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Studying water droplets is a rich lesson in fields of fluid dynamics, nonlinear systems, and differential equations. Understanding various physical aspects of raindrops can help us in understanding drop dynamics, rainfall density…
A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We discuss variance reduced simulations for an individual-based model of chemotaxis of bacteria with internal dynamics. The variance reduction is achieved via a coupling of this model with a simpler process in which the internal dynamics…
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense…
The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
Colliding drops are widely encountered in everyday technologies and natural processes, from combustion engines and commodity sprays to raindrops and cloud formation. The outcome of a collision depends on many factors, including the impact…
In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they…
Wetting and drying of a rigid substrate by a Lennard-Jones fluid in molecular dynamics simulations is reported. The size of the substrate particles, being smaller than the fluid particles in former simulations, is now taken to be equal to,…
We study the spreading dynamics of a sphere-shaped elastic non-Newtonian liquid drop on a spherical substrate in the capillary driven regime. We use the simplified Phan Thien Tanner model to represent the rheology of the elastic…
We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…
We consider a liquid drop placed on a smooth homogeneous solid substrate as it spreads from rest to its eventual equilibrium state. The problem is studied numerically in the framework of a model where the contact angle formed by the drop's…
We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a non-equilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of…
We use molecular dynamics simulations to study the evaporation of particle-laden droplets on a heated surface. The droplets are composed of a Lennard-Jones fluid containing rigid particles which are spherical sections of an atomic lattice,…