Related papers: Some experiments with integral Apollonian circle p…
We investigate paths in the hexagonal circle packing and enumerate them with respect to width, height, number of steps, area, and kissing number. Functional equations and the kernel method yield closed bivariate generating functions…
In this paper we present the results of two detailed N-body simulations of the interaction of a sample of four massive globular clusters in the inner region of a triaxial galaxy. A full merging of the clusters takes place, leading to a…
We give a necessary and sufficient condition for two circles, each with finitely many points added inside, to be betweenness isomorphic. We fully characterize the betweenness isomorphism classes in the family consisting of all circles with…
Circumstellar disks are considered to be the birthplace of planets. Specific structures like spiral arms, gaps, and cavities are characteristic indicators of planet-disk interaction. Investigating these structures can provide insights into…
We systematically investigate the self-assembly of anisotropic cone-shaped particles decorated by ring-like attractive patches. We demonstrate that the self-assembled clusters, which arise due to the conical particle's anisotropic shape…
We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…
The sintering behavior of close packed spheres is investigated using a numerical model. The investigated systems are the body centered cubic (BCC), face centered cubic (FCC) and hexagonal closed packed spheres (HCP). The sintering behavior…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
It has been a challenge to make seven straight round cylinders mutually touch before our now 10-year old discovery [Phys. Rev. Lett. 93, 015505 (2004)] of configurations of seven mutually touching infinitely long round cylinders (then…
In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the curvature of the crystal nucleation free-energy…
The primitive curves are the multiple curves that can be locally embedded in smooth surfaces (we will always suppose that the associated reduced curves are smooth). These curves have been defined and studied by C. Banica and O.Forster in…
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that…
In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For…
We analytically study membrane mediated interactions between inclusions embedded in a tubular membrane. We model inclusions as constraints coupled to the curvature tensor of the membrane tube. First, as special test cases, we analyze the…
We study algebraic curves that are envelopes of families of polygons supported on the unit circle T. We address, in particular, a characterization of such curves of minimal class and show that all realizations of these curves are…
In this article, using the computer, are enumerated all locally-rigid packings by $N$ congruent circles (spherical caps) on the unit sphere ${\Bbb S}^2 $ with $N < 12.$ This is equivalent to the enumeration of irreducible spherical contact…
In view of the many recent observations conducted by ALMA and SPHERE, it is becoming clear that protoplanetary disks form planets in narrow annular gaps at various distances from the central protostars before these protostars are actually…
Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the…