Related papers: Disks that are double spiral staircases
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of…
Dip-coating consists in withdrawing a substrate from a bath to coat it with a thin liquid layer. This process is well-understood for homogeneous fluids, but heterogeneities such as particles dispersed in the liquid lead to more complex…
A solid, withdrawn from a liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
This paper is the second in a two-part exposition on {\it surface-directed spinodal decomposition} (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary…
Alexandrov's Soap Bubble theorem dates back to $1958$ and states that a compact embedded hypersurface in $\mathbb{R}^N$ with constant mean curvature must be a sphere. For its proof, A.D. Alexandrov invented his reflection priciple. In…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
The Brownian diffusion of micron-scale inclusions in freely suspended smectic A liquid crystal films a few nanometers thick and several millimeters in diameter depends strongly on the air surrounding the film. Near atmospheric pressure, the…
Compact analytical forms are derived for the interactions involving thin disks in two dimensions using an integration approach. These include interactions between a disk and a material point, between two disks, and between a disk and a…
[Full abstract in the paper] In recent years, protoplanetary disks with spiral structures have been detected in scattered light, millimeter continuum, and CO gas emission. The mechanisms causing these structures are still under debate. A…
Direct observation of vortices by the scanning SQUID microscopy was made on large mesoscopic disks of an amorphous MoGe thin film. Owing to the weak pinning nature of the amorphous film, vortices are able to form geometry induced,…
Real foams can be viewed as a geometrically well-organized dispersion of more or less spherical bubbles in a liquid. When the foam is so drained that the liquid content significantly decreases, the bubbles become polyhedral-like and the…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
Evaporation of water droplets deposited on metal and polymer substrates was studied. The evaporated droplet demonstrates different behaviors on low-pinning (polymer) and strong-pinning (metallic) surfaces. When deposited on polymer…
This paper exhibits a structural strategy to produce new minimal submanifolds in spheres based on two given ones. The method is to spin the given minimal submanifolds by a curve $\gamma\subset \mathbb S^3$ in a balanced way and leads to…
The sedimentation of two spherical solid objects in a viscous fluid has been extensively investigated and well understood. However, a pair of flat disks (in three dimensions) settling in the fluid shows more complex hydrodynamic behaviors.…
Numerical simulations of spontaneous dewetting of non-slipping, variable viscosity unstable thin liquid films on homogeneous substrates reveal the existence of sub-spinodal lengthscales through formation of satellite holes, a marker of…
We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible…
We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of…
This review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are used in different fields, such as cooling of heated surfaces of electronic…