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Fractal dimensions of aggregates from the paddle mixer and oscillating grid, calculated using cumulative size spectra and assuming pseudo-steady-state conditions, were typical of aggregates formed by reaction-limited conditions or those compacted by aggregate reformation (D=2.2±0.2).
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To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65], [66], [67] generalised to linear order.
Grid was calculated using an in-house modified version of AutoGrid 4.2.2.1 using a 256×256×256 grid with step of 0.5 Å (1 Å = 0.1 nm) enclosing the whole Top1.
The number of points within the G D × G D grid is calculated using the heuristic equation, {N}_{mathrm{grid}}=leftlfloor 2+frac{60}{1+{left R-{z}^{hboxright)}^{0.8}}+0.5rightrfloor, (8 where ⌊⋅⌋ denotes truncation to the nearest lower integer.
The actual width of hydraulic fracture is assumed to be 5 mm; thus, in our numerical model, the effective permeability for HF grids is calculated using the equation: k eff = k F W F/W grid = 20md (Rubin 2010).
Grids were calculated using a 0.375 Å spacing in a 126 Å cube.
The forces on the coarse-grained beads from the grid potentials were calculated using the grid forces feature of NAMD2.
The setup for the rest of the grid hierarchy is calculated using a geometric sequence for grid spacing.
Given the estimated NPPC4 for all parcels of a grid cell, the extensive margin for that grid can be calculated using the following relationship: ETA = A m 1 NPP m 1 C 4 + A m 2 NPP m 2 C 4 + … + A mn NPP mn C 4 A m 1 + A m 2 + … + A mn A c 1 NPP c 1 C 4 + A c 2 NPP c 2 C 4 + … + A cn NPP cn C 4 A c 1 + A c 2 + … + A cn (1).
The ratio λ j for the jth grid point is calculated using all earthquakes within 220 km of the grid point: Fig. 7 Spatial distribution of the ratio of the averaged interplate slip to the sum of averaged interplate and intraplate slip.
Kernels of progressively smaller sizes relative to the landscape grid size were calculated using cell-integration and cell-center methods.
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