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For a given spatial graph $\mathcal{G} \subset \mathbb{R}^3$, we would like to find a closed orientable surface $\mathcal{S}$ embedded in $\mathbb{R}^3$ in which $\mathcal{G}$ is cellular embedded. However, for general $\mathcal{G}$ this is…
For the complex of curves of a closed orientable surface of genus $g$, $\mathcal{C}(S_{g>1})$, the notion of efficient geodesic in was introduced in arXiv:1408.4133. There it was established that there always exists (finitely many)…
A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as…
Slender structures, such as rods, often exhibit large nonlinear geometrical deformations even under moderate external forces (e.g., gravity). This characteristic results in a rich variety of morphological changes, making them appealing for…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
The problem of finding the general classification of geodetic graphs is still open. We believe that one of the obstacles to attain this goal is that geodetic graphs lack a structural description. In other words, their fundamental properties…
This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
The majority of microfabricated ion traps in use for quantum information processing are of the 2D 'surface-electrode' type or of the 3D 'wafer' type. Surface-electrode traps greatly simplify fabrication and hold the promise of allowing…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
Gridshells are defined as structures that have the shape and rigidity of a double curvature shell but consist of a grid instead of a continuous surface. This study concerns those obtained by elastic deformation of an initially flat two-way…
An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and…
Contemporary electricity distribution systems are being challenged by the variability of renewable energy sources. Slow response times and long energy management periods cannot efficiently integrate intermittent renewable generation and…
Predicting relaxed atomic structures of chemically complex materials remains a major computational challenge, particularly for high-entropy systems where traditional first-principles methods become prohibitively expensive. We introduce the…
Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…
Mechanical metamaterials have continued to offer unprecedented tunability in mechanical properties, but most designs to date have prioritized attaining high stiffness and strength while sacrificing deformability. The emergence of woven…
Equivariant Graph Neural Networks (eGNNs) trained on density-functional theory (DFT) data can potentially perform electronic structure prediction at unprecedented scales, enabling investigation of the electronic properties of materials with…