Related papers: A Homogenised Model of Fluid-String Interaction
A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is…
We propose and analyze a generalized two dimensional $XY$ model, whose interaction potential has $n$ weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by $\Gamma$-convergence the…
We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
We propose a method to parameterize a coarse grained model for the hydrodynamic friction between nearly touching rough spheres in suspension flows. The frictional resistance due to surface roughness primarily alters the sliding and rolling…
Double porosity models for the liquid filtration in an absolutely rigid body is derived from homogenization theory. The governing equations of the fluid dynamics on the microscopic level consist of the Stokes system for a slightly…
We consider a microscopic model of $n$ identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress…
Motivated by the observed coordination of nearby beating cilia, we use a scale model experiment to show that hydrodynamic interactions can cause synchronization between rotating paddles driven at constant torque in a very viscous fluid.…
Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
We consider a distributed Lagrange multiplier formulation for fluid-structure interaction problems in the spirit of the fictitious domain approach. This is an unfitted method, which does not require the construction of meshes conforming to…
A generalization of scalar electrodynamics called fluid electrodynamics is presented. In this theory a fluid replaces the Higgs scalar field. Fluid electrodynamics might have application to the theory of low temperature Helium superfluids,…
This paper concerns the rigorous periodic homogenization for a non-linear strongly coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid. The fluid drags the particles,…
A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…
The paper is devoted to homogenization of two-phase incompressible viscoelastic flows with disordered microstructure. We study two cases. In the first case, both phases are modeled as Kelvin-Voight viscoelastic materials. In the second…