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Updated: Jun 1, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Time-dependent correlations in a supercooled liquid from nonlinear fluctuating hydrodynamics
Bhaskar Sen Gupta1, Shankar P Das, Jean-Louis Barrat
1School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India.
Summary
Nonlinear fluctuating hydrodynamics (NFH) simulations reveal how density fluctuations cause slow dynamics in supercooled liquids. The 1/ρ nonlinearity is key to restoring ergodic behavior, with simulations yielding a lower transition temperature than theory predicts.
Area of Science:
- Condensed Matter Physics
- Computational Physics
- Materials Science
Background:
- Supercooled liquids exhibit slow dynamics, a phenomenon crucial for understanding the glass transition.
- Mode coupling theory (MCT) provides a framework for studying these dynamics, predicting an ergodic-nonergodic transition.
- Numerical solutions of nonlinear fluctuating hydrodynamics (NFH) offer a direct approach to investigate these complex behaviors.
Purpose of the Study:
- To numerically solve NFH equations and validate them against molecular dynamics simulations.
- To investigate the role of density fluctuations and the 1/ρ nonlinearity in supercooled liquid dynamics.
- To determine the ergodic-nonergodic transition temperature T(c) from direct NFH solutions.
Main Methods:
- Numerical solution of nonlinear fluctuating hydrodynamics (NFH) equations with coarse-graining to prevent instabilities.
- Analysis of equilibrium correlation functions and relaxation dynamics.
- Comparison of NFH results with molecular dynamics (MD) simulations and predictions from mode coupling theory.
Main Results:
- NFH simulations quantitatively agree with molecular dynamics data for density fluctuation correlations.
- Strongly coupled density fluctuations are shown to drive slow dynamics, with the 1/ρ nonlinearity essential for ergodicity.
- Relaxation time data exhibit time-temperature superposition at moderate supercooling and stretched behavior at higher supercooling.
Conclusions:
- Direct NFH solutions provide a more accurate T(c) than low-order MCT integral equations, aligning with simulation trends.
- The 1/ρ nonlinearity in NFH is critical for capturing the ergodic behavior of supercooled liquids.
- NFH offers a robust numerical tool for studying the complex dynamics of supercooled states.
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