Some kind of pollutant, particularly hydrocarbon, can be removed from the polluted subsoil by means of micro organism activity.
Oxygen is required during the biodegradation process and therefore air is injected in the subsoil.
A multiphase and multicomponent mathematical model describing the biodegradation process in a unsaturated porous media will be presented.
The movement of the different fluids in the porous media and the dynamic of the bacteria population will be described.
A matrix formulation a the DFT of complex even and complex odd sequences will be presented and, respectively, for each one of the two type of sequences a cosine and a sine based matrix will be used.
Recursive expressions for the two matrices will be obtained and it will be shown that the recursive terms involves only both the same cosine and sine matrices, of halved dimension.
The structure of the algorithm is suitable for parallel hardware implementation.
discrete Fourier transform
FFT even sequences
FFT odd sequences
A quasiharmonic field is a pair $\Cal{F} = [B,E]$ of vector fields verifying $div B=0$, $curl E=0$, and coupled by a distorsion inequality. For a given $\Cal {F}$, we construct a matrix field $\Cal{A}=\Cal{A}[B,E]$ such that $\Cal{A} E=B$. This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator $\Cal {A}[B,E]$ and find applications of them to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
