the thermodynamic properties of fluids can be predicted using the global equations of state. among these thermodynamic properties of fluids, we choose the densities of the liquid and vapor phases. this paper considers the application of the crossover model to the vapor-liquid rectilinear diameter of sulfurhexafluoride. we also present a comparison of the crossover model equation with the experi...

We propose a novel model of street network connectivity which uses method from the field applied topology called “persistent homology”. The output this is pair density functions relative strength and frequency connected components cycles in network. In context, function type, such as motorway or residential, with more significant types providing greater connectivity. are easily interpreted prov...

It is proved that any rectilinear polygon on n vertices, possibly with holes, can be partitioned into at most n 4 rectilinear stars each of size at most 12.

A pseudolinear (respectively, rectilinear) drawing of a graph G is optimal if it has the smallest number of crossings among all pseudolinear (respectively, rectilinear) drawings of G. We show that the convex hull of every optimal pseudolinear drawing of the complete graph Kn is a triangle. This is closely related to the recently announced result that the convex hull of every optimal rectilinear...

The stationary isotropic Poisson line network was used to derive upper bounds on mean excess network-geodesic length in Aldous and Kendall (2008). This new paper presents a study of the geometry and fluctuations of near-geodesics in such a network. The notion of a “Poissonian city” is introduced, in which connections between pairs of nodes are made using simple “no-overshoot” paths based on the...

In order to apply advanced high-level concepts for transportation networks, like hypergraphs, multi-level wayfinding and traffic forecasting, to commercially available street network datasets, it is often necessary to generalise from network primitives. However, the appropriate method of generalisation strongly depends on the complex street network feature they belong to. In this paper, we deve...

The paper introduces a shape measure intended to describe the extent to which a closed polygon is rectilinear. Other than somewhat obvious measures of rectilinearity (e.g. the sum of the differences of each corner’s angle from 90◦) there has been little work in deriving a measure that is straightforward to compute, is invarient under scale and translation, and corresponds with the intuitive not...