Unexpected SDF Expansion Coefficient Reduction During Proportional Scaling: Implications for Pressure Calculation

[aidexs]

Hi,
I encountered a strange phenomenon when calculating pressure using the SDF. When I scaled up both the particles and the box proportionally while keeping the particle shape and quantity constant, the SDF expansion coefficient decreased. However, isn't SDF a probability density function? Why does it change when the density remains unchanged? Does this imply a change in the system's pressure? Is this behavior expected? What could be causing it?

[joaander]

$$\beta P = \rho \left(1 + \frac{s_{\mathrm{comp}}(0+) - s_{\mathrm{exp}}(0-)}{2d} \right)$$

Note that $\beta P$ has units of $[\mathrm{length}]^{-d}$. Normalize it appropriately by multiplying by some representative $l^{d}$ in your system, then $\beta P l^{d}$ must theoretically remain constant under any scaling transformation.

In practice, the measurement of the SDF is very noisy. It requires a lot of averaging to obtain good results and you should always make statistically meaningful comparisons using the standard error of the mean from many replicate simulations. In your case, you don't mention also scaling xmax and dx appropriately. Making these two parameters effectively smaller should not lead to incorrect results, but may significantly increase the error bars on the sampling. Making these parameters effectively larger will lead to systematic errors in the estimation of the SDF at x=0. To make a completely identical simulation, you should also scale your translation trial move size accordingly. Using too small or too large a trial move size will reduce the number of independent samples you achieve for a simulation with a fixed number of steps - increasing the standard error of your measurement.

[aidexs]

You're right about the issue with the translation trial move size. I increased the particle area by a factor of 6, but the failure to adjust the translation trial move size correspondingly led to an error of approximately 4%. Once I increased the translation trial move size, the problem was resolved. Incidentally, there seems to be an inconsistency in the pressure formula within the SDF interface of HOOMD-Blue. One version uses addition for the expansion term while the other uses subtraction.

[joaander]

Fixed in #2101.