Related papers: Neutral surface topology
Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liquid crystals models and harmonic maps, lead to consider…
The response of Newtonian liquids to small perturbations is usually considered to be fully described by homogeneous transport coefficients like shear and dilatational viscosity. However, the presence of strong density gradients at the…
We apply a theoretical approach, originally introduced to describe aeolian ripples formation in sandy deserts, to the study of surface instability in ion sputtered surfaces. The two phenomena are distinct by several orders of magnitudes and…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
When stretched in one direction, most solids shrink in the transverse directions. In soft silicone gels, however, we observe that small-scale topographical features grow upon stretching. A quantitative analysis of the topography shows that…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others…
Buoyancy effects in unstably stratified mixing layers express themselves through gravity currents of heavy fluid which propagate in an ambient lighter fluid. These currents are encountered in numerous geophysical flows, industrial safety…
T-curves are piecewise linear curves which have been used with success since the beginning of the 1990's to construct new real algebraic curves with prescribed topology mainly on the real projective plane. In fact T-curves can be used on…
We introduce topological invariants of semi-decompositions (e.g. filtrations, semi-group actions, multi-valued dynamical systems, combinatorial dynamical systems) on a topological space to analyze semi-decompositions from a dynamical…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the…
We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira…
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at…
We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics…
Small planets ($\sim$1--3.9 $\Rearth$) constitute more than half of the inventory of the 4000-plus exoplanets discovered so far. Smaller planets are sufficiently dense to be rocky, but those with radii larger than $\sim$1.6 $\Rearth$ are…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…