Related papers: Braiding a flock: winding statistics of interactin…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
Locomotion of bacteria by actin polymerization, and in vitro motion of spherical beads coated with a protein catalyzing polymerization, are examples of active motility. Starting from a simple model of forces locally normal to the surface of…
We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We investigate the wetting properties of the simplest element of an array of random fibers: two rigid fibers crossing with an inclination angle and in contact with a droplet of a perfectly wetting liquid. We show experimentally that the…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
Fuelled by a desire for greater connectivity, networked systems now pervade our society at an unprecedented level that will affect it in ways we do not yet understand. In contrast, nature has already developed efficient networks that can…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing…
Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces…
We investigate how localized inhomogeneity affects the geometry and stability of migratory bird formations. We use a lifting-line model with a horseshoe-vortex representation to describe the longitudinal dynamics of aerodynamic…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Collective migration of cells and animals often relies on a specialised set of "leaders", whose role is to steer a population of naive followers towards some target. We formulate a continuous model to understand the dynamics and structure…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally…
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…