Related papers: Sandpiles on the heptagonal tiling
We discuss the art and science of producing conformally correct euclidean and hyperbolic tilings of compact surfaces. As an example, we present a tiling of the Chmutov surface by hyperbolic (2, 4, 6) triangles.
A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is…
Rivulets and droplets are naturally appearing shapes when small amounts of liquid are deposited on a partially wettable substrate. Here we study, by means of numerical simulations, the dewetting dynamics of a ring-rivulet on substrates with…
Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their…
The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…
We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context we first review existing models. We argue on the local character of sand ripple formation. Using a hydrodynamical model we derive a…
We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a -phase difference between neighboring spots. It is shown that the multipole-mode…
A water-filled differentially heated rotating annulus with initially prepared stable vertical salinity profiles is studied in the laboratory. Based on two-dimensional horizontal particle image velocimetry (PIV) data, and infrared camera…
We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite…
The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction…
Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…
We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…
In this paper, we prove that the general problem of tiling the hyperbolic plane with \`a la Wang tiles is undecidable.
We study the geometry of the moduli space of planes in a general cubic 5-fold and its deformation. We show that this moduli space is a smooth projective surface whose canonical bundle is ample. We also show that the variation of degree 1…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in…
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
Endohedrally doped Si20 fullerenes appear as appealing building blocks for nanoscale materials. We investigate their structural stability with an unbiased and systematic global geometry optimization method within density-functional theory.…
We review properties of gapless states. We construct a model where a stable breached pair (gapless) state is realized.
Surface states of topological noncentrosymmetric superconductors exhibit intricate helical spin textures, i.e., the spin orientation of the surface quasiparticles is coupled to their momentum. Using quasiclassical theory, we study the spin…