Related papers: Covers, soap films and BV functions
We investigate the sliding dynamics of a millimeter-sized particle trapped in a horizontal soap film. Once released, the particle moves toward the center of the film in damped oscillations. We study experimentally and model the forces…
In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem,…
Given a closed oriented manifold or more generally a group homology class, we introduce the spherical Plateau problem, which is a variational problem corresponding to a topological invariant called the spherical volume. In principle, its…
Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the…
Cleaning surfaces with bubbles has been a topic of discussion in recent years due to the growing interest in sustainable methods for cleaning. Specifically, a method of using air bubbles to sanitize agricultural produce has been proposed as…
We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their…
We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a…
The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A…
Investigations of free-standing liquid films enjoy an increasing popularity due to their relevance for many fundamental and applied scientific problems. They constitute soap bubbles and foams, serve as membranes for gas transport or as…
The analogy between soap films thinning under border capillary suction and lamellar stacks of surfactant bilayers dehydrated by osmotic stress is explored, in particular in the highly dehydrated limit where the soap film becomes a Newton…
The behavior of thin liquid films is known to be strongly affected by the presence of surfactants at the interfaces. The detailed mechanism by which the latter enhance film stability is still a matter of debate, in particular concerning the…
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non…
Abnormality detection in video poses particular challenges due to the infinite size of the class of all irregular objects and behaviors. Thus no (or by far not enough) abnormal training samples are available and we need to find…
Production, drainage and stability of foams films, i.e. films in contact with their menisci, are fascinating problems that remain still unsolved. In this article, we propose to explore the regime of large velocities and large film sizes.…
Bishop's volume comparison theorem states that a compact $n$-manifold with Ricci curvature larger than the standard $n$-sphere has less volume. While the traditional proof uses geodesic balls, we present another proof using isoperimetric…
By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary…
We study a toy model for electrolytic soap films, the two-dimensional two-component plasma. This model is exactly solvable for a special value of the coulombic coupling constant $\beta q^2=2$. This allows us to compute the disjoining…
We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature, viscous friction with the walls, and includes the transport of surfactant within the films and across…
We investigate on the existence of smooth complete hypersurface with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under the assumption that there exists an asymptotic subsolution. We give an…
We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to…