Related papers: Drifting Pattern Domains in a Reaction-Diffusion S…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
In this Letter we present discrete wave turbulence (DWT) as a counterpart of classical statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the size of clusters, i.e. it includes, but is not reduced to,…
Modelling diffusion processes on dynamic contact networks is an important research area for epidemiology, marketing, cybersecurity, and ecology. However, current diffusion models cannot capture transmissions occurring for indirect…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the…
Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to rapid changes in the environment. The non-stationary fading process can be characterized by assuming local…
Solids undergoing a transition from order to disorder experience the proliferation of topological defects. The melting process generates transient quantum states. However, their dynamical nature with femtosecond lifetime hinders exploration…
We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
I review recent results concerning the shape of drifting subpulse patterns, and the relationship to model predictions. While a variety of theoretical models exist for drifting subpulses, observers typically think in terms of a…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…