Density functional theory (DFT) for hard bodies provides a theoretical description of the effect of particle shape on inhomogeneous fluids. We present improvements of the DFT framework fundamental measure theory (FMT) for hard bodies and validate these improvements for hard spherocylinders. To keep the paper self-contained, we first discuss the recent advances in FMT for hard bodies that lead t...

As the graphical and mathematical representation of relationships among traffic flow, speed, and density, the fundamental diagram has been the foundation of traffic flow theory and transportation engineering. Underlying the fundamental diagram is the speed-density relationship which was originally documented in Greenshields’ seminal work and followed by a variety of equilibrium models over the ...

Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the famous (continuous/discrete) Fréchet distance. In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension under the discrete Fréchet distance. Given a ...

Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propaga...

The macroscopic fundamental diagram (MFD) provides a method to evaluate macro traffic operation through micro parameters, which can be applied control prevent congestion transfer and improve road network efficiency. However, due the large scale of urban as well complex temporal spatial distribution congestion, application MFD for signal first requires partition network. Based on analysis purpos...

In design and analysis, standard references assume the pedestrian flow as unidirectional. In reality however, pedestrian flow is usually bi-directional. The main question pursued in this paper is that whether the main characteristics of pedestrian flow the same under uni- and bi-directional conditions. In order to achieve this goal, effect of bi-directional stream is inv...