Related papers: The Complex Structure of 2D Surfaces
The intersection matrix of a finite simplicial complex has as each of its entries the rank of the intersection of its respective simplices. We prove that such matrix defines the triangulation of a closed connected surface up to isomorphism.
We report the first successful simulation of spontaneous formation of surface magnetic structures from a large-scale dynamo by strongly-stratified thermal convection in Cartesian geometry. The large-scale dynamo observed in our…
We investigate the crossover between weak and strong self-avoidance in a simulation of random surfaces with extrinsic curvature. We consider both dynamically triangulated and rigid surfaces with the two possible discretizations of the…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…
The complex physics and numerous failure modes of structural impact creates challenges when designing for impact resistance. While simple geometries of layered material are conventional, advances in 3D printing and additive manufacturing…
We report an observation of a stable soliton-like structure on the surface of a ferrofluid, generated by a local perturbation in the hysteretic regime of the Rosensweig instability. Unlike other pattern-forming systems with localized 2D…
We investigate the behavior of two dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct the network by having a network-element repeat itself $L_x$…
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…
Several mechanisms cause a granular material to strengthen over time at low applied stress. The strength is determined from the maximum frictional force F_max experienced by a shearing plate in contact with wet or dry granular material…
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…
The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical…
The ground state of a classical two-dimensional (2D) system with finite number of charged particles, trapped by two positive impurities charges localized at a distance (zo) from the 2D plane and separated from each other by a distance xp…
The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed time-like distance. The importance of the foliation structure in the 2+1 dimensional model is studied…
Nontrivial infinitesimal bendings for a class of two-dimensional surfaces are constructed. The surfaces considered here are orientable; compact; with boundary; have positive curvature everywhere except at finitely many planar points; and…
Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in R^3. In particular, every noncompact surface has a (3,6)-tight triangulation that…