Related papers: Cone structures from a dynamical and probabilistic…
Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
The paper investigates a hypothesis that our visual system groups visual cues based on how they form a surface, or more specifically triangulation derived from the visual cues. To test our hypothesis, we compare shape recognition with three…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…
Ill-posed configurations, such as collinear or coplanar point arrangements, are a persistent challenge in computational geometry, complicating tasks as in triangulation and convex hull construction. This paper discusses the probability of…
We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…
The goal of nuclear structure theory is to build a comprehensive microscopic framework in which properties of nuclei and extended nuclear matter, and nuclear reactions and decays can all be consistently described. Due to novel theoretical…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
A cone structure on a complex manifold $M$ is a closed submanifold $\mathcal C \subset \mathbb P TM$ of the projectivized tangent bundle which is submersive over $M$. A conic connection on $\mathcal C$ specifies a distinguished family of…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
The paper continues a series of publications devoted to the 3D nonlinear localized coherent structures on the surface of vertically falling liquid films. The work is primarily focussed on experimental investigations. We study: (i)…
The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space in this paper. There are two families of complex hyperbolic structures on the configuration space…