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Geometric topology

Related publications (13)

Capsizing due to friction-induced twist in the failure of stopper knots

Pedro Miguel Nunes Pereira de Almeida Reis, Paul Johanns

We investigate the failure mechanism of stopper knots, with a particular focus on the figure -8 knot as a representative example. Stopper knots are widely used in climbing, sailing, racket stringing, and sewing to maintain tension in ropes, strings, or thr ...

Elsevier2024

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

Paul Johanns

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

EPFL2023

Computational Exploration of Multistable Elastic Knots

Mark Pauly, Yingying Ren, Michele Vidulis

We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, t ...

Association for Computing Machinery (ACM)2023

Hyperbolic representations of PU(1,n)

Gonzalo Emiliano Ruiz Stolowicz

The work is about the study of group representations in the group of isometries of a separable complex hyperbolic space. The main part is the classification of the representations of the group of isometries of a finite dimensional complex hyperbolic spa ...

EPFL2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

The strength of surgical knots involves a critical interplay between friction and elastoplasticity

Pedro Miguel Nunes Pereira de Almeida Reis, Paul Johanns, Paul Grandgeorge

Knots are the weakest link in surgical sutures, serving as mechanical ligatures between filaments. Exceeding their safe operational limits can cause fatal complications. The empirical nature of present guidelines calls for a predictive understanding of the ...

AMER ASSOC ADVANCEMENT SCIENCE2023

A type I conjecture and boundary representations of hyperbolic groups

Nicolas Monod

We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G

G

associated with nonsingular G

G

-spaces. We deduce that any two boundary representations of a hyperbolic locally ...

WILEY2023

Exploring the inner workings of the clove hitch knot

Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano, Paul Johanns, Paul Grandgeorge

We perform a combined experimental and computational investigation of the clove hitch knot. We develop a physical model for the clove hitch by tying an elastic rod onto a rigid cylinder. In the experiments, we characterize the mechanical performance, geome ...

ELSEVIER2022

The shapes of physical trefoil knots

Pedro Miguel Nunes Pereira de Almeida Reis, John Maddocks, Paul Johanns, Tomohiko Sano, Paul Grandgeorge

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly fle ...

2021

Finite Element Modeling of Tight Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis, Paul Johanns, Tomohiko Sano, Paul Grandgeorge

We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D defo ...

2020

Periodic Motion of Sedimenting Flexible Knots

Giovanni Dietler, Krishnan Thyagarajan

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwi ...

APS2018

On chirality of toroidal embeddings of polyhedral graphs

Senja Dominique Barthel

We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a non-split link due to [2, 3]. Building on this and using the chirality of torus knots and ...

World Scientific Publishing2017

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

Giovanni Dietler

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains ...

Royal Society of Chemistry2016

Related publications (13)

G

associated with nonsingular G

G

-spaces. We deduce that any two boundary representations of a hyperbolic locally ...

WILEY2023