Multi-stable elastic knots with self-contact
Event details
| Date | 22.08.2022 |
| Hour | 10:00 › 12:00 |
| Speaker | Michele Vidulis |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Wenzel Jakob
Thesis advisor: Prof. Mark Pauly
Co-examiner: Prof. John Maddocks
Abstract
Knots can be studied from a topological, geometric,
or physical perspective. The topological structure of a closed
curve, encoded by its knot type, constrains the set of geometric
configurations the curve can assume in R3. When the curve is
endowed with material thickness, the impermeability of physical
bodies additionally restricts the shape space. We show how this
space is rich of interesting equilibrium states, and we discuss
how we plan to investigate its properties.
In this proposal, we discuss three papers at the background of
our research. We start by introducing a reduced model for the
simulation of discrete elastic rods. We then discuss how contacts
can be accounted for in physics-based simulation. Finally, we
present an elegant theorem that shows how the topology of a
closed curve can influence its geometry.
Background papers
Exam president: Prof. Wenzel Jakob
Thesis advisor: Prof. Mark Pauly
Co-examiner: Prof. John Maddocks
Abstract
Knots can be studied from a topological, geometric,
or physical perspective. The topological structure of a closed
curve, encoded by its knot type, constrains the set of geometric
configurations the curve can assume in R3. When the curve is
endowed with material thickness, the impermeability of physical
bodies additionally restricts the shape space. We show how this
space is rich of interesting equilibrium states, and we discuss
how we plan to investigate its properties.
In this proposal, we discuss three papers at the background of
our research. We start by introducing a reduced model for the
simulation of discrete elastic rods. We then discuss how contacts
can be accounted for in physics-based simulation. Finally, we
present an elegant theorem that shows how the topology of a
closed curve can influence its geometry.
Background papers
- Discrete elastic rods (Bergou et al. 2008, available here: http://www.cs.columbia.edu/cg/rods/)
- Incremental potential contact: intersection-and inversion-free, large-deformation dynamics (Li et al. 2020, available here: https://ipc-sim.github.io)
- On the total curvature of knots (Milnor 1949, available here: https://www.jstor.org/stable/pdf/1969467.pdf)
Practical information
- General public
- Free