A Data Bottleneck
Studying glassy systems requires capturing dynamics across many orders of magnitude in time. To understand both fast and slow processes, we'd ideally record at high temporal resolution. However, doing so over the enormous timescales where glasses are dynamically interesting creates a storage bottleneck.
Why not linear dumping?
- Linearly-spaced dumps at high resolution generate impractical amounts of data
- Low-resolution linear dumps miss fast dynamics entirely
- Example (low temperature): Capturing 8 decades of time (100 to 108 timesteps) at high resolution would require ~108 frames. With 100,000 particles at ~12 bytes/particle/frame, that's ~120 TB per run. For 5 independent runs (statistical significance), you'd need ~600 TB of storage, and that's just for one temperature!
The Geometric Solution
Geometric spacing (tn = t0 · rn) solves this by providing:
- High density at short times → captures fast dynamics
- Lower density at long times → captures slow dynamics efficiently
- Uniform coverage on a log-time axis
- Typically ~9,000 dumps to span 8 decades with repeated sequences
- Example (low temperature): Using ~9,000 dumps: 9,000 × 1.2 MB ≈ 11 GB per run, or ~55 GB for 5 runs. That's about 11,000× less storage than linear dumping!
Repeated Geometric Sequence Approach
For typical analysis of equilibrated systems, we use repeated short geometric sequences. This preserves time-translation invariance (TTI) in two-time correlation measurements, allowing us to select short or long lag times (τ) without being restricted to fixed high temporal resolution.
For studying aging effects, we add a long geometric sequence during the equilibration/aging period to capture the system's evolution.
About This Tool
This tool was created by Max Meinke and adabted for the web by Collin. It generates utility files (dump_times.txt, run_times.txt, file_names.txt) to be looped over in LAMMPS for saving trajectory data following this geometric dump schedule.
Preserving Time-Translation Invariance
In equilibrated (quasi-stationary) systems, correlation functions depend only on the lag time:
$$C(t, t + \tau) = C(\tau)$$
This is time-translation invariance (TTI). With the approach of repeating the geometric sequences at linear intervals, if a sequence starts at time $t$, the next identical sequence begins at $t + \Delta$, where $\Delta$ is the fixed sequence duration:
$$t_{\text{start}}^{(k)} = t_{\text{equil}} + k \cdot \Delta$$
This linear repetition preserves TTI: within each sequence, we can compute correlation functions at various lag times τ from the geometrically-spaced dumps, and average across sequences:
$$C(\tau) = \langle A(t) A(t + \tau) \rangle$$
The Geometric Spacing
Within each sequence, dumps are placed at times $t_n = t_0 \cdot r^n$, giving uniform spacing on a logarithmic axis:
$$\log(t_n) = \log(t_0) + n\log(r)$$
This efficiently samples relaxation processes that span many decades, allowing us to measure both short and long lag times τ.
Capturing Aging Dynamics
During aging, TTI is broken. Correlations non-negligibly depend on the waiting time $t_w$ in addition to the lag time $\tau$:
$$C(t_w, t_w + \tau) \neq C(\tau)$$
The long geometric sequence captures this non-equilibrium regime, recording the system's evolution during equilibration.