Enhancing efficient computation of long-wavelength relaxation dynamics in a 2D liquid involving millions of particles

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<jats:title>Abstract</jats:title> <jats:p>Recently, a two-dimensional liquid cooled toward the glass transition was found to exhibit a <jats:italic>t</jats:italic> <jats:sup>−1</jats:sup> long-time tail in the velocity autocorrelation function (VACF) owing to the presence of long-wavelength fluctuations. To directly observe this power-law behaviour, it is necessary to simulate a large system with millions of particles, which is a challenging task from the computational viewpoint. In this study, to address this difficulty, I first show that this power-law tail can be reproduced by differentiating the finite-time diffusivity with respect to time. In addition, the feasibility of another direction, a direct on-the-fly computation of the VACFs utilizing GPGPUs, wherein VACFs are evaluated as the simulation runs, is also demonstrated. A performance benchmark was executed on Wisteria/BDEC-01 (Aquarius subsystem) supercomputer using a simulation code developed by the author, which enabled the direct computation of the VACF of 4 million particlesx for as long as the 10<jats:sup>8</jats:sup> simulation steps within 10 days.</jats:p>

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