We develop computational methods for the simulation of osmotic swelling phenomenarelevant to microscopic vesicles containing transformable solute molecules. We introduce StochasticImmersed Boundary Methods (SIBM) that can capture osmotically driven fluid transport throughsemi-permeable elastic membranes subject to thermal fluctuations. We also develop numerical meth-ods to handl...

Can there be infinitely many minimal hypersurfaces with a given boundary in a Riemannian manifold? A number of previous results, positive and negative, already indicated that the answer depends on the definition of surface, on orientability, on stability and minimizing properties of the surface, on the smoothness and geometry of the boundary, and on the ambient manifold. 1. Finiteness for area-...

We present results from a series of compute-intensive simulation experiments employing a realistic and detailed three-dimensional model of the human cochlear macro-mechanics. Our model uses the immersed boundary method to compute the fluid-structure interactions within the cochlea. It is a three-dimensional model based on an accurate cochlear geometry obtained from physical measurements. It inc...

The objective of this work is to develop numerical tools useful for the understanding of fundamental phenomena in Blood Flow, including some biochemistry and cellular dynamics. An open problem that may benefit from multi-scale numerical tools is for example the understanding of the relation ship between inflammation and cholesterol plaque. The corresponding topics we address in this paper are (...

Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart val...

The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semiimplicit schemes to remove this stiffness from the Immer...

A bifurcation occurs when an elastic filament rotates in a viscous fluid at frequency ω (bifurcation parameter). We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical.

In this paper, we present an immersed boundarymethod for modeling a contractile elastic ring in a three-dimensional Newtonian fluid. The governing equations are themodified Navier–Stokes equations with an elastic force from the contractile ring. The length of the elastic ring is time dependent and the ring shrinks with time because of its elastic nature in our proposed model. We dynamically red...

Many problems involving internal interfaces can be formulated as partial differential equations with singular source terms. Numerical approximation to such problems on a regular grid necessitates suitable regularizations of delta functions. We study the convergence properties of such discretizations for constant coefficient elliptic problems using the immersed boundary method as an example. We ...

In this paper we outline a front-tracking method for computing the moving contact line. In particular, we are interested in the motion of two-dimensional drops and bubbles on a partially wetting surface exposed to shear flows. Peskin’s Immersed Boundary Method is used to model the liquid-gas interface, similar to the approach used by Unverdi and Traggvason. The movement near the moving contact ...