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Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
We investigate novel fitted finite element approximations for two-phase Navier--Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian--Eulerian (ALE) finite element formulations. The moving interface is approximated…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…
The concept of a fluid algebra was introduced by Sullivan over a decade ago as an algebraic construct which contains everything necessary in order to write down a form of the Euler equation, as an ODE whose solutions have invariant…
The vertex model of epithelia describes the apical surface of a tissue as a tiling of polygonal cells, with a mechanical energy governed by deviations in cell shape from preferred, or target, area, $A_0$, and perimeter, $P_0$. The model…
We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…
The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid-structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB…
Interfacial fluctuations in a two-phase binary fluid mixture reveal signatures of underlying physical processes that occur within each phase and on a range of spatial and temporal scales. In this study, we investigate a model binary fluid…
We develop computational methods that incorporate shear into fluctuating hydrodynamics methods. We are motivated by the rheological responses of complex fluids and soft materials. Our approach is based on continuum stochastic hydrodynamic…
The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively…
Particles added to a fluid interface can be used as a surface stabilizer in the food, oil and cosmetic industries. As an alternative to rigid particles, it is promising to consider highly deformable particles that can adapt their…
We present a simple, and physically motivated, coarse-grained model of a lipid bilayer, suited for micron scale computer simulations. Each ~25 nm^2 patch of bilayer is represented by a spherical particle. Mimicking forces of hydrophobic…
In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses and perform work on the external environment. To study a minimal model of such a system, we perform particle-based simulations of an…
We provide an implementation of the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface-Tracking method for simulating incompressible, immiscible two-phase flows as an OpenFOAM module. In addition to…
Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue…
Filaments are ubiquitous within the microscopic world. They occur frequently in both biological and industrial environments and display varied and rich dynamics. Their wide range of applications has spurred the development of a special…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is…
We present a method for computing fluid-structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann [J. Comput Phys. 209…