Oscillation Model different zones

Fig. 39. Periodic oscillations in pore-water NH/ concentrations predicted for the bio-turbated zone by the one-dimensional model Eq. (6.15). The profiles represent A of a year separation and corresponding months are indicated. The different temperature dependence of D, and R as illustrated in Fig. 38 produces the oscillations. Three maximum values of De were assumed 1 x 10 (dashed line), 2 x 10 (solid), and 6 x 10 cm /sec (dotted).

The application of this method requires knowledge of the explicit form of at least one of the two funetions (F(/)F(0)> or y t), in order to find a solution of the equation. Variants of the approaeh, developed up to the present time are based on different ways of modeling of the dissipation term y(t), conneeted with the secondary zone of atoms [ 18-20]. Adelman and Garrison use Debye s model for phonons of the solid and obtain an equation for the dissipation term whieh, ean be solved numerically. Doll and Dion propose y t) as a linear combination of conveniently chosen functions, where the coefficients are determined by numerieal self-consistency. Another possibility is to model the microscopic interactions in the lattice of the solid in order to derive a dissipation term. Tully presents the friction as a white noise or positionally autocorrelated function of a Brownian oscillator, including both oscillation and dissipation terms. 

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