Related papers: Instabilities and Patterns in Coupled Reaction-Dif…
We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
The stability of two bubbles rising initially in-line through a viscous liquid is revisited using a global linear stability analysis formulated within an Arbitrary Lagrangian-Eulerian framework, complemented by fully resolved Embedded…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
A simplified phenomenological model is proposed to couple the long-wave Darrieus--Landau (DL) instability and the short-wave diffusive-thermal (DT) instability in premixed flames. By identifying a cubic coupling term in the linear…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Semiconductor $p^+ - p^- - n - p^+ - n^{++}$ structures with large junction and contact areas are treated as 1 \times 2-dimensional active media, in which self-organized pattern formation can be expected. The local bistable behavior of the…
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The…
This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an…
We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of…
We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic with respect to a square or hexagonal…
Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming,…
Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that…