Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example, in granular and glassy systems. Compounding complexity, in many scientific and industrial applications, particles are polydisperse, aspherical, or even of varying shape. Here, we investigate a generalization of the classical kissing problem in order to unde...

This paper reports the results of the numerical study of the formation of aspherical Planetary Nebulae through the Generalised Interacting Winds Model, taking into account the eeects caused by the evolving central star and fast wind. The results show for the rst time that aspherical nebulae do form within the required time scale. Consideration of the development of the nebula shows that in the ...

We study random 2-dimensional complexes in the Linial Meshulam model and prove that for the probability parameter satisfying p ≪ n a random 2-complex Y contains several pairwise disjoint tetrahedra such that the 2-complex Z obtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complex Z satisfies the Whitehead conjecture, i.e. any subcom...

We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These “gravitational monopoles” have the following equivalent properties: (i) they generate, outside them, a spherically-symmetric gravitational potential M/|x − xO| ; (ii) their interaction energy with an external gravitational potential U(x) is −M U(xO) ; and (iii) all t...

OBJECTIVE To evaluate the theoretical effect of decentration of aspherical intraocular lenses (IOLs) and wavefront-corrected IOLs up to the sixth order on higher-order aberrations (HOAs) (third through sixth order) of the eye. METHODS An aspherical IOL with HOAs of fourth-order spherical aberrations only (-0.287 microm with a 6-mm pupil) and a wavefront-corrected IOL with HOAs of equal magnit...

Using the Hubble Space Telescope (HST), we have carried out a survey of candidate preplanetary nebulae (PPNs). We report here our discoveries of objects having well-resolved geometrical structures, and use the large sample of PPNs now imaged with HST (including previously studied objects in this class) to devise a comprehensive morphological classification system for this category of objects. T...

Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.