Related papers: Growing Perfect Decagonal Quasicrystals by Local R…

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…

For the study of crystal formation and dynamics we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a…

This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…

Silicene growth on graphene has emerged as a novel method for fabricating silicon-based van der Waals heterostructures. However, the silicene flakes produced in this manner are the result of an exotic growth mode characterized by metastable…

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…

We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After re-scaling by the characteristic size, the interface becomes progressively more…

In many areas of research it is interesting how lattices can be filled with particles that have no nearest neighbors, or they are in limited quantities. Examples may be found in statistical physics, chemistry, materials science, discrete…

We report on the synthesis of carbon nanotubes on quasicrystalline alloys. Aligned multiwalled carbon nanotubes (MWNTs) on the conducting faces of decagonal quasicrystals were synthesized using floating catalyst chemical vapor deposition.…

The generation of quadrilateral-dominant meshes is a cornerstone of professional 3D content creation. However, existing generative models generate quad meshes by first generating triangle meshes and then merging triangles into…

We present some results of Monte Carlo simulations for the deposition of particles of different sizes on a two-dimensional substrate. The particles are linear, height one, and can be deposited randomly only in the two, $x$ and $y$…

In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…

In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…

This paper gives a summary of basic concepts of density-functional theory (DFT) and its use in state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how microscopic…

We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…

We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We…

Electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing 'forbidden' symmetries via quasiperiodic ordering with low-dimensionality into a…

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted…

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…

Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the…

High-order methods for convex and nonconvex optimization, particularly $p$th-order Adaptive Regularization Methods (AR$p$), have attracted significant research interest by naturally incorporating high-order Taylor models into adaptive…