Related papers: Pattern formation in annular convection
We discuss spatio-temporal pattern formation in two separate thermal convective systems. In the first system, hydrothermal waves (HTW) are modeled numerically in an annular channel. A temperature difference is imposed across the channel,…
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$.…
Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard convection in the form of straight rolls or of an array of dislocations may…
Pattern forming with externally imposed symmetry is ubiquitous in nature but lightly studied.We present experimental studies of pattern formation and selection by spatial periodic forcing in rapidly rotating convection. We observe symmetric…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating…
The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is…
We consider a model of electroconvection motivated by studies of the motion of a two dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two cylindrical electrodes. We prove…
Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Granular media such as sand and sugar are ubiquitous in nature and industry but are less well understood than fluids or solids. We consider the behavior of rapid granular flows where the transfer of momenta by collisions dominates. The…
Motivated by recent experimental studies of Bodenschatz et al. [E. Bodenschatz, J.R. de Bruyn, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. {\bf 67}, 3078 (1991) ], we present a numerical study of a generalized two dimensional…
In this paper, we consider dynamics defined by the Navier-Stokes equations in the Oberbeck-Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involve fundamental physical effects: convection, and diffusion.…
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by…
We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from…
We describe experiments on B{\'e}nard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a…
We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two dimensional case. We show that more complicated bifurcations can appear in this system for a…