Related papers: Turing instability for nonlocal heterogeneous reac…
We outline a novel linear instability that may arise in the dead-zones of protostellar disks, and possibly the fluid interiors of planets and protoplanets. In essence it is an axisymmetric buoyancy instability, but one that would not be…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
Observations show that radial metallicity gradients in disk galaxies are relatively shallow, if not flat, especially at large galactocentric distances and for galaxies in the high-redshift universe. Given that star formation and metal…
In this paper, we study the null and approximate controllability of a class of fully nonlocal coupled stochastic reaction--convection--diffusion systems. The system consists of two forward stochastic parabolic equations driven by general…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
Differentially rotating stars and planets transport angular momentum internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure…
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…
In this paper we show numerically that for nonlinear Schrodinger type systems the presence of nonlocal perturbations can lead to a beyond-all-orders instability of stable solutions of the local equation. For the specific case of the…
We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a…
We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schr\"{o}dinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which…
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…
This is a truncation of the second year group project at Imperial college london. In this paper, we consider a semilinear reaction diffusion system of SIR model which involves the birth rate and the death rate. We first prove the…
We study a quasi-two-dimensional electrostatic drift kinetic system as a model for near-marginal ion temperature gradient (ITG) driven turbulence. A proof is given of the nonlinear stability of this system under conditions of linear…
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…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
The vertical shear instability and the streaming instability are two robust sources of turbulence in protoplanetary disks. The former has been found to induce anisotropic turbulence that is stronger in the vertical than in the radial…
Recent work by Pringle and by Maloney, Begelman & Pringle has shown that geometrically thin, optically thick, accretion disks are unstable to warping driven by radiation torque from the central source. In this paper we generalize the study…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
Ambient interstellar material may become entrained in outflows from massive stars as a result of shear flow instabilities. We study the linear theory of the Kelvin - Helmholtz instability, the simplest example of shear flow instability, in…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…