Related papers: Geometry of small causal diamonds
Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…
Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is…
Asteroids are frequently colliding with small projectiles. Although each individual small collision is not very important, their cumulative effect can substantially change topography and also the overall shape of an asteroid. We run…
The surface topography of diamond coatings strongly affects surface properties such as adhesion, friction, wear, and biocompatibility. However, the understanding of multi-scale topography, and its effect on properties, has been hindered by…
We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…
Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum…
Let $M_j$ be a sequence of Riemannian manifolds with sectional curvature bound below collapsing to a compact Alexandrov space $X$ of dimension $k$. Suppose that all but finitely many points of $X$ are $(k,\delta)$-strained and that the…
We study independent long-range percolation on $\mathbb{Z}^d$ where the nearest-neighbor edges are always open and the probability that two vertices $x,y$ with $\|x-y\|>1$ are connected by an edge is proportional to…
It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal…
Surfaces of natural diamonds etched in high-pressure experiments in H2O, CO2 and H2O-NaCl fluids were investigated using Atomic Force Microscopy. Partial dissolution of the crystals produced several types of surface features including the…
We report fabrication and results of high-resolution X-ray topography characterization of diamond single crystal plates with a large surface area (10$\times$10 mm$^2$) and (111) crystal surface orientation for applications in high-heat-load…
We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological…
Based on a novel type of Sobolev-Poincar\'e inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of generalised compact connected surfaces-with-boundary of…
We investigate a \Pi-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions…
Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…
In our tunneling investigation using Andreev superconductor - normal metal - superconductor contacts on LiFeAs single crystals we observed two reproducible independent subharmonic gap structures at dynamic conductance characteristics. From…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…
The Light-cone distribution amplitudes (LCDAs) of the $\Sigma^\pm$ baryons up to twist six are investigated on the basis of QCD conformal partial wave expansion approach. The calculations are carried out to the next-to-leading order of…
Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between…
We present the design of two-dimensional photonic crystal microcavities in thin diamond membranes well suited for coupling of color centers in diamond. By comparing simulated and ideal field distributions in Fourier and real space and by…