This note revisits a paper from Velan and Florian [Velan and Florian(2002)] dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for non-differentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. Notably, this note clearly exhibits that the non-smoothness of the fundamental d...

A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed measure theory and freely minimized numerically for hard discorectangles. The phase diagram, which involves stable isotropic, nematic, smectic, and crystalli...

A band diagram is the fundamental for investigation of the electromagnetic properties of periodic structures such as photonic crystals in optics or electromagnetic band gap structures in antenna engineering. In this paper, the two famous computational methods, finite difference frequency domain (FDFD) and finite difference time domain (FDTD) methods are applied for band diagram calculation of 2...

In this paper we discuss a four-dimensional autonomous circuit which includes one hysteresis element. This circuit is governed by two symmetric three dimensional linear equat ions which are connected to each other by hysteresis switchings. Then we can derive the two-dimensional return map and show the following novel results: 1) Fundamental bifurcation diagram from periodic attractor to hyperch...

This paper concerns the behavior of an SINR diagram of wireless systems, composed of a set S of n stations embedded in R, when restricted to the corresponding Voronoi diagram imposed on S. The diagram obtained by restricting the SINR zones to their corresponding Voronoi cells is referred to hereafter as an SINR+Voronoi diagram. The study of SINR+Voronoi diagrams is motivated by the following tw...

We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars moving in opposite directions along a narrow road. Our main results concern the Fundamental diagram of the system describing the dependence of average particl...

M. Khovanov and L. Rozansky gave a categorification of the HOMFLY-PT polynomial. This study is a generalization of the Khovanov-Rozansky homology. We define a homology associated to the quantum (sln,∧Vn) link invariant, where ∧Vn is the set of the fundamental representations of the quantum group of sln. In the case of a [1, k]-colored link diagram, we prove that its homology is a link invariant...

Given a protein, analyzing the geometric structure of protein is fundamental for the study of a protein folding, docking, interactions between proteins, and so on. One of the important geometric analyses is computing the molecular surface of protein. Discussed in this paper is an efficient algorithm to compute such a molecular surface of protein via the concept of blending operation among atoms...

Using Monte Carlo simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbor finite repulsive interaction. The model presents two competing ranges of interaction and, in common with many experimental systems, exhibits a low density solid phase, which melts back to the flui...

Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voro...