相关论文: Uniform line fillings
Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
Various two-dimensional fabrication methods, such as deposition, etching, milling, laser cutting, and water jetting, suffer from asymmetry between the top and the bottom surface of fabricated parts. Such asymmetry is usually undesirable and…
Heterogeneous materials consisting of different phases are ideally suited to achieve a broad spectrum of desirable bulk physical properties by combining the best features of the constituents through the strategic spatial arrangement of the…
Mossel and Ross raised the question of when a random colouring of a graph can be reconstructed from local information, namely the colourings (with multiplicity) of balls of given radius. In this paper, we are concerned with random…
Granular media near jamming exhibit fascinating properties, which can be harnessed to create jammed-granulate metamaterials: materials whose characteristics arise not only from the shape and material properties of the particles at the…
The generation of high-order harmonics in finite, hexagonal nanoribbons is simulated. Ribbons with armchair and zig-zag edges are investigated by using a tight-binding approach with only nearest neighbor hopping. By turning an alternating…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Since the new millennium coherent extreme ultra-violet and soft x-ray radiation has revolutionized the understanding of dynamical physical, chemical and biological systems at the electron's natural timescale. Unfortunately, coherent…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. However, conventional methods for…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
A set of chords of a circle of given radius is represented as a metric space w.r.t. a metric introduced by Hausdorf. The form of open and closed balls with respect to this metric is established. We consider a family of Hausdorff outer…
We study random surfaces constructed by glueing together $N/k$ filled $k$-gons along their edges, with all $(N-1)!! = (N-1)(N-3)...3\cdot 1$ pairings of the edges being equally likely. (We assume that lcm $\{2,k\}$ divides $N$.) The Euler…
There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
In this paper we discuss the number of regions in a unit circle after drawing $n$ i.i.d. random chords in the circle according to a particular family of distribution. We find that as $n$ goes to infinity, the distribution of the number of…
The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…
Recently W. Lao and M. Mayer [6], [7], [9] considered $U$-max - statistics, where instead of sum appears the maximum over the same set of indices. Such statistics often appear in stochastic geometry. The examples are given by the largest…
Mechanical metamaterials are structures designed to exhibit an exotic response, such as topological soft modes at a surface. Here we explore single-material 3D prints of these topological structures by translating a ball-and-spring model…