Conditional stability and symmetry in hydrodinamics and mathematical biology
Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating
The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer,...
Convection with temperature dependent viscosity in a porous medium: nonlinear stability and the Brinkman effect.
We establish a nonlinear energy stability theory for the problem of convection in a porous medium when the viscosity depends on the temperature. This is, in fact, the situation which is true in real life and has many applications to geophysics. The nonlinear analysis presented here would appear to require the presence of a Brinkman term in the momentum equation, rather than just the normal form of Darcy's law.
Dynamics of a Reactive Thin Film
Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler...
Finite amplitude thermal convection with variable gravity.
Finite bandwidth, long wavelength convection with boundary imperfections: Near-resonant wavelength excitation.
Les équations de Kelvin-Helmotz. Un problème bien posé uniquement dans le cadre analytique
Linear instability implies nonlinear instability for various types of viscous boundary layers
Marangoni Convection in a Photo-Chemically Reacting Liquid
Marangoni convection caused by a photochemical reaction of the type A B in a deep liquid layer is studied. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that increasing the rate of the direct reaction, for example, by increasing the light intensity, destabilizes the steady state and causes convective motion of the fluid, whereas increasing the rate of the inverse reaction stabilizes the steady state. A weakly nonlinear analysis...
Nonlinear instability in an ideal fluid
Nonlinear interaction of waves in a hot inhomogeneous magnetized plasma.
Note on modulational instability of Boussinesq wavetrains.
On a model equation that reflects some of the shear flow hydrodynamic stability properties
Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs
Shear layer solutions of incompressible MHD and dynamo effect
Stability of oscillating boundary layers in rotating fluids
We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.
The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model
The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of...
The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films
The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities...
Unconditional nonlinear exponential stability in the Bénard problem for a mixture: necessary and sufficient conditions
The Lyapunov direct method is applied to study nonlinear exponential stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl numbers is...
Unconditional nonlinear stability in a polarized dielectric liquid
We derive a very sharp nonlinear stability result for the problem of thermal convection in a layer of dielectric fluid subject to an alternating current (AC). It is particularly important to note that the size of the initial energy in which we establish global nonlinear stability is not restricted whatsoever, and the Rayleigh-Roberts number boundary coincides with that found by a formal linear instability analysis.