The control methods developed are illustrated with simple examples using two-dimensional dispersion models.
The one-dimensional dispersion model successfully predicts the tracer concentration profile and the longitudinal dispersion coefficient.
The transport model considers advection, retardation, three-dimensional dispersion, and sequential first-order decay/production of several species.
Solid distribution along the column axis was well explained by one-dimensional dispersion model.
A further confirmation of the effective in-plane mechanical anisotropy on the GNRs is apparent also from the non-dimensional dispersion curves shown in Figure 4.
The energy dissipated by the material is analyzed to avoid the problems associated with the three-dimensional dispersion and randomness of fatigue cracking.
A unit cell with double-C perforations is selected as a test article suitable to investigate two-dimensional dispersion characteristics, group velocities, and internal resonances.
The three-dimensional dispersion process occurs as grains are transported and mixed with bed sediment, driven by the interactions between the flow, bed, and transport fields.
However, while the first non-dimensional dispersion curve is identical, the following dispersion characteristics show a marked difference between zigzag and armchair configurations, with the zigzag GNRs having the highest ω/ω 0 values.
The one-dimensional dispersion model has been solved analytically as well as numerically to describe flow in continuous "closed" boundary systems using the celebrated Danckwerts boundary conditions.
Two-dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of re-entrant configurations and investigate the directional behavior of hexagonal lattices for varying construction angles.
