Related papers: Skew-Varicose Instability in Two Dimensional Gener…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
We study the two-phase, horizontally periodic, quasistationary Stokes flow in two dimensions driven by surface tension and gravity effects in the general context of fluids with (possibly) different viscosities and densities. The sharp…
We derive here a new stability criterion for two-fluid interfaces. This criterion ensures the existence of "stable" local solutions that do no break down too fast due to Kelvin-Helmholtz instabilities. It can be seen both as a two-fluid…
The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modelled as an exponential function of…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
We study the flow map associated to the cubic Schrodinger equation in space dimension at least three. We consider initial data of arbitrary size in $H^s$, where $0<s<s_c$, $s_c$ the critical index, and perturbations in $H^\si$, where…
We study theoretically pressure driven planar channel flow of shear thinning viscoelastic fluids. Combining linear stability analysis and full nonlinear simulation, we study the instability of an initially one-dimensional base state to the…
Modal instabilities in a flow through a channel at high Reynolds and Mach numbers are studied for three-dimensional perturbations. In addition to the Tollmien-Schlichting modes, there exist higher modes in a channel flow that do not have a…
We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or…
The Reynolds stress in Holmboe instabilities at moderate Reynolds numbers is investigated using single wavelength simulations (SWS), multiple wavelength simulations (MWS), and laboratory experiments. The rightward and leftward propagating…
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of…
We deal with the as yet unresolved exponential stability problem for Beck's Problem on a metric star graph with three identical edges. The edges are stretched Euler--Bernoulli beams which are simply supported with respect to the outer…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and study the eigenvalue distribution of the linearized Euler…
A linear stability analysis is performed on a tilted parallel wake in a strongly stratified fluid at low Reynolds numbers. A particular emphasis of the present study is given to the understanding of the low-Froude-number mode observed by…
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger…
Plane Couette flow of visco-elastic fluids is shown to exhibit a purely elastic subcritical instability in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette…
Computational modeling of pattern formation in nonequilibrium systems is a fundamental tool for studying complex phenomena in biology, chemistry, materials science and engineering. The pursuit for theoretical descriptions of some among…