The wave solution propagating with (against) the main flow is represented by a solid (dotted) line.
One of the solutions to this problem would be to apply leaching solutions with various ionic strengths immediately after a bacterial pulse since the input of lower ionic strength will generate various situations in the interaction energy between bacteria and particle surfaces as leaching solutions propagate down the column system.
However, these results indicate that for the same number of modes, the finite element solution propagates faster than the eigenfunction solution.
It is based on the derivation of a matrix relation which determines how an arbitrary but small perturbation at the beginning of a periodic solution propagates to the end of a response period.
The proposed solution propagates not only the partial derivatives, as usual in automatic differentiation, but also the input uncertainties, so to make their various modifications visible to the user of the evaluation system, and give him the opportunity to analyze the partial contributions to the standard uncertainty of the output measurands.
computes the new value at,, and, ; thus information for the solution propagates from left to right.
At a particular parameter range, a solution propagating against the main flow is also destabilized.
computes the new value at, and,, thus information for the solution propagates from both sides.
where computes the new value at,, and, ; thus information for the solution propagates from right to left.
Figures 3 and 5, show that the solution propagates and diffuses with time, which means that the solution continuously depends on the fractional derivatives.
