arXiv subjects

Noel C. Perkins

Publications and source records attributed to Noel C. Perkins.

5 recordsLinked to original sources

arXiv2007

Modeling of Cables with High and Low Tension Zones using a Hybrid Rod-Catenary Formulation

Cables under very low tension may become highly contorted and form loops, tangles, knots and kinks. These nonlinear deformations, which are dominated by flexure and torsion, pose serious concerns for cable deployment. Simulation of the three-dimensional nonlinear dynamics of loop and tangle formation requires a 12th order rod model and the computational effort increases rapidly with increasing cable length and integration time. However, marine cable applications which result in local zones of low-tension very frequently involve large zones of high-tension where the effects of flexure and torsion are insignificant. Simulation of the three-dimensional dynamics of high-tension cables requires only a 6th order catenary model which significantly reduces computational effort relative to a rod model. We propose herein a hybrid computational cable model that employs computationally efficient catenary elements in high-tension zones and rod elements in localized low-tension zones to capture flexure and torsion precisely where needed.

physics.comp-ph↗

arXiv2007

Cable dynamics applied to long-length scale mechanics of DNA

This paper introduces the use of cable dynamics models as a means to explore the mechanics of DNA on long-length scales. It is on these length scales that DNA forms twisted and curved three-dimensional shapes known as supercoils and loops. These long-length scale DNA structures have a pronounced influence on the functions of this molecule within the cell including the packing of DNA in the cell nucleus, transcription, replication and gene repair. We provide a short background to the mechanics of DNA and suggest the logical connection to the mechanics of a low tension cable. A computational model is then summarized and example results are presented for DNA supercoiling and looping.

physics.bio-ph↗

arXiv2007

Writhing Dynamics of Cables with Self-contact

Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is reviewed herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-alpha method for finite differencing in both space and time. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, through the dynamic collapse of this helix into a loop, and subsequent intertwining of the loop with multiple sites of self-contact.

physics.comp-ph↗

arXiv2007

Structural Modeling of DNA Loops in Lactose-Repressor

It is well known that the structural deformations (stressed states) of DNA molecule play a crucial role in its biological functions including gene expression. For instance, looping in DNA (often mediated by protein binding) is a crucial step in many gene regulatory mechanisms. We use the mechanical rod model of DNA molecules to simulate its structural interactions with proteins (enzymes) during gene expression. Our rod model can simulate the nonlinear dynamics of loop and supercoil formation in DNA on long length scales. The formulation accounts for the structural stiffness of the DNA strand, its intrinsic curvature, chiral (right-handed helical) construction and its physical interactions with the surrounding medium. The simulations of protein-mediated DNA looping illustrate how the mechanical properties of DNA may affect the chemical kinetics of DNA-protein interactions and thereby regulate gene expression.

physics.bio-ph↗

arXiv2007

Nonlinear dynamic strand model with coupled tension and torsion

We simulate the nonlinear dynamic responses in Kirchhoff rod by including the important effects due to inertia and kinematic coupling of tension and torsion. We begin by reviewing a dynamic rod model of a strand (length of cable or DNA) in the form of a 12th order partial differential equation system. Numerical solutions reveal the effects of dynamics on clamped strands due to slow movements of their ends. We note that inertia plays a critical role in this process, particularly under loading conditions that pass through an instability. For example, we simulated a dynamic trasition path between two possible equilibria of a clamped rod subject to very slow compression.

physics.comp-ph↗