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Computing the 3D Radial Distribution Function from Particle Positions: An Advanced Analytic Approach.

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Calculating the radial distribution function, g(r), for finite particulate systems is challenging. This study introduces a simple analytic algorithm to accurately compute g(r) in finite samples, overcoming boundary limitations.

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Area of Science:

  • Materials Science
  • Statistical Mechanics
  • Computational Physics

Background:

  • The radial distribution function, g(r), is crucial for analyzing particulate system structures.
  • Experimentally derived particle data is limited to finite sample volumes, posing challenges for accurate g(r) computation.
  • Existing methods like artificial periodic boundary conditions can distort g(r) by ignoring sample finiteness.

Purpose of the Study:

  • To develop a simple, analytic algorithm for computing the radial distribution function, g(r), in finite samples.
  • To address the significant deviations in g(r) that occur when radial distances exceed sample boundaries.
  • To provide a method that requires no additional assumptions about the sample's properties.

Main Methods:

  • Developed an analytic algorithm for computing g(r) in finite sample volumes.
  • Utilized an analytic solution for the intersection volume between a spherical shell and the finite sample.
  • Identified a natural upper bound for radial distance based solely on sample size and shape.

Main Results:

  • Presented a novel, simple analytic algorithm for finite sample g(r) computation.
  • Demonstrated that the algorithm accurately accounts for sample boundaries without distortion.
  • Discovered a sample-size and shape-dependent upper bound for radial distance analysis.

Conclusions:

  • The new analytic approach accurately computes the radial distribution function, g(r), in finite samples.
  • This method overcomes limitations of existing algorithms by analytically handling boundary effects.
  • The approach is valuable for quantitative analysis of experimental tomography data from finite systems.