Related papers: Comparison between advected-field and level-set me…
Quantitative modeling has become an essential tool in modern biophysics, driven by advances in both experimental techniques and theoretical frameworks. Powerful high-resolution techniques now provide detailed datasets spanning molecular to…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line…
Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We…
Vesicular capsules are used to carry biochemicals in biology and liposome technology. Being water-permeable with differing interior and exterior compositions, they are necessarily under osmotic stress. Recent studies have underlined the…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
Cellular membranes are a heterogeneous mix of lipids, proteins and small molecules. Special groupings of saturated lipids and cholesterol form a liquid-ordered phase, known as `lipid rafts,' serving as platforms for signaling, trafficking…
A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104},…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
Computer simulations of coarse-grained molecular models for amphiphilic systems can provide insight into the the structure of amphiphiles at interfaces. They can help to identify the factors that determine the phase behavior, and they can…
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
Phase separated macromolecules play essential roles in many biological and synthetic systems. Physical characterization of these systems can be challenging because of limited sample volumes, particularly for phase-separated proteins. Here,…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level…
The flow field generated by a swimming bacterium serves as a fundamental building block for understanding hydrodynamic interactions between bacteria. Although the flow field generated by a force dipole (stresslet) well captures the fluid…
The dynamics and rheology of suspensions of fluid vesicles or red blood cells is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
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…