Related papers: Deterministic 2-Dimensional Temperature-1 Tile Ass…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
Thermoelectric (TE) generators can directly convert heat into electricity, but their performance is often constrained by limited temperature gradients. Here it is shown that width-modulated metamaterials with constrictions and expansions…
We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or…
Under the Ansatz that the occupation times of a system with finitely many states are given by the Gibbs distribution, an effective temperature is uniquely determined (up to a choice of scale), and may be computed de novo, without any…
In this paper we consider the time complexity of computing the sum and product of two $n$-bit numbers within the tile self-assembly model. The (abstract) tile assembly model is a mathematical model of self-assembly in which system…
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…
Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…
We give the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong…
In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
Apparently, some form of local superconducting pairing persists to temperatures well above the maximum observed $T_c$ in underdoped cuprates, \textit{i.e.} $T_c$ is suppressed due to the small phase stiffness. With this in mind, we consider…
In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to…
We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a…
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…
We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…
A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete…
We discuss the $\phi^4$ and $\phi^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion…
We consider topological entanglement entropy (TEE) at finite temperature for CSS codes, which include some ordinary topological-ordered systems such as the toric code and some fracton models such as the Haah's code and the X-cube model. We…