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We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and…
The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry,…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
We study in some generality intertwinings between $h$-transforms of Karlin-McGregor semigroups associated with one dimensional diffusion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes…
In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish…
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…
We report new chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between 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…
In this paper, we study weakly interacting diffusion processes on random graphs. Our main focus is on the properties of the mean-field limit and, in particular, on the nonuniqueness and bifurcation structure of stationary states. By…
We show that the flagellar beat of bull spermatozoa and Chlamydomonas Reinhardtii can be modelled by a minimal, geometrically nonlinear reaction-diffusion system. Model solutions are spatio-temporally animated patterns describing flagellar…
The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion…
This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in…
Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
We study the reaction-diffusion process $A+B\to \emptyset$ with injection of each species at opposite boundaries of a one-dimensional lattice and bulk driving of each species in opposing directions with a hardcore interaction. The system…
In a highly turbulent medium characterized by a low Damk\"ohler number Da, reactions are commonly considered to occur in distributed zones broadened by small-scale turbulent eddies. In the present communication, an alternative regime of…
We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional traps across the thermal crossover from an amorphous solid- to liquid-like behaviors. While static correlations, that…