Related papers: Imaginary crystals made real
We generate random Gaussian turbulent velocity fields with a Kolmogorov spectrum and use these to obtain synthetic line-of-sight velocity profiles. The profiles are found to be similar to line profiles observed in molecular clouds. We…
We examine, using molecular dynamics simulation, the structure and thermodynamics of the (100) and (111) disordered face-centered cubic (FCC) crystal/melt interfaces for a binary hard-sphere system. This study is an extension of our…
Recently, novel crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. We show that Cayley-Schreier lattices can…
Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that,…
The goal of this article is to initiate the study of estimates of the non-classical Schottky structure in the discrete subgroups of the projective special linear group over the real numbers degree $2$. In fact, in this paper, we have…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we…
Gravity simulators are laboratory systems where small excitations like sound or surface waves behave as fields propagating on a curved spacetime geometry. The analogy between gravity and fluids requires vanishing viscosity, a feature…
We study Legendrian surfaces determined by cubic planar graphs. Graphs with distinct chromatic polynomials determine surfaces that are not Legendrian isotopic, thus giving many examples of non-isotopic Legendrian surfaces with the same…
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference…
Steady structures originating from dynamic self-assembly have begun to show their advantages in new generation materials, and pose challenges to equilibrium self-assembly. In view of the important role of confinement in self-assembly, here,…
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an…
In this paper we present a theoretical method, together with its experimental confirmation, to obtain structures of light by connecting diffraction-resistant cylindrical beams of finite lengths and different radii. The resulting…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
This manuscript examines viability and stability of anisotropic compact objects in the framework of $f(Q,L_m)$ gravity ($Q$ is the non-metricity and $L_m$ is the matter Lagrangian). We assume a particular functional form of this theory to…
We consider stable minimal surfaces of genus 1 in Euclidean space and in Riemannian manifolds. Under the condition of covering stability (all finite covers are stable) we show that a genus 1 finite total curvature minimal surface in…
For any non-elementary hyperbolic group $\Gamma$, we find an outer automorphism invariant geodesic bicombing for the space of metric structures on $\Gamma$ equipped with a symmetrized version of the Thurston metric on Techim\"uller space.…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
In this review, we present our recent computational work on carbon-based nanostructured composites. These materials consist of carbon crystallites embedded in an amorphous carbon matrix and are modeled here through classical and…