192 research outputs found
A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number
This contribution provides a general framework to use Lagrange multipliers
for the simulation of low Reynolds number fiber dynamics based on Bead Models
(BM). This formalism provides an efficient method to account for kinematic
constraints. We illustrate, with several examples, to which extent the proposed
formulation offers a flexible and versatile framework for the quantitative
modeling of flexible fibers deformation and rotation in shear flow, the
dynamics of actuated filaments and the propulsion of active swimmers.
Furthermore, a new contact model called Gears Model is proposed and
successfully tested. It avoids the use of numerical artifices such as repulsive
forces between adjacent beads, a source of numerical difficulties in the
temporal integration of previous Bead Models.Comment: 41 pages, 15 figure
A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number
This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models
Nucleation at the DNA supercoiling transition
Twisting DNA under a constant applied force reveals a thermally activated
transition into a state with a supercoiled structure known as a plectoneme.
Using transition state theory, we predict the rate of this plectoneme
nucleation to be of order 10^4 Hz. We reconcile this with experiments that have
measured hopping rates of order 10 Hz by noting that the viscosity of the bead
used to manipulate the DNA limits the measured rate. We find that the intrinsic
bending caused by disorder in the base-pair sequence is important for
understanding the free energy barrier that governs the transition. Both
analytic and numerical methods are used in the calculations. We provide
extensive details on the numerical methods for simulating the elastic rod model
with and without disorder.Comment: 18 pages, 15 figure
Methods for suspensions of passive and active filaments
Flexible filaments and fibres are essential components of important complex
fluids that appear in many biological and industrial settings. Direct
simulations of these systems that capture the motion and deformation of many
immersed filaments in suspension remain a formidable computational challenge
due to the complex, coupled fluid--structure interactions of all filaments, the
numerical stiffness associated with filament bending, and the various
constraints that must be maintained as the filaments deform. In this paper, we
address these challenges by describing filament kinematics using quaternions to
resolve both bending and twisting, applying implicit time-integration to
alleviate numerical stiffness, and using quasi-Newton methods to obtain
solutions to the resulting system of nonlinear equations. In particular, we
employ geometric time integration to ensure that the quaternions remain unit as
the filaments move. We also show that our framework can be used with a variety
of models and methods, including matrix-free fast methods, that resolve low
Reynolds number hydrodynamic interactions. We provide a series of tests and
example simulations to demonstrate the performance and possible applications of
our method. Finally, we provide a link to a MATLAB/Octave implementation of our
framework that can be used to learn more about our approach and as a tool for
filament simulation
The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
Elastic filaments are vital to biological, physical and engineering systems,
from cilia driving fluid in the lungs to artificial swimmers and
micro-robotics. Simulating slender structures requires intricate balance of
elastic, body, active, and hydrodynamic moments, all in three-dimensions. Here,
we present a generalised 3D coarse-graining formulation that is efficient,
simple-to-implement, readily extendable and usable for a wide array of
applications. Our method allows for simulation of collections of 3D elastic
filaments, capable of full flexural and torsional deformations, coupled
non-locally via hydrodynamic interactions, and including multi-body
microhydrodynamics of structures with arbitrary geometry. The method exploits
the exponential mapping of quaternions for tracking three-dimensional rotations
of each interacting element in the system, allowing for computation times up to
150 times faster than a direct quaternion implementation. Spheres are used as a
`building block' of both filaments and solid micro-structures for
straightforward and intuitive construction of arbitrary three-dimensional
geometries present in the environment. We highlight the strengths of the method
in a series of non-trivial applications including bi-flagellated swimming,
sperm-egg scattering, and particle transport by cilia arrays. Applications to
lab-on-a-chip devices, multi-filaments, mono-to-multi flagellated
microorganisms, Brownian polymers, and micro-robotics are straightforward. A
Matlab code is provided for further customization and generalizations.Comment: 16 pages, 6 figure
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