相关论文: Stability of the Stokes Immersed Boundary Problem …

We study coupled motion of a 1-D closed elastic string immersed in a 2-D Stokes flow, known as the Stokes immersed boundary problem in two dimensions. Using the fundamental solution of the Stokes equation and the Lagrangian coordinate of…

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle…

In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…

We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…

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…

We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our…

The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integro-differential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters.…

We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…

Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes' first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a…

We consider the problem of a one dimensional elastic filament immersed in a two dimensional steady Stokes fluid. Immersed boundary problems in which a thin elastic structure interacts with a surrounding fluid are prevalent in science and…

The 2-D Peskin problem describes a 1-D closed elastic string immersed and moving in a 2-D Stokes flow that is induced by its own elastic force. The geometric shape of the string and its internal stretching configuration evolve in a coupled…

Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary…

Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…

In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…

The mechanics and statistical mechanics of a suspension of active particles are determined by the traction (force per unit area) on their surfaces. Here we present an exact solution of the direct boundary integral equation for the traction…

A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe…

We consider a nonlocal curve evolution belonging to a hierarchy of models for the dynamics of an inextensible elastic filament in a 3D Stokes fluid. This model captures the principal part of a full free boundary problem for an elastic…

We consider a simplified extensible version of a dynamic free boundary problem for a thin filament with radius $\epsilon>0$ immersed in 3D Stokes flow. The 3D fluid is coupled to the quasi-1D filament dynamics via a novel type of…

In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking…