Related papers: Intermediate physical interactions induce spatiote…
Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…
In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamic environment. We claim our model calculations can explain the diffusion of…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input for example…
This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
We discuss the microscopic origin of dynamical instabilities and segregation patterns discovered in granular mixtures under oscillating horizontal shear, by investigating, via molecular dynamics simulations, the effective interaction…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases,…
Phase separation in passive systems leads to uncontrolled droplet growth, limiting structural control in soft materials and cells. We identify a generic mechanism to arrest coarsening based on chemical interconversion between molecular…