Related papers: Quasiperiodic packings of two-shell decagonal clus…
Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodic-orbit…
A grid method using tiling by fundamental domain of simple 2D lattices is presented. It refer to a previous work done by Stampfli in $1986$ using two tilings by regular hexagons, one rotate by $\pi/2$ relatively to the other. This allows to…
We show that the simultaneous (de)grafting of a complex projective structure with quasi-Fuchsian holonomy along a multicurve can be performed by a simple sequence of one bubbling and one debubbling. As a consequence we obtain that any…
We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…
In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…
Using X-ray tomography, we experimentally investigate the structural evolution of packings composed of 3D-printed hexapod particles, each formed by three mutually orthogonal spherocylinders, during tap-induced compaction. We identify two…
We propose the theory which unifies the description of quasicrystal assembly thermodynamics and quasicrystal structure formation by combining the Landau theory of crystallization and the cluster approach to quasicrystals. The theory is…
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with…
Plots of quadratic residues display some features that are analyzed mathematically.
In previous approaches to form quasicrystals, multiple competing length scales involved in particle size, shape or interaction potential are believed to be necessary. It is unexpected that quasicrystals can be self-assembled by…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.
Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial AC electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in…
We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…
We investigate the necessary features of the pair interaction for the stabilization of self-assembled quantum quasicrystals in two-dimensional bosonic systems. Unlike the classical scenario, our results show that two-dimensional octagonal,…