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In contrast, analytical tools provide required simplicity while capturing the events occurring at smaller time scales, which are ordinarily sacrificed in numerical simulations to keep the run time reasonable.
The pore-fluid inside the cracks and the pores of host matrix may interact and exchange fluid mass, but the difference in hydraulic properties of these pores often means that a single homogenized effective permeability tensor field is insufficient to characterize the evolving hydraulic properties of these materials at smaller time scale.
Dynamic The characteristics of changes among component lineages or at smaller time scales that underlie a large-scale trend.
Simulations at smaller time steps with 0.5 and 0.2 ms were also performed for extreme conditions (the high end values of gc = 1000 pS and gc = 500 pS), and randomly chosen cases through out our parameter spectrum, to ensure this choice of time step.
In addition, monitoring generally applied exposure metrics of daily or hourly values and therefore has been unable to illuminate heterogeneity in exposure at smaller time scales.
This apparent increase to MSD makes a larger difference at smaller time lags, as the storage and loss modulus are dependent on the slope of the MSD on a log-log scale (Fig. 4 ).
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We observe that the linear relation at large times becomes quadratic at smaller times.
This means that diffusion occurs after sufficient time has elapsed so that scattering events become significant, while at smaller times the motion is essentially ballistic.
Some traces, however, do exhibit moderately large scaling exponents (≈0.7) at small time scales.
In addition, the traces manifest mostly monofractal behaviors at small time scales.
We show from our studies that the rate of adsorption is controlled by diffusion at small time scales.
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