Related papers: Discrete Gliding Along Principal Curves
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour…
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the…
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from…
We use numerical simulations and linear stability analysis to study active nematic droplets, in the regime where the passive phase is isotropic. We show that activity leads to the emergence of nematic order and of spontaneous rotation in…
We study the dynamics of a certain discrete model of interacting particles that comes from the so called shuffling algorithm for sampling a random tiling of an Aztec diamond. It turns out that the transition probabilities have a…
Discrete Darboux-Manakov-Zakharov systems possess two distinct Hamiltonian forms. In the framework of discrete-differential geometry one Hamiltonian form appears in a geometry of circular net. In this paper a geometry of second form is…
By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of "neighboring" agents is responsible for maintaining a prescribed target distance between them. In a recent paper…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
This paper presents a pedestrian motion model that includes both low level trajectory patterns, and high level discrete transitions. The inclusion of both levels creates a more general predictive model, allowing for more meaningful…
Recently, there is much interest in droplet condensation on soft or liquid/liquid-like substrates. Droplets can deform soft and liquid interfaces resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g., increased…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…
The dynamics of moving solids with unilateral contacts are often modeled by assuming rigidity, point contacts, and Coulomb friction due to the simplicity of these models. The canonical example of a rigid rod with one endpoint slipping in…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic…
Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two discretizations of principal curvature line…