Continuum Model of Thin-Film Deposition and Growth

A continuum theory for the deposition and growth of solid films is presented. The theory is developed in a coordinate-independent manner and so incorporates the fully nonlinear physics. The evolution of the film is modeled in three steps. First, the adsorption of atoms in the incident beam is modeled as a ballistic process. Second, the random motion of the adatoms is treated as a diffusive process. Finally, sticking of adatoms to the film occurs as a Poisson process. The resulting system of differential equations is examined in several parameter limits. The diffusively dominated limit appears similar to zone 1 of the structure-zone model. Generically the surface slope develops discontinuities; these ‘‘kinks’’ play the role of grain boundaries. In the ballistically dominated case these kinks may be advected along the surface giving rise to columnarlike microstructures, as is observed in zone 2

Microtubule-driven conformational changes in platelet -morphogenesis

The influence of the range of the involved geometric and material parameters, such as the available area for conformational changes, the bilayer thickness, the interaction energy between transmembrane domains and lipids, is largely explored. Bounds on the available conformations experienced by the transmebrane domains are also provided

Viscous Cross-waves: An Analytical Treatment

Viscous effects on the excitation of cross‐waves in a semi‐infinite box of finite depth and width are considered. A formalism using matched asymptotic expansions and an improved method of computing the solvability condition is used to derive the relative contributions of the free‐surface, sidewall, bottom, and wavemaker viscous boundary layers. This analysis yields an expression for the damping coefficient previously incorporated on heuristic grounds. In addition, three new contributions are found: a viscous detuning of the resonant frequency, a slow spatial variation in the coupling to the progressive wave, and a viscous correction to the wavemaker boundary condition. The wavemaker boundary condition breaks the symmetry of the linear neutral stability curve at leading order for many geometries of experimental interest

The Interaction of a Point Vortex with a Wall-bounded Vortex Layer

The interaction of a point vortex with a layer of constant vorticity, bounded below by a wall and above by an irrotational flow, is investigated as a model of vortex–boundary layer interaction. This model calculates both the evolution of the interface which separates the vortex layer from the irrotational flow and the trajectory of the vortex. In order to determine the conditions which lead to sustained unsteady interaction, three cases are investigated where the mutual interaction between the vortex and interface is initially assumed to be weak. (i) When a weak point vortex lies outside the layer, the vortex moves with a horizontal speed that is small relative to the long-wave phase speed of interfacial waves. A uniformly valid solution is found for the interface evolution. This solution shows that for long times the interface and the vortex approach an equilibrium state. (ii) When a weak vortex lies inside the layer, the vortex is convected by the mean flow and moves with a horizontal speed which matches the phase speed of an interfacial wave. This results in a strong interaction between the vortex and the interfacial wave. On the interface, a monochromatic wavetrain forms upstream of the vortex and acts to attract or repel the point vortex. The displacement of the vortex due to the wavetrain results in the modulation of the amplitude and wavelength of the wavetrain. If the point vortex is attracted toward the interface the horizontal speed of the vortex slows and disturbances directly above the vortex focus and grow leading to the ejection of vorticity. (iii) When the point vortex lies close to the wall and it is sufficiently strong it propagates downstream with a large horizontal velocity. In this case, the amplitude of the interfacial disturbance is independent of the vortex strength. Again, the vortex and the interface approach an equilibrium state. The results of this paper indicate that when the horizontal speed of the vortex matches the phase speed of the interfacial disturbance, it is necessary to account for the vertical displacement of the vortex in order to predict the behaviour of vortex–boundary layer interactions

Modulated, Frequency-locked, and Chaotic Cross-waves

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by the circle-map theory describing weakly coupled oscillators. Some of the observed tongues are apparently folded by a subcritical bifurcation, with the tips of the tongues lying on the unstable manifold folded under the observed stable manifold. Near the intersection of the neutral stability curves for two adjacent modes, a standing wave localized on one side of the tank was observed in agreement with the coupled-mode analysis of Ayanle, Bernoff & Lichter (1990). At large cross-wave amplitudes, the spanwise wave structure apparently breaks up, because of modulational instability, into coherent soliton-like structures that propagate in the spanwise direction and are reflected by the sidewalls

Stability of Steady Cross-waves: Theory and Experiment

A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling

The Steady Boundary Layer due to a Fast Vortex

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex cv is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances