Related papers: Convective instability on a crystal surface
Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that for inclination angle larger than a threshold, global fractal patterns are formed. The fractal dimensions…
In this study, the phase field model of crack propagation is used to study the dynamic branching instability in the case of inplane loading in two dimensions. Simulation results are in good agreement with theoretical predictions and…
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…
Morphological instabilities of growing tissues that impinge on passive materials are typical of invasive cancers. To explain these instabilities in experiments on breast epithelial spheroids in an extracellular matrix, we develop a…
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable…
The paper is devoted to the study of the formation of stratification in an incompressible fluid due to convective laminar flows in horizontal layers heated from the side. Medium and intensive modes of stationary laminar thermal,…
Ring-like ripples on the surface of icicles are an example of morphological instability of the ice-water interface during ice growth under supercooled water film flow. The surface of icicles is typically covered with ripples of about 1 cm…
We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known F\"oppl--von K\'arm\'an number $\Gamma$ and the recently…
We report experimental study of the secondary modulational instability of a one-dimensional non-linear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatio-temporal defects are…
Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. A: Math. Theor.} (2023), under the assumption…
Active stresses can cause instabilities in contractile gels and living tissues. Here we describe a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (1995) developed a simple model of reactive porous flow and numerically analysed its…
The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
The steps at the crystal surfaces could be transparent for the migrating adatoms. In the case of significant transparency the velocity of a given step in a given moment is affected by detachment of atoms from rather distant steps in rather…
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively…
Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory. In contrast, the `emergent elasticity' of amorphous solids, rigid materials characterized by an underlying…
Paths of tetragonal states between two phases of a material, such as bcc and fcc, are called Bain paths. Two simple Bain paths can be defined in terms of special imposed stresses, one of which applies directly to strained epitaxial films.…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…