Related papers: Instability in Ostwald ripening processes
The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been…
The growth rate of the filamentation instability triggered when a diluted cold electron beam passes through a cold plasma is evaluated using the quantum hydrodynamic equations. Compared with a cold fluid model, quantum effects reduce both…
In this paper, we consider a class of evolution equations driven by finite-dimensional $\gamma$-H\"{o}lder rough paths, where $\gamma\in(1/3,1/2]$. We prove the global-in-time solutions of rough evolution equations(REEs) in a sutiable…
When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a…
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
In this work, we revisit the question of the linear stability of superfluid phases of matter. Famously, Landau predicted superfluid Helium would become unstable for large enough superfluid velocities. We demonstrate that this instability…
Dust grains embedded in gas flow give rise to a class of hydrodynamic instabilities, called resonant drag instabilities. These instabilities have predominantly been studied for single grain sizes, in which case they are found to grow fast.…
Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the {\it spectral} support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable…
Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences…
A systematic analysis of the Eckhaus instability in the one-dimensional Ginzburg-Landau equation is presented. The analysis is based on numerical integration of the equation in a large (xt)-domain. The initial conditions correspond to a…
A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is rapidly increasing in time, the corresponding laminar profile of the…
We identify a finite wavenumber instability of a 90$^{\circ}$ tilt grain boundary in three dimensional lamellar phases which is absent in two dimensional configurations. Both a stability analysis of the slowly varying amplitude or envelope…
Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the…
Bubble solutions are of growing interest because of various technological applications in surface cleaning, water treatment, and agriculture. However, their physicochemical properties such as the stability and interfacial charge of bubbles…
Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
We estimate the importance of the nonlinear terms in the Vlasov equation for the development of the unstable modes. The results allow to identify the region of wavelength where the linear evolution is justified.
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…