Related papers: Tilings With Very Elastic Tiles
We study single-flip dynamics in sets of three-dimensional rhombus tilings with fixed polyhedral boundaries. This dynamics is likely to be slowed down by so-called ``cycles'': such structures arise when tilings are encoded via the…
The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the tensor of turbulent stress as a function of the time average of the velocity field. Based on the idea…
In solid phase the pressure correlates to the elastic related volume change while the temperature to the thermal related volume change. These volume changes are not compatible with the exception of constant volume condition when the…
A comprehensive overview of lattice rules and polynomial lattice rules is given for function spaces based on $\ell_p$ semi-norms. Good lattice rules and polynomial lattice rules are defined as those obtaining worst-case errors bounded by…
We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this…
Penrose tilings form lattices, exhibiting 5-fold symmetry and isotropic elasticity, with inhomogeneous coordination much like that of the force networks in jammed systems. Under periodic boundary conditions, their average coordination is…
We turn the long time puzzle of the free volume, known for its highly irregular form, into exact analytical formulae and develop statistical mechanics of the hard disk model. The free volume is exactly expressed in terms of the intersection…
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics…
A tromino tiling problem is a packing puzzle where we are given a region of connected lattice squares and we want to decide whether there exists a tiling of the region using trominoes with the shape of an L. In this work we study a slight…
We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk spacetime with a variable equation of state for the fluid presented on the shell. In such a fluid the angular pressure $p$ is a function of both surface energy…
Jamming is a fundamental transition that governs the mechanical behavior of particulate media, including sand, foam and dense suspensions but also biological tissues: Upon compression, particulate media can change from freely flowing to a…
We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek…
The art of making structural, polymeric and metallic glasses is rapidly developing with many applications. A limitation to their use is their mechanical stability: under increasing external strain all amorphous solids respond elastically to…
The lattice of the set partitions of $[n]$ ordered by refinement is studied. Given a map $\phi: [n] \rightarrow [n]$, by taking preimages of elements we construct a partition of $[n]$. Suppose $t$ partitions $p_1,p_2,\dots,p_t$ are chosen…
We explore the pressure of active particles on curved surfaces and its relation to other interfacial properties. We use both direct simulations of the active systems as well as simulations of an equilibrium system with effective (pair)…
Many soft jammed materials, such as pastes, gels, concentrated emulsions, and suspensions, possess a threshold stress, known as yield stress, that must be exceeded to cause permanent deformation or flow. In rheology, the term plastic flow…
A finite set of integers $A$ tiles the integers by translations if $\mathbb{Z}$ can be covered by pairwise disjoint translated copies of $A$. Restricting attention to one tiling period, we have $A\oplus B=\mathbb{Z}_M$ for some…
Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…
We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can…
We study the spreading of elastoviscoplastic (EVP) droplets under surface tension effects. The non- Newtonian material flows like a viscoelastic liquid above the yield stress and behaves like a viscoelastic solid below it. Hence, the…