Related papers: How they (should have) built the pyramids
Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to…
Droplet deposition onto a hydrophobic surface is studied experimentally and numerically. A wide range of droplet sizes can result from the same syringe, depending strongly on the needle retraction speed. Three regimes are identified…
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…
A new type of water droplet transportation on microstructured hydrophobic surface is proposed and investigated experimentally and theoretically - water droplet could be driven by scale effect which is different from the traditional methods.…
In this paper we present the construction of several aggregates of tetrahedra. Each construction is obtained by performing rotations on an initial set of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or (2) exhibits…
We borrow a classical construction from the study of rational billiards in dynamical systems known as the "unfolding construction" and show that it can be used to study the automorphism group of a Platonic surface. More precisely, the…
In the present paper we construct plans orthogonal through the block factor (POTBs). We describe procedures for adding blocks as well as factors to an initial plan and thus generate a bigger plan. Using these procedures we construct POTBs…
Large molecules have complex potential-energy surfaces with many local minima. They exhibit multiple stereo-isomers, even at very low temperatures. In this paper we discuss the different approaches for the manipulation of the motion of…
In this paper, we show how regular convex 4-polytopes - the analogues of the Platonic solids in four dimensions - can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan-Dieudonne…
The surprising recent discoveries of quasicrystals and their approximants in soft matter systems poses the intriguing possibility that these structures can be realized in a broad range of nano- and micro-scale assemblies. It has been…
We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities, using a multicomponent pseudopotential lattice Boltzmann method. For…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
Mg represents a group of technically important hexagonal-close packed (hcp) metals whose mechanical behaviors are very different from body-centered cubic (bcc) and face-centered cubic (fcc) metals and the underlying mechanisms remain…
Polyhedra called Siamese dipyramids are known to be non-flexible, however their physical models behave like physical models of flexible polyhedra. We discuss a simple mathematical method for explaining the model flexibility of the Siamese…
Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms…
The glass transition is a long-standing problem in physics. Identifying the structural origin of the transition may lead to the ultimate solution to the problem. Here, for the first time, we discover such a structural origin by proposing a…
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies these are nondegenerate maxima, minima, and…
Building and Construction have recently become an exciting application ground for robotics. In particular, rapid progress in materials formulation and in robotics technology has made robotic 3D Printing of concrete a promising technique for…