A381701 Decimal expansion of the universal aspect ratio, also called the magic box length ratio, L_z/L_x = L_z/L_y, for which the finite-size error of the self-diffusion coefficient vanishes.

2, 7, 9, 3, 3, 5, 9, 6, 4, 9

Offset: 1

Author

Alex Eduardo Delhumeau, Mar 04 2025

Keywords

• nonn
• cons
• more

Comments

Derived by Kikugawa et al. (2015) for a rod-shaped rectangular box (box with lengths L_x = L_y <= L_z) with periodic boundary conditions. The self-diffusion coefficient in the x (and y) direction of a monoatomic Lennard-Jones fluid, calculated from molecular dynamics simulation using the Einstein-Helfand formula, D_xx ( = D_yy), becomes system-size independent and represents the true self-diffusion coefficient, D_0.

Based on the expression for the finite-size correction to the self-diffusion coefficient derived from hydrodynamic theory by B. Dünweg and K. Kremer (1993) and greatly popularized by I.-C. Yeh and G. Hummer (2004). Computed to nine decimal places by J. Busch and D. Paschek (2023).

Examples

			2.793359649...
		

Links

• J. Busch and D. Paschek, OrthoBoXY: A Simple Way to Compute True Self-Diffusion Coefficients from MD Simulations with Periodic Boundary Conditions without Prior Knowledge of the Viscosity. J. Phys. Chem. B 127 (2023), 7983-7987.
• B. Dünweg and K. Kremer, Molecular dynamics simulation of a polymer chain in solution. J. Chem. Phys. 99 (1993), 6983-6997.
• G. Kikugawa, T. Nakano, and T. Ohara, Hydrodynamic consideration of the finite size effect on the self-diffusion coefficient in a periodic rectangular parallelipiped system. J. Chem. Phys. 143 (2015), 024507.
• I.-C. Yeh and G. Hummer, System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions. J. Phys. Chem. B 108 (2004), 15873-15879.

Crossrefs

Cf. A185576.