Related papers: Bistable Quad-Nets Composed of Four-Bar Linkages
Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface (called a surface-link) embedded in 4-space. In this paper,…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
We give a full classification of continuous flexible discrete axial cone-nets, which are called axial C-hedra. The obtained result can also be used to construct their semi-discrete analogs. Moreover, we identify a novel subclass within the…
We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are…
In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangements of bitangents associated with highly symmetric quartic…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
We demonstrate from a fundamental perspective the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. Remarkably, we find a robust presence and connection with pairs of…
Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Disjointness, bands, and band projections are a classical and essential part of the structure theory of vector lattices. If $X$ is such a lattice, those notions seem - at first glance - intimately related to the lattice operations on $X$.…
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conformal structures and their link to differential equations. In…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial…
We show that every ridge unfolding of an $n$-cube is without self-overlap, yielding a valid net. The results are obtained by developing machinery that translates cube unfolding into combinatorial frameworks. Moreover, the geometry of the…
The transition in random fiber networks from two-dimensional to three-dimensional planar structure driven by increasing coverage (total fiber length per unit area) is studied with a deposition model. At low coverage the network geometry…