Related papers: Maze solvers demystified and some other thoughts

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…

Inside every living cell is the cytoplasm: a fluid mixture of thousands of different macromolecules, predominantly proteins. This mixture is where most of the biochemistry occurs that enables living cells to function, and it is perhaps the…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…

We use a one dimensional symmetric exclusion model to study pressure and osmosis driven flows through molecular-sized channels, such as biological membrane channels and zeolite pores. Analytic expressions are found for the steady-state flow…

This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated…

Despite the wide existence of vesicles in living cells as well as their important applications like drug-delivery, the underlying mechanism of vesicle fusion/fission remains under debate. Here, we develop a constrained self-consistent field…

Many biological networks grow by elongation of filaments that can branch and fuse -- typical examples include fungal mycelium or slime mold. These networks must simultaneously perform multiple tasks such as transport, exploration, and…

Unraveling the relation between the chemical structure of small drug-like compounds and their rate of passive permeation across lipid membranes is of fundamental importance for pharmaceutical applications. The elucidation of a comprehensive…

Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…

A theoretical model is developed for predicting dynamic polymer depletion effects under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform…

Diffusive transport of small molecules within the internal structures of biological and synthetic material systems is complex because the crowded environment presents chemical and physical barriers to mobility. We explored this mobility…

A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…

A dynamic self-organized morphology is the hallmark of network-shaped organisms like slime moulds and fungi. Organisms continuously re-organize their flexible, undifferentiated body plans to forage for food. Among these organisms the slime…

How internal forces are transduced into motion through soft, fluid membranes remains a fundamental question in the study of active systems. To investigate this coupling, we develop a minimal system consisting of a single ferromagnetic…

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the flow-field is governed by the interaction between elasticity and viscosity, as well as…

Microfluidic channels are integral to biomedical technology and process engineering, offering versatility in handling fluids with complex properties, often a combination of viscous and elastic attributes. Despite significant advancements in…

The study of geological systems requires the solution of complex geochemical relations. We present an implementation of a chemical solver which can handle various types of models, including surface chemistry. The implementation is done in…

In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. We consider a two-component…

Emulsions often act as carriers for water-insoluble solutes that are delivered to a specific target. The molecular transport of solutes in emulsions can be facilitated by surfactants and is often limited by diffusion through the continuous…