Fluid–structure interaction is ubiquitous in nature and occurs at all biological scales.
Immersed methods provide mathematical and computational frameworks for modeling fluid …

We consider the Brownian motion of a particle and present a tutorial review over the last 111
years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and …

This paper is concerned with the mathematical structure of the immersed boundary (IB)
method, which is intended for the computer simulation of fluid–structure interaction …

Electroosmosis is a fascinating effect where liquid motion is induced by an applied electric
field. Counter ions accumulate in the vicinity of charged surfaces, triggering a coupling …

Results of a mathematical modeling of metal substrate melting and formation of a solid
cladding layer by injection of powder particles through a coaxial nozzle during laser …

We review recent advances in multiscale modeling of the mechanics of healthy and
diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the …

The cell is a mechanical machine, and continuum mechanics of the fluid cytoplasm and the
viscoelastic deforming cytoskeleton play key roles in cell physiology. We review …

The immersed boundary (IB) method originated by Peskin has been popular in modeling
and simulating problems involving the interaction of a flexible structure and a viscous …

This paper describes the development and analysis of finite-volume methods for the Landau–
Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations …

We develop numerical schemes for solving the isothermal compressible and incompressible
equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a …