Related papers: Instability patterns, wakes and topological limnit…
The wake of a body moving across the isopycnals of a strongly stratified fluid is characterized by the presence of an intense jet which, under certain circumstances, may become unstable. To get insight into the phenomenology of this…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
The existence of unique scaling in a crossover regime between viscous and inertial hydrodynamic regimes is revealed for homogeneous, isotropic, incompressible, spinodal turbulence which is characterized, to begin with, by three different…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
Warped astrophysical discs are usually treated as laminar viscous flows, which have anomalous properties when the disc is nearly Keplerian and the viscosity is small: fast horizontal shearing motions and large torques are generated, which…
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjortoft's criterion of…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the…
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
We experimentally study the occurrence of pattern formation during the slot-die coating of low-viscosity nearly Newtonian liquids onto Polyethylenterephthalat (PET)-substrates. In particular, it is demonstrated that with increase of the…
The scale dependent intermittency exponents in developed hydrodynamic turbulence are calculated assuming a natural hierarchy of correlations in the turbulence. The major correlations are taken into account explicitly, while the remaining…
The topological dynamics of the horocyclic flow h_R on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular on such a surface the flow h_R is minimal or the minimal sets are the periodic orbits.…
Discontinuities in relativistic hydrodynamics - shock waves and freeze-out shocks - are considered across both space-like and time-like hypersurfaces. We analyze the peculiar features of the freeze-out discontinuities and their connection…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that…
In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and…
A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent…
We present a dissipative system with unstable dynamics called unstable dissipative system which are capable of generating a multi-stable behavior, i.e., depending on its initial condition the trajectory of the system converge to a specific…