This work concerns the development and calibration of several classes of mathematical models describing ecological and bio-geochemical aspects of aquatic systems. We focus our experimental analysis on the Serra da Mesa lake in Brazil, from which the biological information is extracted by real online measurements provided by the SIMA monitoring program of the Brazilian Institute for Space Research (INPE).
A preliminary analysis is carried out so as to define the input-output data to be accounted for by the models. Furthermore, several classes of mathematical models are considered for fitting real data of biological processes. In order to do that, a two-step parameter identification/validation procedure is applied: the first step uses the integrals of the differential equations to reduce the nonlinear estimation problem to a linear least squares one. The parameter vector resulting from the first step is used for initializing a nonlinear minimization procedure. The results are discussed to assess the fitting performances of the physical and black-box models proposed in the paper. Several simulations are presented that could be used for developing scenario analysis and managing the real system
We address the problem of parametrizing the boundary data for reactiondiffusion partial differential equations associated to distributed systems that possess rough boundaries. The boundaries are modeled as fast oscillating periodic structures and are endowed with Neumann or Dirichlet boundary conditions. Using techniques from homogenization theory and multiple-scale analysis we derive the effective equation and boundary conditions that are satisfied by the homogenized solution. We present numerical simulations that validate our theoretical results and compare it with the alternative approach based on solving the same equation with a smoothed version of the boundary. The numerical tests show the accuracy of the homogenized solution to the effective system vis a vis the numerical solution of the original differential equation. The homogenized solution is shown undergoing dynamical regime shifts, such as anticipation of pattern formation, obtained by varying the diffusion coefficient.
We address the problem of parametrizing the boundary data for reaction-diffusion partial differential equations associated to distributed systems that possess rough boundaries. Using techniques from homogenization theory and multiplescale analysis we present the effective equation and boundary conditions that are satisfied by the homogenized solution. We present numerical simulations that validate our theoretical results.
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