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Related Experiment Video

Updated: Mar 6, 2026

Optimization of the Ugi Reaction Using Parallel Synthesis and Automated Liquid Handling

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Published on: November 11, 2008

Method to manage integration error in the Green-Kubo method.

Laura de Sousa Oliveira¹, P Alex Greaney¹

¹Mechanical Engineering Department, University of California, Riverside, California, USA.

Physical Review. E

|March 17, 2017

Summary

This study introduces a method to quantify uncertainty in Green-Kubo transport property predictions. It addresses noise in autocorrelation functions, enabling optimized calculations for reduced uncertainty and efficient resource allocation.

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Area of Science:

Computational physics
Materials science
Statistical mechanics

Background:

The Green-Kubo method predicts transport properties using equilibrium molecular dynamics.
It relies on the fluctuation dissipation theorem, linking properties to thermodynamic potential fluctuations.
Lattice thermal conductivity calculations integrate heat flux autocorrelation, but noise poses a significant error source.

Purpose of the Study:

To develop a method for quantifying uncertainty in Green-Kubo transport property calculations.
To address the issue of noise in the tail of autocorrelation functions.
To optimize integration conditions for minimizing uncertainty within computational resource constraints.

Main Methods:

Utilizing the Green-Kubo formulation for transport property prediction.
Analyzing the autocorrelation function of the instantaneous heat flux.
Characterizing integrated noise as a random walk with a growing uncertainty envelope.

Main Results:

A novel method to quantify uncertainty in Green-Kubo predictions is presented.
The integrated noise in autocorrelation functions is identified as a random walk.
The approach allows for informed choices in integration conditions to balance errors.

Conclusions:

The developed method quantifies uncertainty in Green-Kubo calculations.
Understanding noise as a random walk aids in optimizing calculations.
This facilitates minimizing uncertainty for transport properties with efficient computational resource usage.