Related papers: Geometry of small causal diamonds
Persistent tensions in the $\Lambda$CDM cosmological model underline the importance of tests of its basic assumptions. One such potential test arises from the fact that the surface of zero expansion around the collapsing object with…
In this paper, we introduce constructions of the high-dimensional generalizations of the kagome and diamond crystals. The two-dimensional kagome crystal and its three-dimensional counterpart, the pyrochlore crystal, have been extensively…
The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The…
We construct rotating magnetic solutions to the three-dimensional Einstein-Maxwell-Chern-Simons-dilaton theory with a Liouville potential. These include a class of black hole solutions which generalize the warped AdS black holes. The…
A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main…
We propose an analytical model to describe the mechanical deformation of single-crystal diamond following the local sub-superficial graphitization obtained by laser beams or MeV ion microbeam implantation. In this case, a local mass-density…
We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of…
We consider a model of a quenched disordered geometry in which a random metric is defined on ${\mathbb R}^2$, which is flat on average and presents short-range correlations. We focus on the statistical properties of balls and geodesics,…
This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in…
This paper begins the study of relations between Riemannian geometry and contact topology in any dimension and continues this study in dimension 3. Specifically we provide a lower bound for the radius of a geodesic ball in a contact…
The electronic structure and dielectric properties of the diamond, body centered cubic diamond (bc8), and hexagonal diamond (lonsdaleite) phases of carbon are computed using density functional theory and many-body perturbation theory with…
In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic with a single double point is asymptotic to L raised to the dimension…
The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the…
Light-cone cuts have recently been proposed as a method to reconstruct the conformal metric of a holographic spacetime. We explore how additional information about the bulk geometry gets encoded in the structure of these light-cone cuts. In…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
This paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra…
A regular graph $G = (V,E)$ is an $(\varepsilon,\gamma)$ small-set expander if for any set of vertices of fractional size at most $\varepsilon$, at least $\gamma$ of the edges that are adjacent to it go outside. In this paper, we give a…
The problem of the physicochemical synthesis of diamond spans more than 200 years, involving many giants of science. Many technologies have been discovered, realized and used to resolve this diamond problem. Here the origin, definition and…
We investigate through direct molecular mechanics calculations the geometrical properties of hydrocarbon mantles subjected to percolation disorder. We show that the structures of mantles generated at the critical percolation point have a…
In this work we are interested in studying deformations of the $\sigma_2$-curvature and the volume. For closed manifolds, we relate critical points of the total $\sigma_2$-curvature functional to the $\sigma_2$-Einstein metrics and, as a…