Related papers: Planar polycrystals with extremal bulk and shear m…
Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that…
A projective hyperk\"ahler manifold of Kummer-type is said to be twisted modular if it is birational to the Albanese fiber of a moduli space of twisted sheaves on an abelian surface. We prove that, with the exception of certain cases of…
A polyomino is a polygonal region with axis parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container $P$. We give…
Colloidal particles can spontaneously self-assemble into ordered structures, which not only can manipulate the propagation of light, but also vibration or phonons. Using Monte Carlo simulation, we study the self-assembly of perfectly…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-quartz crystal…
Most granular packings possess shear moduli ($G$) that increase with the applied external pressure, and bulk moduli ($B$) that increase or remain constant with pressure. This paper presents "tessellated" granular metamaterials for which…
Inorganic crystal materials have broad application potential due to excellent physical and chemical properties, with elastic properties (shear modulus, bulk modulus) crucial for predicting materials' electrical conductivity, thermal…
This work investigates dense packings of congruent hard infinitesimally--thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $\theta \in \left ( \pi, 2\pi \right ]$.…
Asteroids, planets, stars in some open clusters, as well as molecular clouds appear to possess a preferential spin-orbit alignment, pointing to shared processes that tie their rotation at birth to larger parent structures. We present a new…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…
Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral…
If we fix the angles at the vertices of a convex planar $n$-gon, the lengths of its edges must satisfy two linear constraints in order for it to close up. If we also require unit perimeter, our vectors of $n$ edge lengths form a convex…
A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
We demonstrate that hierarchical backmapping strategies incorporating generic blob-based models can equilibrate melts of high-molecular-weight polymers, described with chemically specific, atomistic, models. The central idea behind these…
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…
We consider the space $\mathcal M$ of ordered quadruples of distinct points in the boundary of complex hyperbolic $n$-space, $\ch{n},$ up to its holomorphic isometry group ${\rm PU}(n,1).$ One of the important problems in complex hyperbolic…
Using molecular dynamics simulation, we examine the dynamics of crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of small and large particles in two dimensions. The crossovers occur among these states as the…