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 ethane. We also present a comparison of the crossover model equation with the experimental data....

The diameter of a set S of points is the maximal distance between a pair of points in S. The center of S is the set of points that minimize the distance to their furthest neighbours. The problem of nding the diameter and center of a simple polygon with n vertices for diierent distance measures has been studied extensively in recent years. There are algorithms that run in linear time if the geod...

Precise calculations of the coexistence-curve diameters of a hard-core square-well (HCSW) fluid and the restricted primitive model (RPM) electrolyte exhibit marked deviations from rectilinear behavior. The HCSW diameter displays a |t| singularity that sets in sharply for |t| ≡ |T −Tc|/Tc . 10; this compares favorably with extensive data for SF6, also reflected in C2H6, N2, etc. By contrast, the...

Many problems in computational geometry are not stated in graphtheoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm depends on the special properties of the graph constructed in this way. We survey the art gallery problem, partition into rectangles, minimum-diameter clustering, ...

Given a set of obstacles and two distinguished points in the plane the problem of nding a collision free path subject to a certain optimization function is a fundamental problem that arises in many elds, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinea...

We present eecient algorithms for nding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. Our results improve the time complexity of previous results for nding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For nding the shortest rectilinear...