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Schwarzites are 3D crystalline porous materials exhibiting the shape of Triply Periodic Minimal Surfaces (TPMS). They possess negative Gaussian curvature, created by the presence of rings with more than six sp2-hybridized carbon atoms.…
Schwarzites are crystalline, 3D porous structures with stable negative curvature formed of sp2-hybridized carbon atoms. These structures present topologies with tunable porous size and shape and unusual mechanical properties. In this work,…
Since graphene was synthesized the interest for building new 2D and 3D structures based on the carbon allotropes has been growing every day. One of these 3D structures is know as carbon schwarzites. Schwarzites consist of carbon…
Schwarzites are porous crystalline structures with Gaussian negative curvature. In this work, we investigated the mechanical behavior and energy absorption properties of two carbon-based diamond schwarzites (D688 and D8bal). We carried out…
Triply Periodic Minimal Surfaces (TPMS) possess locally minimized surface area under the constraint of periodic boundary conditions. Different families of surfaces were obtained with different topologies satisfying such conditions. Examples…
Nature-occurring structures exhibiting unique topological features such as complex and gradient porosity has been the basis to create new materials and/or structures. Most studies have been focused on complex periodic porous structures but…
The 3D porous carbon-based structures called Schwarzites have been recently a subject of renewed interest due to the possibility of being synthesized in the near future. These structures exhibit negatively curvature topologies with tuneable…
We carried out fully atomistic reactive molecular dynamics simulations to study the mechanical behavior of six newly proposed hybrid schwarzite-based structures (interlocked petal-schwarzites). Schwarzites are carbon crystalline…
Schwarzites are porous structures that present negative Gaussian curvatures. Although initially proposed for carbon, in principle, schwarzites of other elements are possible. In this work, we have carried out a detailed investigation of the…
We use ab initio density functional calculations to study the stability, elastic properties and electronic structure of sp2 carbon minimal surfaces with negative Gaussian curvature, called schwarzites. We focus on two systems with cubic…
We investigated through fully atomistic molecular dynamics simulations, the mechanical behavior (compressive and tensile) and energy absorption properties of two families (primitive (P688 and P8bal) and gyroid (G688 and G8bal)) of…
In the last three decades or so, we have witnessed an extraordinary progress in the research and technology of carbon-based nanomaterials. Among the peculiar highlights are the discoveries of fullerene, the carbon nanotubes and the…
Topological quantum field theories can be used to probe topological properties of low dimensional manifolds. A class of these theories known as Schwarz type theories, comprise of Chern-Simons theories and BF theories. In three dimensions…
We lay the groundwork for a UV-complete formulation of the Euclidean Jackiw-Teitelboim two-dimensional models of quantum gravity when the boundary lengths are finite, emphasizing the discretized approach. The picture that emerges is…
The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We…
Black holes are among the most intriguing objects in nature. They are believed to be fully described by General Relativity (GR), and the astrophysical black holes are expected to belong to the Kerr family, obeying the no-hair theorems.…
Carbon nanotubes are a feverishly-studied topic in the scientific community as of late. Mathematically, they can be modeled with a quantum graph. Here we consider a structure somewhat similar to carbon nanotubes, another quantum graph that…
The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces.…
A number of `modified' Newtonian potentials of various forms are available in the literature which accurately approximate some general relativistic effects important for studying accretion discs around a Schwarzschild black hole. Such…
This article gives an invariant representation of the curvature of a plane wave spacetime in terms of the Schwarzian of a curve in the Lagrangian Grassmannian. It develops a general theory of cross ratios and Schwarzians of curves in what…