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Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and…
We investigate some unstable behavior of the interface given by two incompressible fluids of different densities evolving by the regular Stokes law with gravity force. In the unstable scenario, where the denser fluid lies above the lighter…
A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are…
The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…
We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, and…
A dynamic crack will travel in a straight path up to a material-dependent critical speed beyond which its path becomes erratic. Predicting this critical speed and discovering the origin of this instability are two outstanding problems in…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated…
We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a `weaving' pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact…
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of…
Various experimental settings that involve drying solutions or suspensions of nanoparticles -- often called nanofluids -- have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a…
The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a…
The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a…
We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…