相关论文: Hard Discs on the Hyperbolic Plane

We show that the perimeter of the convex hull of finitely many disks lying in the hyperbolic or Euclidean plane, or in a hemisphere does not increase when the disks are rearranged so that the distances between their centers do not increase.…

The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…

By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…

The thermodynamic and dynamical behavior of a gas of hard disks in a narrow channel is studied theoretically and numerically. Using a virial expansion we find that the pressure and collision frequency curves exhibit a singularity at a…

We consider discretized gravity in six dimensions, where the two extra dimensions have been compactified on a hyperbolic disk of constant curvature. We analyze different realizations of lattice gravity on the disk at the level of an…

The fluid-structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re=133 000 and can rotate…

We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions,…

In this note, we survey recent advances in the study of dynamical properties of the space of surfaces with constant curvature in three-dimensional manifolds of negative sectional curvature. We interpret this space as a two-dimensional…

We study stationary configurations of compressible barotropic fluids lying inside an incompressible fluid and acted upon by a constant gravitational field. Without gravity, it is a simple matter to construct solutions consisting of…

A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation…

We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for…

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and…

In this paper we use the notion of stability for free boundary surfaces with constant higher order mean curvature to obtain rigidity results for $H_2$-surfaces with free boundary of a geodesic ball of a simply connected $3$-dimensional…

We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force…

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…

Inspired by [6, 7], we study the boundary regularity of constant curvature hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$, which have prescribed asymptotic boundary at infinity. Through constructing the boundary expansions of the…

We consider curvature flows in hyperbolic space with a monotone, symmetric, homogeneous of degree 1 curvature function F. Furthermore we assume F to be either concave and inverse concave or convex. For compact initial hypersurfaces, which…

We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean…

While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…