Related papers: New bounds on the tile complexity of thin rectangl…
Let n integer greater or equal to 4 and even and let T_n be the set of ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by T_n. Our main result shows a remarkable rigidity property: a tiling of the first…
Extensive Monte Carlo simulations are carried out to study thermal stability of an infinite standalone silicon sheet. We used the Tersoff potential that has been used with success for silicon at low temperatures. However, the melting…
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of…
A simple and predictive model is put forward explaining the experimentally observed substantial shift of the glass transition temperature, Tg, of sufficiently thin polymer films. It focuses on the limit of small molecular weight, where…
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…
Many thermal measurements in high magnetic fields require thermometers that are sensitive over a wide temperature range, are low mass, have a rapid thermal response, and have a minimal, easily correctable magnetoresistance. Here we report…
This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D…
The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop…
We study the effects of time-dependent substrate/film temperature in the deposition of a mesoscopically thick film using a statistical model that accounts for diffusion of adatoms without lateral neighbors whose coefficients depend on an…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that…
Superconducting properties of thin films can be vastly different from those of bulk materials. Seminal work has shown the critical temperature Tc of elemental superconductors decreases with decreasing film thickness when the normal-state…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point…
We have investigated the temperature dependence of the crystal structure of quasi-one-dimensional monoclinic BaIrO$_3$ using X-ray diffraction. Diffraction patterns were measured across a temperature range from 13 K to 300 K, with 5-degree…
In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the…
This paper considers $n$-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by $\log_2 n$. This…
In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and…