to the transverse profile, of the nonlinear inter-atomic interaction term of the GPE). It is found that the longitudinal profile supports localized solutions in the form of bright, dark or grey solitons with time-dependent amplitudes, widths and centroids. The related longitudinal phase is varying in space and time with time-dependent curvature radius and wavenumber. In turn, all the above parameters (i.e. amplitudes, widths, centroids, curvature radius and wavenumbers) can be easily expressed in terms of the controlling parameter. It is also found that the transverse profile has the form of Hermite-Gauss functions (depending on the transverse coordinates), and the explicit spatio-temporal dependence of the controlling potential is self-consistently determined. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.

In optimizing the topology of wireless networks built of a dynamic set of spatially embedded agents, there are many trade-offs to be dealt with. The network should preferably be as small (in the sense that the average, or maximal, pathlength is short) as possible, it should be robust to failures, not consume too much power, and so on. In this paper, we investigate simple models of how agents can choose their neighbors in such an environment. In our model of attachment, we can tune from one situation where agents prefer to attach to others in closest proximity, to a situation where agents attach to random others regardless of distance (which thus are, on average, further away than the connections to the spatial neighbors). We evaluate this scenario with several performance measures and find that the optimal topologies, for most of the quantities, is obtained for strategies resulting in a mix of most local and a few random connections.

We propose that the ubiquitous scale free nature of many real world networks may emerge from a steady state process where nodes are created and merged randomly. The merging may be viewed as an optimization of efficiency by minimizing redundancy.

Two-dimensional polymerisation of a C60 single crystal has been obtained under high-pressure high temperature conditions (700 K - 2 GPa). Crystalline order is preserved but the crystal splits into variants (orientational domains). The analysis of X-ray diffraction and Raman spectroscopy data reveals that the polymer crystal is primarily tetragonal with some admixture of rhombohedral phase. Furthermore, Raman spectroscopy gives evidence for additional C60-C60 dimers, which are probably disordered. For the tetragonal phase, it is shown that successive polymer layers are rotated by about the stacking axis, according to the P42/mmc space group symmetry. The structure of the rhombohedral phase is also clarified. The role of the interlayer interactions in stabilising the two-dimensional polymer phases of C60 is discussed.

We provide evidence that high-pressure high-temperature (2.5 GPa and 1040 K) treatment of mixtures of iron with fullerene powders leads to the complete transformation of iron into iron carbide Fe3C. The comparison of the magnetic properties (Curie temperature and magnetic moment) of the here studied samples and those for the ferromagnetic polymer Rh-C-60 indicates that the main ferromagnetic signal reported in those samples is due to Fe3C and not related to the ferromagnetism of carbon as originally interpreted. Taking into account the results obtained in this study the original paper on "Magnetic carbon" [Nature 413, 716 (2001)] was recently retracted.

We report the first X-ray diffraction and Raman spectroscopy study of a single crystal of the rare-earth endohedral fullerene Dy@C-82. The lattice is found to be body-centered cubic (a = 25.79 Angstrom, space group I (4) over bar 3d) which is at variance with previous reports and confirms that several types of structures can be stabilized in Dy@C-82. X-ray diffraction/diffuse scattering methods reveal no low-temperature change down to 12 K for the present structure. The Raman spectroscopy data are comparable to those of other M@C-82 endohedral compounds. However, the Dy oxidation state and the force constant of the low-frequency metal-cage stretching mode do not follow the simple relationship observed before.