Related papers: A Tiling Approach to Counting Inherent Structures …
We prove a Pumping Lemma for the noncooperative abstract Tile Assembly Model, a model central to the theory of algorithmic self-assembly since the beginning of the field. This theory suggests, and our result proves, that small differences…
Via large-scale molecular dynamics simulations, we observe the melting of a topological glass of stiff ring polymers by incorporating flexible ring polymers, along an isobaric path. As more flexible ring polymers are introduced, cluster…
For two-component assemblies, an inherent structure diagram (ISD) is the relationship between set inter-subunit energies and the types of kinetic traps (inherent structures) one may obtain from those energies. It has recently been shown…
In this document, we collected the most important complexity results of tilings. We also propose a definition of a so-called deterministic set of tile types, in order to capture deterministic classes without the notion of games. We also…
We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was…
We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…
The structure-thermodynamic stability relationship in vitreous silica is investigated using machine learning and a library of 24,157 inherent structures generated from melt-quenching and replica exchange molecular dynamics simulations. We…
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…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections of the so-called strongly separated, weakly separated, and chord separated subsets of a set…
We utilize the lattice cluster theory (LCT) of polymer fluids to show that the configurational entropy, enthalpy, and internal energy are all closely interrelated, as suggested by recent measurements by Caruthers and Medvedev, so that the…
For substitutional alloys, typically refered to as classical discrete systems under constant composition, we theoretically examine the role of hidden structure information on evolution of nonlinearity (i.e., correspondence between a set of…
It is possible to formulate the thermodynamics of a glass forming system in terms of the properties of inherent structures, which correspond to the minima of the potential energy and build up the potential energy landscape in the…
In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…
A fundamental characteristic of matter is its ability to form ordered structures under the right thermodynamic conditions. Predicting these structures - and their properties - from the attributes of a material's building blocks is the holy…
Jammed packings' mechanical properties depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres.…
Hard disks systems are often considered as prototypes for simple fluids. In a statistical mechanics context, the hard disk configuration space is generally quotiented by the action of various symmetry groups. The changes in the topological…