A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for plate-like fillers such as graphene and graphite nanoplatelets

Alignments of Voids in the Cosmic Web

We investigate the shapes and mutual alignment of voids in the large scale matter distribution of a LCDM cosmology simulation. The voids are identified using the novel WVF void finder technique. The identified voids are quite nonspherical and slightly prolate, with axis ratios in the order of c:b:a approx. 0.5:0.7:1. Their orientations are strongly correlated with significant alignments spanning scales >30 Mpc/h. We also find an intimate link between the cosmic tidal field and the void orientations. Over a very wide range of scales we find a coherent and strong alignment of the voids with the tidal field computed from the smoothed density distribution. This orientation-tide alignment remains significant on scales exceeding twice the typical void size, which shows that the long range external field is responsible for the alignment of the voids. This confirms the view that the large scale tidal force field is the main agent for the large scale spatial organization of the Cosmic Web.Comment: 10 pages, 4 figures, submitted to MNRAS, for high resolution version, see http://www.astro.rug.nl/~weygaert/tim1publication/voidshape.pd

The Fermi surface and f-valence electron count of UPt3

Combining old and new de Haas-van Alphen (dHvA) and magnetoresistance data, we arrive at a detailed picture of the Fermi surface of the heavy fermion superconductor UPt3. Our work was partially motivated by a new proposal that two 5f valence electrons per formula unit in UPt3 are localized by correlation effects -- agreement with previous dHvA measurements of the Fermi surface was invoked in its support. Comprehensive comparison with our new observations shows that this 'partially localized' model fails to predict the existence of a major sheet of the Fermi surface, and is therefore less compatible with experiment than the originally proposed 'fully itinerant' model of the electronic structure of UPt3. In support of this conclusion, we offer a more complete analysis of the fully itinerant band structure calculation, where we find a number of previously unrecognized extremal orbits on the Fermi surface.Comment: 23 pages, 12 figures, latex, iopart clas

Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.Comment: 39 pages, including 14 figure