Related papers: New bounds on the tile complexity of thin rectangl…
Major challenges of micro thermal machines are the thermal insulation and mechanical tolerance in the case of sliding piston. Switching from piston to membrane in microengines can alleviate the latest and lead to planar architectures.…
We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its n-by-n squares. We construct tile sets for which this…
We study thin films with residual strain by analyzing the $\Gamma-$limit of non-Euclidean elastic energy functionals as the material's thickness tends to $0.$ We begin by extending prior results \cite{bhattacharya2016plates}…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
We study the finite size scaling behaviour of the specific heat of thin films in the neighbourhood of the lambda-transition. To this end we have simulated the improved two-component phi^4 model on the simple cubic lattice. We employ free…
The demand for the three-dimensional (3D) integration of electronic components is on a steady rise. The through-silicon-via (TSV) technique emerges as the only viable method for integrating single-crystalline device components in a 3D…
Three-dimensional icosahedral random tilings are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in orthogonal space. The specific heat shows a pronounced Schottky…
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…
Lower thermal stability due to thinning often leads to unprecedented hidden phases in low-dimensional materials. Such hidden phases can coexist or compete with preexisting electronic phases. We investigate hidden phases observed in…
Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of…
We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a…
If most of the pixels in an $n \times m$ digital image are the same color, must the image contain a large connected component? How densely can a given set of connected components pack in $\mathbb{Z}^2$ without touching? We answer these two…
We have studied the temperature dependencies of the complex sheet conductance of 1-3 unit cell (UC) thick YBa2Cu3O7-x films sandwiched between semiconducting Pr0.6Y0.4Ba2Cu3O7-x layers at high frequencies. Experiments have been carried out…
The regulation of temperature at the macro and microscale is a major energy-consuming process of humankind. Modern cooling systems account for 15% of the global energy consumption and are responsible for 10% of greenhouse gas emissions. Due…
Despite tremendous progress in the research on self-assembled nanotechnological building blocks such as macromolecules, nanowires, and two-dimensional materials, synthetic self-assembly methods bridging nanoscopic to macroscopic dimensions…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
Let $R$ be an $n\times n$ expanding matrix with integral entries. A fundamental question in the fractal tiling theory is to understand the structure of the digit set $\mathcal{D}\subset\mathbb{Z}^n$ so that the integral self-affine set…
We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the…
We study self-similar attractors in the space $\mathbb{R}^d$, i.e., self-similar compact sets defined by several affine operators with the same linear part. The special case of attractors when the matrix $M$ of the linear part of affine…
A limitation to molecular implementations of tile-based self-assembly systems is the high rate of mismatch errors which has been observed to be between 1% and 10%. Controlling the physical conditions of the system to reduce this intrinsic…