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Here we extend the approach developed in \cite{adel_2} to study the thermodynamics of Taub-NUT-AdS and dyonic Taub-NUT-AdS solutions. Furthermore, we investigate in details the possible phase structures of the dyonic Taub-NUT-AdS solution.…
The existence of stationary finitely dependent processes on combinatorial models like $\mathbb Z^d$ subshifts can be quite mysterious. For instance, Holroyd and Liggett constructed such processes on proper $4$-colorings of $\mathbb Z^d$ for…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…
In the family of area-contracting H\'enon-like maps with zero topological entropy we show that there are maps with infinitely many moduli of stability. Thus one cannot find all the possible topological types for non-chaotic area-contracting…
Flexibility governs the many properties of materials and is crucial for the function of proteins and biopolymers. However, how the self-assembly of flexibly bonded particles can lead to larger structures with global reconfigurability is…
We elucidate the properties of a gas of free closed bosonic strings in thermal equilibrium. Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral.…
We prove that for any infinite countable amenable group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K;…
Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge,…
In the 60's, Berger famously showed that translational tilings of $\mathbb{Z}^2$ with multiple tiles are algorithmically undecidable. Recently, Bhattacharya proved the decidability of translational monotilings (tilings by translations of a…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…
We introduce a new family of nonperiodic tilings, based on a substitution rule that generalizes the pinwheel tiling of Conway and Radin. In each tiling the tiles are similar to a single triangular prototile. In a countable number of cases,…
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…
Multi-component self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial…
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative its size. These…
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To…
In this paper we prove that if two self-similar tiling systems, with respective stretching factors $\lambda_1$ and $\lambda_2$, have a common factor which is a non periodic tiling system, then $\lambda_1$ and $\lambda_2$ are…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
We consider the 2PI Cornwall-Jackiw-Tomboulis effective action at finite temperature for a noncommutative real scalar field theory in 4 dimensions, with noncommutativity among space and time variables. By means of a Rayleig-Ritz variation,…
In view of making progress towards establishing a holographic duality for theories defined on a discrete tiling of the hyperbolic plane, we consider a recently proposed boundary spin chain Hamiltonian with aperiodic couplings that are…
We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of…