Exact steady states to a nonlinear surface growth model

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.     

Darcy–Forchheimer flow under rotating disk and entropy generation with thermal radiation and heat source/sink

Journal of Thermal Analysis and Calorimetry - This article investigates the second law of thermodynamics for chemically reactive Sisko nanofluid by a rotating disk saturated with non-Darcy porous...     

Effect of cationic and anionic surfactants on the addition–elimination-type interaction between o-toluidine and d-glucose

The kinetics of the o-toluidine–d-glucose reaction has been studied as a function of [o-toluidine], [d-glucose], [acetic acid], and temperature by UV–visible spectrophotometry at 630 nm in the absence and presence of cetyltrimethylammonium bromide (CTAB) and sodium dodecyl sulfate (SDS). The reaction follows second-order kinetics, being unity in each of the reactants in both media. The effect of added surfactants has also been investigated. The model of micellar catalysis, such as the Menger–Portony model modified by Bunton, is applied to explain the catalytic role of CTAB and SDS micelles. The association/incorporation constants (K _s and K _n), the rate constant in micellar media (k _m), and the activation parameters of this system have been calculated and discussed. The value of the rate constant is found to be higher in SDS than in CTAB. Hydrophobic and electrostatic interactions are responsible for higher reaction rates in SDS. From all observed facts, a reaction mechanism involving a nucleophilic addition–elimination path has been suggested.     

Vacillating breathing and tumbling of vesicles under shear flow

The dynamics of vesicles under a shear flow are analyzed analytically in the small deformation regime. We derive two coupled nonlinear equations which describe the vesicle orientation in the flow and its shape evolution. A new type of motion is found, namely, a "vacillating-breathing" mode: the vesicle orientation undergoes an oscillation around the flow direction, while the shape executes breathing dynamics. This solution coexists with tumbling. Moreover, we provide an explicit expression for the tumbling threshold. A rheological law for a dilute vesicle suspension is outlined.     

Nonlinear study of symmetry breaking in actin gels: implications for cellular motility

Force generation by actin polymerization is an important step in cellular motility and can induce the motion of organelles or bacteria, which move inside their host cells by trailing an actin tail behind. Biomimetic experiments on beads and droplets have identified the biochemical ingredients to induce this motion, which requires a spontaneous symmetry breaking in the absence of external fields. We find that the symmetry breaking can be captured on the basis of elasticity theory and linear flux-force relationships. Furthermore, we develop a phase-field approach to study the fully nonlinear regime and show that actin-comet formation is a robust feature, triggered by growth and mechanical stresses. We discuss the implications of symmetry breaking for self-propulsion.     

Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces

We report on peculiar behaviors due to anisotropic terrace diffusion on step meandering on a vicinal surface. We find that anisotropy triggers tilted ripples. In addition, if the fast diffusion direction is perpendicular to the steps, the instability is moderate and coarsening is absent, while in the opposite case the instability is promoted, and interrupted coarsening may be observed. Strong enough anisotropy restabilizes the step for almost all step orientations. These findings point to the nontrivial effect of anisotropy and open promising lines of inquiries in the design of surface architectures.     

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher-order nonlinear term in the equation leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations. Received 20 January 2000