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Diffusion models have emerged as a leading framework in generative modeling, poised to transform the traditionally slow and costly process of drug discovery. This review provides a systematic comparison of their application in designing two…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
Very simple organisms, such as the single-celled amoeboid slime mould Physarum polycephalum possess no neural tissue yet, despite this, are known to exhibit complex biological and computational behaviour. Given such limited resources, can…
A highly organized and densely packed lattice of molecular machinery within the sarcomeres of muscle cells powers contraction. Although many of the proteins that drive contraction have been studied extensively, the mechanical impact of…
The properties of semidilute polymer solutions are investigated at equilibrium and under shear flow by mesoscale simulations, which combine molecular dynamics simulations and the multiparticle collision dynamics approach. In semidilute…
In conflict with standard notions of thermodynamics, mesoscopically-sized inclusions (``clusters'') of a solute-rich liquid have been observed in equilibrated solutions of proteins and other molecules. According to a complexation scenario…
Giant micelles are elongated, polymer-like objects created by the self-assembly of amphiphilic molecules (such as detergents) in solution. Giant micelles are typically flexible, and can become highly entangled even at modest concentrations.…
The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes, but also in materials science and biological applications. Connected fractures totally dominate…
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…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…
When two binary solutions are separated by a permeable barrier, the individual species typically diffuse and mix, dissipating their chemical potential gradients. However, we use model lattice simulations to show that single-file…
Biomolecular condensates are formed via liquid-liquid phase separation of proteins, often together with nucleic acids, typically driven by interactions between low-affinity binding sites. The computational study of such condensates that…
Complex fluids such as emulsions, colloidal gels, polymer or surfactant solutions are all characterized by the existence of a "microstructure" which may couple to an external flow on timescales that are easily probed in experiments. Such a…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
Hypothesis: Immiscible liquids are commonly used to achieve unique functions in many applications, where the breakup of compound droplets in airflow is an important process. Due to the existence of the liquid-liquid interface, compound…
Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenization-based macroscopic boundary condition…
It is well known that jammed soft materials will flow if sheared above their yield stress - think mayonnaise spread on bread - but a complete microscopic description of this seemingly sim- ple process has yet to emerge. What remains elusive…
Diffusion of particles in complex fluids and gels is difficult to describe and often lies beyond the scope of the classical Stokes-Einstein relation. One of the main lines of research over the past few decades has sought to relate…
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…