Related papers: Sandpiles on the heptagonal tiling
Balanced double-null configurations are of general interest for boundary plasma physics, and they have been proposed for some future designs. Experimental observations demonstrate absence of plasma fluctuations in tokamak high-field side…
Multi-stable mechanical structures find cutting-edge applications across various domains due to their reconfigurability, which offers innovative possibilities for engineering and technology advancements. This study explores the emergence of…
We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…
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We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every…
We discuss stability of Q-balls interacting with fermions in theory with small coupling constant g. We argue that for configurations with large global U(1)-charge Q the problem of classical stability becomes more subtle. For example, in…
We study the segregation of granular mixtures in two-dimensional silos using a set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…
Employing ab initio calculations, we discuss chemical, mechanical, and dynamical stability of MoN-TaN solid solutions together with cubic-like MoN/TaN superlattices, as another materials design concept. Hexagonal-type structures based on…
Our model of shaken sand, presented in earlier work, has been extended to include a more realistic `glassy' state, i.e., when the sandbox is shaken at very low intensities of vibration. We revisit some of our earlier results, and compare…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding…
Capillary forces significantly affect the stability of sandpiles. We analyze the stability of sandpiles with such forces, and find that the critical angle is unchanged in the limit of an infinitely large system; however, this angle is…
In this paper we give an upper bound of the first eigenvalue of the Laplace operator on a complete stable minimal hypersurface $M$ in the hyperbolic space which has finite $L^2$-norm of the second fundamental form on $M$. We provide some…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
We show that in superfluids with fermionic imbalance and uniform ground state, there are stable solitons. These solutions are formed of radial density modulations resulting in nodal rings. We demonstrate that these solitons exhibit…
We analyze superpositions of ortho- and para-Helium states, considering the possible existence of stationary and metastable states in the system. In particular, the metastable superposition of 1s2s ortho and para states seems to be…