Related papers: Maze solvers demystified and some other thoughts
This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
Pathogens in droplets on fomites and aerosols go through extreme physiochemical conditions, such as confinement and osmotic stress, due to evaporation. Still, these droplets are the predominant transmission routes of many contagious…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic…
We study self-assembly of a binary mixture of components A and B confined in a slit-like pore with the walls modified by the stripes of tethered brushes made of beads of a sort A. The emphasis is on solvent mediated transitions between…
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a…
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or…
We investigate the dispersion of solutes in active nematic fluids confined in narrow channels based on simulations of nematohydrodynamics. The study focuses on two pre-turbulent regimes: oscillatory flow, with net mass flux, and dancing…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical…
A mathematical model for the evolution of, and deposition from, a thin particle-laden droplet on an infinitely thick, isotropic, flooded, porous substrate with interconnected pores undergoing simultaneous evaporation and imbibition is…
We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…
We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time…
In laboratory experiments we demonstrate that protoplasmic tubes of acellular slime mould \emph{Physarum polycephalum} show current versus voltage profiles consistent with memristive systems and that the effect is due to the living…
We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized…
Osmosis plays a central role in the function of living and soft matter systems. While the thermodynamics of osmosis is well understood, the underlying microscopic dynamical mechanisms remain the subject of discussion. Unraveling these…