Related Experiment Video
Updated: Jul 5, 2025

High-speed Particle Image Velocimetry Near Surfaces
Published on: June 24, 2013
Pair correlation function based on Voronoi topology
Vasco M Worlitzer1, Gil Ariel1, Emanuel A Lazar1
1Department of Mathematics, Bar Ilan University, Ramat Gan 5290002, Israel.
Abstract:
The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability for simulated and experimental data. However, as an averaged quantity, the PCF can fail to capture subtle structural differences in particle arrangements, even when those differences can have a major impact on system properties. Here, we use Voronoi topology to introduce a discrete version of the PCF that highlights local interparticle topological configurations. The advantages of the Voronoi PCF are demonstrated in several examples including crystalline, hyperuniform, and active systems showing clustering and giant number fluctuations.
Related Concept Videos
Coordination Number and Geometry
Dot Product
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...
Correlation
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Coefficient of Correlation
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
Vector Algebra: Graphical Method
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Area Computation by the Alternative Coordinate Method

