Related papers: Linear stability of ultrathin spherical coatings
The force between two approaching solids in a liquid medium becomes increasingly large with decreasing separation, a phenomenon that prevents contact between the two solids. This growth in force occurs because of the intervening liquid,…
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a "vertical-shear instability", which recent nonlinear…
We study the stability properties of boundary layer-type shear flows for the three-dimensional Navier-Stokes equations in the limit of small viscosity $0<\nu\ll 1$. When the streamwise and spanwise velocity profiles are linearly independent…
We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…
We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary…
This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the strong instability of standing waves associated with ground state solutions in the $L^2$-supercritical case.…
We study the conformation of a heterogeneous surfactant monolayer at a fluid-fluid interface, near a boundary between two lateral regions of differing elastic properties. The monolayer attains a conformation of shallow, steep `mesas' with a…
The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have…
I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a non-uniform function of…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Levy index (LI) taking values LI < 2. Fractional…
Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…
We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. While the flow in a funnel may be related to a number of other flow configurations as limiting cases,…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
This second part of the study develops a geometric and asymptotic description of how surface tension governs the modulational stability of interfacial waves in a two-layer fluid. Extending the analytical framework of Part~I, surface tension…
We investigate here linear stability in a canonical three-dimensional boundary layer generated by the superposition of a spanwise pressure gradient upon an otherwise standard channel flow. As the main result, we introduce a simple…
We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone…
Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a…
The drag-out problem for small Reynolds numbers ($\rm Re$) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers ($\rm Ca$), and Derjaguin's solution for large $\rm Ca$. We investigate whether these solutions are…