A method for computing the three-dimensional radial distribution function of cloud particles from holographic images

Abstract

Abstract. Reliable measurements of the three-dimensional radial distribution function for cloud droplets are desired to help characterize microphysical processes that depend on local drop environment. Existing numerical techniques to estimate this three-dimensional radial distribution function are not well suited to in situ or laboratory data gathered from a finite experimental domain. This paper introduces and tests a new method designed to reliably estimate the three-dimensional radial distribution function in contexts in which (i) physical considerations prohibit the use of periodic boundary conditions and (ii) particle positions are measured inside a convex volume that may have a large aspect ratio. The method is then utilized to measure the three-dimensional radial distribution function from laboratory data taken in a cloud chamber from the Holographic Detector for Clouds (HOLODEC).

Particle radial distribution function and relative velocity measurement in turbulence at small particle-pair separations

“…A recent study by Larsen and Shaw (2018) discussed the boundary treatment for RDF in depth, outlining two methods suitable for RDF experiments: the guard area approach, which allows the user to define the volume within a distance δx from the boundary edges wherein particles may only be considered as satellites for pairing, and their new effective volume approach, which accounts for the edgeeffects of primary particles near the volume boundary and does not exclude these particles. The former is computationally inexpensive but loses data, while the latter retains data for statistical convergence but is computationally expensive when used at high resolution.…”

Application of the Spatial Distribution Function to Colloidal Ordering

“…Both have limitations, either through the introduction of incorrect assumptions and artifacts or the loss of valuable data. Recent studies suggested bypassing these methods by calculating the effective volume (3D) or area (2D) over which the particles are being counted. , A process inspired by this technique was implemented herein through tracking the area covered by the shifted array to normalize the SDF.…”

Active cell divisions generate fourfold orientationally ordered phase in living tissue

“…All the pairs of cells whose separation lay between r and r + dr, and whose relative orientation lay along the appropriate axes in the case of g AP (r) and g DV (r), were consolidated into histograms within a set of bins (of width dr) segmenting the intercellular spacing. The histograms were then normalized using an 'effective volume method' that directly accounts for and ameliorates finite size effects 55 . In the following explanation, we focus on the radially symmetric pair correlation function g(r) for simplicity.…”