Related papers: Space-filling bearings in three dimensions
Various examples of folding curves in $R^{2}$ have been considered: dragons and other square curves, terdragons and other triangular curves, Peano-Gosper curves based on hexagons. They are self-avoiding. They form coverings of $R^{2}$, by…
We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or…
The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement,…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
In the 3-dimensional Berwald-Moor space are bingles and tringles constructed, as additive characteristic objects associated to couples and triples of unit vectors - practically lengths and areas on the unit sphere. In analogy with the…
We introduce cosymplectic circles and cosymplectic spheres, which are the analogues in the cosymplectic setting of contact circles and contact spheres. We provide a complete classification of compact 3-manifolds that admit a cosymplectic…
In a previous paper, we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfy an integral pinching. In this article, we use the same integral Bochner technique to extend…
We study circular shells in a (2+1)-dimensional background within the framework of Einstein-Born-Infeld theory. For shells around black holes we analyze the mechanical stability under perturbations preserving the symmetry. Shells around…
We prove that every nondegenerate contact form on a closed connected three-manifold, such that the associated contact structure has torsion first Chern class, has either two or infinitely many simple Reeb orbits. By previous results it…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…
Gravitational collapse of matter in the presence of rotation is a mostly unexplored topic but it might have important implications for cosmic censorship. Recently a convenient setup was identified to address this problem, by considering…
Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…
Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we…
Existing digital manufacturing methods can be broadly divided into subtractive approaches, where material is removed from a bulk to reveal the desired form, and additive methods, in which material is introduced voxel-by-voxel to create an…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…
We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packing $\cal P$ with congruent…
We simulate the self-propulsion of devices in a fluid in the regime of low Reynolds numbers. Each device consists of three bodies (spheres or capsules) connected with two damped harmonic springs. Sinusoidal driving forces compress the…
In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…