Related papers: Mathematics of Floating 3D Printed Objects
Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an…
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse…
In this work, asymptotically stable state estimation schemes are proposed for rigid body motion, using the framework of geometric mechanics. Rigorous stability analyses of the estimation schemes presented here guarantee the nonlinear…
Modeling humans in physical scenes is vital for understanding human-environment interactions for applications involving augmented reality or assessment of human actions from video (e.g. sports or physical rehabilitation). State-of-the-art…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries.…
We report high-resolution measurements of three-dimensional (3D) turbulence in a rapidly rotating fluid. By decomposing the velocity field into a vertically averaged component and a three-dimensional residual, we show that each dominates…
Molecular gas disks are generally Toomre stable ($Q_T>$1) and yet clearly gravitationally unstable to structure formation as evidenced by the existence of molecular clouds and ongoing star formation. This paper adopts a 3D perspective to…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
Recent studies have highlighted the sensitivity of active matter to boundaries and their geometries. Here we develop a general theory for the dynamics and statistics of active particles on curved surfaces and illustrate it on two examples.…
The equations governing the motion of a three-dimensional liquid drop moving freely in an unbounded liquid reservoir under the influence of a gravitational force are investigated. Provided the (constant) densities in the two liquids are…
The stable propagation of jets in FRII sources is remarkable if one takes into account that large-scale jets are subjected to potentially highly disruptive three-dimensional (3D) Kelvin-Helmholtz instabilities. Numerical simulations can…
A light-weight "inflatable" tensioned-membrane-structure vacuum container is proposed and its stability is analyzed. The proposed structure consists of a pressurized lobed cylindrical "wall" surrounding a central evacuated space. Stability…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
We present an experimental study of the statistical properties of millimeter-size spheres floating on the surface of a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. By using two magnet…
Additive manufacturing technologies are positioned to provide an unprecedented innovative transformation in how products are designed and manufactured. Due to differences in the technical specifications of AM technologies, the final…
Experimental measurements of the response of a two dimensional system of plastic beads subjected to steady shear are reported. The beads float at the surface of a fluid substrate and are subjected to a slow, steady-shear in a Couette…