Anomalous dimensions of the Smoluchowski coagulation equation.

The coagulation (or aggregation) equation was introduced by Smoluchowski in 1916 to describe the clumping together of colloidal particles through diffusion, but has been used in many different contexts as diverse as physical chemistry, chemical engineering, atmospheric physics, planetary science, and economics. The effectiveness of clumping is described by a kernel K(x,y), which depends on the sizes of the colliding particles x,y. We consider kernels K=(xy)^{γ}, but any homogeneous function can be treated using our methods.

Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.

The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale.

A note on the self-similar solutions to the spontaneous fragmentation equation.

We provide a method to compute self-similar solutions for various fragmentation equations and use it to compute their asymptotic behaviours. Our procedure is applied to specific cases: (i) the case of mitosis, where fragmentation results into two identical fragments, (ii) fragmentation limited to the formation of sufficiently large fragments, and (iii) processes with fragmentation kernel presenting a power-like behaviour.

From individual to collective dynamics in Argentine ants (Linepithema humile).

In this paper we propose a model for the formation of paths in Argentine ants when foraging in an empty arena. Based on experimental observations, we provide a distribution for the random change in direction that they approximately undergo while foraging as a mixture of a Gaussian and a Pareto distribution. By following the principles described in previous work, we consider persistence and reinforcement to create a model for the motion of ants in the plane.

The microfluidic Kelvin water dropper.

The so-called "Kelvin water dropper" is a simple experiment demonstrating the spontaneous appearance of induced free charge in droplets emitted through a tube. As Lord Kelvin explained, water droplets spontaneously acquire a net charge during detachment from a faucet due to the presence of electrical fields in their surroundings created by any metallic object. In his experiment, two streams of droplets are allowed to drip from separate nozzles into separate buckets, which are, at the same time, interconnected through the dripping needles.