Related papers: Turing instability for nonlocal heterogeneous reac…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent…
The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…
Collective motion of chemotactic bacteria as E. Coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to a temporal sensingof…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
Our recent development of a novel research burner has made it possible to experimentally investigate truly unstretched and planar diffusion flames. Hence it has become feasible to directly validate theoretical models for thermal-diffusive…
Aims. We aim to determine how ion neutral coupling and ambipolar diffusion affect the linear and the nonlinear growth of the RTinstability under astrophysically relevant conditions, and to identify the coupling regimes in which departures…
We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The…
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and…
We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends…
Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation,…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
The vertical shear instability (VSI) is a hydrodynamical instability likely to produce turbulence in the dead zones of protoplanetary disks. Various aspects of this instability remain to be understood, including the disk regions where it…
In this paper, a new stabilized discontinuous Galerkin method within a new function space setting is introduced, which involves an extra stabilization term on the normal fluxes across the element interfaces. It is different from the general…
The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…