Related papers: The N-link model for slender rods in a viscous flu…
Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. While appropriate theoretical modelling is available to capture flagella locomotion in simple, Newtonian fluids, formidable…
The deformations of flagella are important in the motility of single- and multi-flagellated bacteria. Existing numerical methods have treated flagella as extensible filaments with a large extensional modulus, resulting in a stiff numerical…
We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
In this paper we mainly investigate the inviscid limit for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. By virtue of the Littlewood-Paley theory, we first obtain a uniform estimate for the solution…
The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter…
We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so…
We are interested in studying a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper…
The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…
This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…
We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic…
We consider the slender body free boundary problem describing the evolution of an inextensible, closed elastic filament immersed in a Stokes fluid in $\mathbb{R}^3$. The filament elasticity is governed by Euler-Bernoulli beam theory, and…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at…
A coarse-grained molecular simulation approach originally developed for entangled polymeric liquids is extended to model the mechanical behavior of long-fiber networks. The model, based on the slip-link picture of chain entanglements,…
The propulsion of many eukaryotic cells is generated by flagella, flexible slender filaments that are actively oscillating in space and time. The dynamics of these biological appendages have inspired the design of many types of artificial…
We analyze the three-dimensional buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Peclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
Diffusion of particles in complex fluids and gels is difficult to describe and often lies beyond the scope of the classical Stokes-Einstein relation. One of the main lines of research over the past few decades has sought to relate…
The dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared to the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a…