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When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…

An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice…

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…

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…

Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations…

Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid-vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work…

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…

Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…

A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is…

Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the…

The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…

We present a robust and efficient numerical framework based on a median filter scheme for solving a broad class of interface-related optimization problems, from image segmentation to topology optimization. A key innovation of our work is…

Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing in particular the importance of interfaces that emerge in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of…

Implicit solvent models, such as Poisson-Boltzmann models, play important roles in computational studies of biomolecules. A vital step in almost all implicit solvent models is to determine the solvent-solute interface, and the solvent…

At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting…

We resolve the issue of uniqueness of weak solutions for linear, inertial fluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot poroelastic system coupled to a 3D incompressible Stokes flow via a 2D interface, where…

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…