Related papers: New bounds on the tile complexity of thin rectangl…
We report results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using parallel tempering Monte Carlo. In two dimensions, we find strong evidence for a zero-temperature transition. By means of…
We study the self-assembly of halogen-based organic molecules on a passivated silicon surface. The room temperature adsorption of 2,4,6-tris(4-iodophenyl)-1,3,5-triazine (TIPT) on the Si(111)-$\surd$3$\times$$\surd$3-Ag surface is…
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based on partitions of triangles or rectangles. The fractal example…
We consider the thermal softening of crystals due to anharmonicity. Self-consistent methods find a maximum temperature for a stable crystal, which gives an upper bound to the melting temperature. Previous workers have shown that the…
Quasi-one-dimensional (1D) materials provide a superior platform for characterizing and tuning topological phases for two reasons: i) existence for multiple cleavable surfaces that enables better experimental identification of topological…
We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to…
We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et…
We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale…
In this work, we study the number of finite tiles $A\subset\mathbb{Z}^{d}$ of size $\alpha$ that translationally tile a finite $C\subset\mathbb{Z}^{d}$. We consider two tiles $A$ and $A'$ to be congruent if and only if one can be…
Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions…
Self-limiting assembly of particles represents the state-of-the-art controllability in nanomanufacturing processes where the assembly stops at a designated stage1,2, providing a desirable platform for applications requiring delicate…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain. Following our recently developed analytical theory for the athermal limit, here and in the…
In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…
Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here we use molecular dynamics (MD) to study the…
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile),…
We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses. We develop a method which…
We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to implement these limits in three models of increasing chemical complexity and mathematical…
In this paper, we show that any scaled-up version of any discrete self-similar {\it tree} fractal does not strictly self-assemble, at any temperature, in Winfree's abstract Tile Assembly Model.
In self-assembly, a $k$-counter is a tile set that grows a horizontal ruler from left to right, containing $k$ columns each of which encodes a distinct binary string. Counters have been fundamental objects of study in a wide range of…
The crystal structure of the new superconductor UTe2 has been investigated for the first time at low temperature (LT) of 2.7 K, just closely above the superconducting transition temperature of about 1.7 K by single crystal neutron…