4 papers · 1 filter
Elastic Curves via Geometric Mechanics
Oliver Gross, Rohit Jammula, Albert Chern
Elastic curves are the mathematical shapes of thin elastic rods in equilibrium, with deep connections to mechanics, geometry, and computer graphics. Traditionally described as stat…
Vakonomic Fluids
Ritoban Roy-Chowdhury, Mohammad Sina Nabizadeh, Oliver Gross +2
We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms.…
(Semi-)Invariant Curves from Centers of Triangle Families
Klara Mundilova, Oliver Gross
We study curves obtained by tracing triangle centers within special families of triangles, focusing on centers and families that yield (semi-)invariant triangle curves, meaning tha…
Sub--Riemannian boundary value problems for Optimal Geometric Locomotion
Oliver Gross, Florine Hartwig, Martin Rumpf +1
We propose a geometric model for optimal shape-change-induced motions of slender locomotors, e.g., snakes slithering on sand. In these scenarios, the motion of a body in world coor…