scholarly journals Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

2018 ◽  
Author(s):  
Soheil Fatehiboroujeni ◽  
Arvind Gopinath ◽  
Sachin Goyal
Keyword(s):  
Geometric Constraints ◽  
Elastic Rod ◽  
Mucus Clearance ◽  
Drag Forces ◽  
Fluid Drag ◽  
Non Linear ◽  
Follower Forces ◽  
Elastic Rod Model ◽  
Spatiotemporal Response ◽  
The Continuum

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for pre-stressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.

scholarly journals Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag

2018 ◽  
Vol 13 (12) ◽  
Author(s):  
Soheil Fatehiboroujeni ◽  
Arvind Gopinath ◽  
Sachin Goyal
Keyword(s):  
Drag Force ◽  
Nonlinear Oscillations ◽  
Critical Force ◽  
Geometric Constraints ◽  
Elastic Instability ◽  
Compatibility Conditions ◽  
Nonlinear Buckling ◽  
Fluid Drag ◽  
Follower Forces ◽  
Instability Energy

Elastic-driven slender filaments subjected to compressive follower forces provide a synthetic way to mimic the oscillatory beating of biological flagella and cilia. Here, we use a continuum model to study the dynamical, nonlinear buckling instabilities that arise due to the action of nonconservative follower forces on a prestressed slender rod clamped at both ends and allowed to move in a fluid. Stable oscillatory responses are observed as a result of the interplay between the structural elastic instability of the inextensible slender rod, geometric constraints that control the onset of instability, energy pumped into the system by the active follower forces, and motion-driven fluid dissipation. Initial buckling instabilities are initiated by the effect of the follower forces and inertia; fluid drag subsequently allows for the active energy pumped into the system to be dissipated away and results in self-limiting amplitudes. By integrating the equations of equilibrium and compatibility conditions with linear constitutive laws, we compute the critical follower forces for the onset of oscillations, emergent frequencies of these solutions, and the postcritical nonlinear rod shapes for two forms of the drag force, namely linear Stokes drag and quadratic Morrison drag. For a rod with fixed inertia and drag parameters, the minimum (critical) force required to initiate stable oscillations depends on the initial slack and weakly on the nature of the drag force. Emergent frequencies and the amplitudes postonset are determined by the extent of prestress as well as the nature of the fluid drag. Far from onset, for large follower forces, the frequency of the oscillations can be predicted by evoking a power balance between the energy input by the active forces and the dissipation due to fluid drag.

scholarly journals Non-linear evolution of the resonant drag instability in magnetized gas

2019 ◽  
Vol 485 (3) ◽  
pp. 3991-3998 ◽  
Author(s):  
Darryl Seligman ◽  
Philip F Hopkins ◽  
Jonathan Squire
Keyword(s):  
Linear Theory ◽  
Coherent Structures ◽  
Magnetic Energy ◽  
Density Fluctuations ◽  
Linear Evolution ◽  
Drag Forces ◽  
Non Linear ◽  
Magnetohydrodynamic Simulations ◽  
First Time ◽  
Different Parts

Abstract We investigate, for the first time, the non-linear evolution of the magnetized ‘resonant drag instabilities’ (RDIs). We explore magnetohydrodynamic simulations of gas mixed with (uniform) dust grains subject to Lorentz and drag forces, using the gizmo code. The magnetized RDIs exhibit fundamentally different behaviour than purely acoustic RDIs. The dust organizes into coherent structures and the system exhibits strong dust–gas separation. In the linear and early non-linear regime, the growth rates agree with linear theory and the dust self-organizes into 2D planes or ‘sheets.’ Eventually the gas develops fully non-linear, saturated Alfvénic, and compressible fast-mode turbulence, which fills the underdense regions with a small amount of dust, and drives a dynamo that saturates at equipartition of kinetic and magnetic energy. The dust density fluctuations exhibit significant non-Gaussianity, and the power spectrum is strongly weighted towards the largest (box scale) modes. The saturation level can be understood via quasi-linear theory, as the forcing and energy input via the instabilities become comparable to saturated tension forces and dissipation in turbulence. The magnetized simulation presented here is just one case; it is likely that the magnetic RDIs can take many forms in different parts of parameter space.

scholarly journals Equilibrium Configurations of the Noncircular Cross-Section Elastic Rod Model with the Elliptic KB Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Yongzhao Wang ◽  
Qichang Zhang ◽  
Wei Wang
Keyword(s):  
Cross Section ◽  
Dynamical Behavior ◽  
Elliptic Functions ◽  
Physical Parameters ◽  
Valuable Insight ◽  
Elastic Rod ◽  
Noncircular Cross Section ◽  
Equilibrium Configurations ◽  
Rational Expressions ◽  
Elastic Rod Model

The mechanical deformation of DNA is very important in many biological processes. In this paper, we consider the reduced Kirchhoff equations of the noncircular cross-section elastic rod characterized by the inequality of the bending rigidities. One family of exact solutions is obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behavior of the system in response to changes in physical parameters that concern asymmetry. The effects of the factor on the DNA conformation are discussed. A qualitative analysis is also conducted to provide valuable insight into the topological configuration of DNA segments.

scholarly journals Asymmetric elastic rod model for DNA

2009 ◽  
Vol 80 (1) ◽  
Author(s):  
B. Eslami-Mossallam ◽  
M. R. Ejtehadi
Keyword(s):  
Elastic Rod ◽  
Rod Model ◽  
Elastic Rod Model

A Model for Highly Strained DNA in a Cavity

2011 ◽  
Author(s):  
Andrew D. Hirsh ◽  
Todd D. Lillian ◽  
N. C. Perkins
Keyword(s):  
Small Volume ◽  
Biological Function ◽  
Double Helix ◽  
Dna Bending ◽  
Elastic Rod ◽  
Viral Capsids ◽  
Elastic Rod Model ◽  
Highly Strained ◽  
Single Dna Molecule

A single DNA molecule is a long and flexible biopolymer that contains the genetic code. Building upon the discovery of the iconic double helix over 50 years ago, subsequent studies have emphasized how its biological function is related to the mechanical properties of the molecule. A remarkable system which high-lights the role of DNA bending and twisting is the packing and ejection of DNA into and from viral capsids. A recent 3D reconstruction of bacteriophage φ29 reveals a novel toroidal structure thought to be 30–40 bp of highly bent/twisted DNA contained in a small cavity below the capsid. Here, we extend an elastic rod model for DNA to enable simulation of the toroid as it is compacted and subsequently ejected from a small volume. We compute biologically-realistic forces required to form the toroid and predict ejection times of several nanoseconds.

Enhanced Nanoparticle Removal Using Surfactants

MRS Advances ◽  
2016 ◽  
Vol 1 (31) ◽  
pp. 2213-2224
Author(s):  
Michael L. Free
Keyword(s):  
Critical Micelle Concentration ◽  
Semiconductor Manufacturing ◽  
Chemical Mechanical Planarization ◽  
Ionic Surfactant ◽  
Electrostatic Repulsion ◽  
Particle Removal ◽  
Precision Manufacturing ◽  
Manufacturing Operations ◽  
Drag Forces ◽  
Fluid Drag

ABSTRACTNanoparticles are used in chemical mechanical planarization for semiconductor manufacturing as well as in other precision manufacturing operations. Particles used in processing need to be removed from surfaces in order to enhance yields. Nanoparticles are difficult to remove from surfaces during cleaning due to the high van der Waals attractive forces between particles and surfaces relative to the low fluid drag forces that are used for typical removal methods. Ionic surfactant molecules can adsorb on particles and surfaces to create an electrostatic repulsion between particles and surfaces as well as provide a steric barrier to mitigate adsorption and adhesion. The effectiveness of the surfactant in enhancing particle removal is related to surfactant properties, and it can be correlated with and modeled relative to the critical micelle concentration of the surfactant. The general approach for modeling will be discussed, and the model will be compared with particle removal data.

Analysis of Attitude and Dynamics Characteristic of a Kind of Submerged Buoy

2012 ◽  
Vol 226-228 ◽  
pp. 516-520 ◽  
Author(s):  
Jian Xun Wang ◽  
Hong Bin Gui ◽  
Xi Chen ◽  
Qiang Fu
Keyword(s):  
Low Frequency ◽  
Small Scale ◽  
Normal Fluid ◽  
Fluid Forces ◽  
Dynamical Characteristics ◽  
Drag Forces ◽  
Low Frequency Vibration ◽  
Fluid Drag ◽  
Mooring Cable ◽  
Dynamics Characteristic

In this paper, the attitude and dynamical characteristics of a kind of submerged buoy are studied. The attitude of the buoy system is calculated relatively accurately by mathematical derivations and programming, in which all the tangent and normal fluid drag forces and elastic deformation of the mooring cable are considered. Based on the ANSYS FEA software, the model of system in fluid is established, which takes the effects of fluid drag forces, pretension and additional mass into account. Then the analysis of the effect on dynamics characteristic of the system by considering the attitude or not is carried out. The results indicate that, for small-scale submerged buoy system, the completed fluid forces should not be ignored, and the vibration of mooring system of submerged buoy is most likely to be low-frequency vibration, which should be avoided in some ways.

scholarly journals Vibrations due to Flow-Driven Repeated Impacts

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Sumin Jeong ◽  
Natalie Baddour
Keyword(s):  
Failure Mechanism ◽  
Resonance Condition ◽  
Coefficient Of Restitution ◽  
Flowing Fluid ◽  
Drag Forces ◽  
Fluid Drag ◽  
Repetitive Impact ◽  
Ice Failure ◽  
Two Degree Of Freedom ◽  
Good Agreement

We consider a two-degree-of-freedom model where the focus is on analyzing the vibrations of a fixed but flexible structure that is struck repeatedly by a second object. The repetitive impacts due to the second mass are driven by a flowing fluid. Morison’s equation is used to model the effect of the fluid on the properties of the structure. The model is developed based on both linearized and quadratic fluid drag forces, both of which are analyzed analytically and simulated numerically. Conservation of linear momentum and the coefficient of restitution are used to characterize the nature of the impacts between the two masses. A resonance condition of the model is analyzed with a Fourier transform. This model is proposed to explain the nature of ice-induced vibrations, without the need for a model of the ice-failure mechanism. The predictions of the model are compared to ice-induced vibrations data that are available in the open literature and found to be in good agreement. Therefore, the use of a repetitive impact model that does not require modeling the ice-failure mechanism can be used to explain some of the observed behavior of ice-induced vibrations.

Sign in / Sign up

Export Citation Format

Share Document