Concept

Knot (mathematics)

Related publications (26)

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

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

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

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

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, Michele Vidulis, Yingying Ren

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 ...

2023

Exploring the inner workings of the clove hitch knot

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

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, Tomohiko Sano, Paul Johanns, Changyeob Baek, 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, Tomohiko Sano, Paul Johanns, Changyeob Baek, 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

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei, Juan Cao

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019

Periodic Motion of Sedimenting Flexible Knots

Giovanni Dietler, Krishnan Thyagarajan, Andrzej Stasiak

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

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser

Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the gener ...

OSA2016

Mechanical form-finding of timber fabric structures

Seyed Sina Nabaei

How about fastening a knot? not with ropes... but with timber panels. Timber Fabric Structures (TFS) originate from such an inspiration. An architectural reinterpretation of fabric techniques (mainly braiding) using building scale timber panels to design ...

EPFL2014

Investigating Reliability on Fuel Cell Model Identification. Part III: Behavior of Assessment Criteria and Limits in Identification

Daniel Favrat, Jan Van Herle, Leonidas Tsikonis

The present paper is the third and last part of an investigation on what determines reliability in fuel cell model identification. In continuation to the effect of experimental design (Part I) and a process method for stochastic calculation of a model's pa ...

Wiley-V C H Verlag Gmbh2013

Long knots and maps between operads

Kathryn Hess Bellwald

We identify the space of tangentially straightened long knots in R^m, for m greater than or equal to 4, as the double loops on the space of derived operad maps from the associative operad into a version of the little m-disk operad. This verifies a conjectu ...

Geometry & Topology Publications2012

Fourier Approximation Of Symmetric Ideal Knots

Henryk Gerlach, Mathias Carlen

Enforcing a specific symmetry group on a curve, knotted or not, is not trivial using standard interpolations such as polygons or splines. For a prescribed symmetry group we present a symmetrization process based on a Fourier description of a knot. The pres ...

2012

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Giovanni Dietler, Andrzej Stasiak, Guillaume Witz

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between ...

2011

Computation and visualization of ideal knot shapes

Mathias Carlen

We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...

EPFL2010

Ideal knots and other packing problems of tubes

Henryk Gerlach

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

DNA Topology : A Biophysical Study of DNA Rings, Knots, and Catenanes by Means of Atomic Force Microscopy and Numerical Simulations

Guillaume Witz

This thesis explores different aspects of DNA topology through experimental and numerical techniques. Topology is a vast mathematical field, that deals with the spatial properties of objects undergoing continuous deformations, but here it is restricted to ...

EPFL2010