相关论文: Collapsed heteroclinic snaking near a heteroclinic…

A thin-film model for a meniscus driven by Rayleigh surface acoustic waves (SAW) is analysed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath. We…

We study stationary, periodic solutions to the thermocapillary thin-film model \begin{equation*} \partial_t h + \partial_x \Bigl(h^3(\partial_x^3 h - g\partial_x h) + M\frac{h^2}{(1+h)^2}\partial_xh\Bigr) = 0,\quad t>0,\ x\in \mathbb{R},…

We study two-dimensional, stationary square and hexagonal patterns in the thermocapillary deformational thin-film model for the fluid height $h$\begin{equation*} \partial_t h+\nabla\cdot\left(h^3\left(\nabla\Delta h-g\nabla…

In this paper, we discuss a particular model arising from sinking of a rigid solid into a thin film of fluid, i.e. a fluid contained between two solid surfaces and part of the fluid surface is in contact with the air. The fluid is governed…

We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed $U$, there is a range of ``thick'' film solutions whose thickness scales like…

We report on localized patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighborhood of the unstable branch of the domain…

Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially…

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions…

We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear…

We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface,…

We apply spatial dynamical-systems techniques to prove that certain spatiotemporal patterns in reversible reaction-diffusion equations undergo snaking bifurcations. That is, in a narrow region of parameter space, countably many branches of…

When a plate is withdrawn from a liquid bath, either a static meniscus forms in the transition region between the bath and the substrate or a liquid film of finite thickness (a Landau-Levich film) is transferred onto the moving substrate.…

We investigate experimentally the receding of a contact line when a Peltier module is pulled out of a water bath at constant speed, while a ice layer is also growing at constant speed on the Peltier module. A steady regime is therefore…

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free…

An investigation is undertaken of coupled reaction-diffusion systems in one spatial dimension that are able to support, in different regions of their parameter space, either an isolated spike solution, or stable localized patterns with an…

Liquid foams are widely used in industry for their high effective viscosity, whose local origin is still unclear. This Letter presents new results on the extension of a suspended soap film, in a configuration mimicking the elementary…

The coupled dynamics of two conjugated liquid layers of disparate thicknesses, which coat a solid substrate and are subjected to a transverse temperature gradient, is investigated. The upper liquid layer evolves under the short-wavelength…

When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid…

We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic long-wave model for the three-dimensional B\'enard-Marangoni problem, which is close to a Turing instability. We derive the model from the full…

Homoclinic snaking is a widespread phenomenon observed in many pattern-forming systems. Demonstrating its occurrence in non-perturbative regimes has proven difficult, although a forcing theory has been developed based on the identification…