Related papers: Eutectic Colony Formation: A Stability Analysis
We analyze the effect of interphase boundary anisotropy on the dynamics of lamellar eutectic solidification fronts, in the limit that the lamellar spacing varies slowly along the envelope of the front. In the isotropic case, it is known…
In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elas- ticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is…
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…
In this paper, we investigate three-phase eutectic growth during thin-film directional solidification of a model symmetric ternary eutectic alloy. In contrast to two-phase eutectics that have only a single possibility,…
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable…
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…
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 linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
Several meters below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of…
In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the…
The effects of entropic-instabilities on the laminar-turbulent transition dynamics of a blunted flat plate at Mach~$4$ are numerically investigated through linear and nonlinear approaches. Linear wavepacket analysis reveals amplifying…
Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In…
We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by \textit{Kepler} and \textit{K2}. We propagated 21,400 simulated planetary…
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
We present a linear stability analysis to demonstrate that a flat coherent phase boundary formed by the (de)intercalation of solutes into a compound is unstable against perturbations with wavelengths larger than a critical wavelength. This…
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant instability refers to the fact that the spatially constant…