Related papers: Topological Analysis of Foams and tetrahedral stru…
We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the…
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…
A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…
We introduce a new computational methodology for the identification and characterization of free volume within/around atomistic configurations. This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We investigate bulk structural properties of tetravalent associating particles within the framework of classical density functional theory, building upon Wertheim's thermodynamic perturbation theory. To this end, we calculate density…
Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry…
In this article, we investigate the topological structure of large scale interacting systems on infinite graphs, by constructing a suitable cohomology which we call the uniform cohomology. The central idea for the construction is the…
Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent…
This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…
The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A…
In this combined experimental and simulation study, we utilize bond-order topology to quantitatively match particle volume fraction in mechanically uniformly compressed colloidal suspensions with temperature in atomistic simulations. The…
The monodromy of torus bundles associated to completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article we…
In this paper, we present a framework for multiscale topology optimization of fluid-flow devices. The objective is to minimize dissipated power, subject to a desired contact-area. The proposed strategy is to design optimal microstructures…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…