Related papers: How they (should have) built the pyramids
In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…
Putting several hard balls into a two-dimensional bowl can form a very basic two-dimensional model of hard-ball system. When the two-dimensional bowl has a parallel-rotation at a uniform speed around a center, when the number of balls is…
We propose a novel class of spirals that are based on perfect polygonal formations. The spirals are defined by a fractal of right triangles that delineate their geometry and determine their progression rates and modes. We show how these…
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…
A new approach is proposed for finding the "best cut" in a hierarchy of partitions by energy minimization. Said energy must be "climbing" i.e. it must be hierarchically and scale increasing. It encompasses separable energies and those…
Diamond particles have many interesting properties and possible applications. However, producing diamond particles with well-defined shapes at scale is challenging because diamonds are chemically inert and extremely hard. Here, we show air…
In this paper we study planar morphs between straight-line planar grid drawings of trees. A morph consists of a sequence of morphing steps, where in a morphing step vertices move along straight-line trajectories at constant speed. We show…
A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…
A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To…
The use of cables for aerial manipulation has shown to be a lightweight and versatile way to interact with objects. However, fastening objects using cables is still a challenge and human is required. In this work, we propose a novel way to…
We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4x5x1…
We perform a comprehensive study of the formation of three dimensional (pyramidal) structures in a large range of conditions, including the possible evaporation of adatoms from the surface and the presence of surface defects. We compare our…
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understanding by employing techniques from algebraic geometry. The…
One of the longstanding unsolved problems of planet formation is how solid bodies of a few decimeters in size can "stick" to form large planetesimals. This is known as the "meter size barrier". In recent years it has become increasingly…
We construct an explicit Hamiltonian cycle in the state graph of the 5-puzzle on a toroidal 2x 3 grid, a graph with 720 vertices. The cycle is described by a short symbolic sequence of 48 moves over the alphabet {L,R,V}, repeated $15$…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
Novel geometries can be created by coupling internal states of atoms or molecules to mimic movement in real-space
We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a cartogram is a…
In a recent paper published in Nature, Y.I. Sobolev et al. introduced the concept of trajectoids: convex, rigid objects, which roll without slip or spin on a flat plane along a prescribed periodic, unbounded planar path. A geometric…