相关论文: Helical close packings of ideal ropes
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
For Reeb vector fields on closed 3-manifolds, cylindrical contact homology is used to show that the existence of a set of closed Reeb orbit with certain knotting/linking properties implies the existence of other Reeb orbits with other…
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
First we express the holonomy along a boundary curve as the integral on the domain, of an expression which is linear in the curvature. Then we provide a rigorous justification of the definition of curvature in Regge calculus.
Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure…
An internal characterization of complete metric mappings (by means of Cauchy nets tied at a point) is given and a construction of the completion of a metric mapping is presented.
Planar/flat configurations of fixed-angle chains and trees are well studied in the context of polymer science, molecular biology, and puzzles. In this paper, we focus on a simple type of fixed-angle linkage: every edge has unit length…
Simply-connected manifolds of positive sectional curvature $M$ are speculated to have a rigid topological structure. In particular, they are conjectured to be rationally elliptic, i.e., all but finitely many homotopy groups are conjectured…
The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected space (a flip is the elementary operation on rhombus tilings which rotates 180{\deg} a hexagon made of three rhombi). Motivated by…
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
Analyses of two-particle correlations have provided the chief means for determining spatio-temporal characteristics of relativistic heavy ion collisions. We discuss the theoretical formalism behind these studies and the experimental methods…
The functionality of proteins is related to their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…
A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…
A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The local density profile is well understood from theory, simulation, and experiment. Here, pair correlations are…
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability measures characterizes lower bounds of the…
This contribution summarizes the on-going activities connected to the evaluation of higher order radiative corrections in the context of a future international linear collider (ILC).