Additionally, based on some of the open data, alternate equations are derived for key variables in the annular flow descriptions, like liquid film thickness and wave celerity and frequency.
Conditional on a set of initial centroids, this minimization is iteratively realized by the following alternating equations C n ∗ = { θ ( k, l ) | n = argmin n D n ( k, l ) }, ∀ n, k, l, (16) v n ∗ ← E { θ ( k, l ) } θ ( k, l ) ∈ C n, ∀ n, (17).
We therefore subsequently used the alternate exponential equation.
To calculate an expected IAP from a given additional IAV, the alternate exponential equation V = v + k × Ln (P 0 − p) can be rearranged to P 0 = p + Exp (V − v /k.
Second, an alternate exponential equation, V = v + k × Ln (P 0 − p) where V represented additional IAV, P 0 represented resting IAP (no additional IAV), and v, k, p represent fitting parameters, was tested.
Fig. 3 Effect of the two alternate biomass equations as relative difference in stock (panel a, positive difference, panel b, negative).
For successful optimization, computational issues such as (i) alternating governing equations with respect to spatially defined design variables, (ii) imposing interaction boundary conditions between insulator (air) and conductor (solid) and (iii) control of minimum geometrical feature sizes must be addressed.
Yang et al. [18] recommended an alternate form of (Equation 1), when the specific energy input is stable and the volume of dispersion is constant: L = B t n (2).
At each time step, the calculations performed in DEM alternate between integrating equations of motion for each particle, and applying the force displacement law at each contact, through which the contact forces are updated based on the relative motions between two particles and their relevant contact stiffness.
In comparison with the Venegas equation, the alternate exponential equation produced a P-V curve that better fitted the measured values (lower root mean square) (Additional file 1: Figure S1 P-V curveS1 P-Vg Venegas and exponential equation, Additional file 2: Table S1—Equation parameters of intra-abdominal and airway pressure-volume curves).
