Related papers: A Tiling Approach to Counting Inherent Structures …
A comparative study of the dynamics of inherent structures at low temperatures is performed on different models of glass formers: a three dimensional Lennard-Jones binary mixture (LJBM), facilitated spin models (either symmetrically…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement,…
In previous work the parameter of glassiness was introduced to distinguish between a liquid and a glass, using a formal analogy with the quantum Bose system. The glassiness is defined in such a way that it is unity in a frozen system and…
We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical…
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, often takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal…
Using molecular dynamics simulations, with a realistic many-body embedded-atom potential, and a novel method to characterize local order, we study the structure of pure nickel during the rapid quench of the liquid and in the resulting…
Motivated by the problem of domino tilings of the Aztec diamond, a weighted particle system is defined on $N$ lines, with line $j$ containing $j$ particles. The particles are restricted to lattice points from 0 to $N$, and particles on…
The paper presents a concept/technique to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a…
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for…
Topologically interlocked materials and structures, which are assemblies of unbonded interlocking building blocks, are promising concepts for versatile structural applications. They have been shown to exhibit exceptional mechanical…
All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system.…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…
We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile…