Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Differential in vitro pathogenicity of predatory fungi of the genus Monacrosporium for phytonematodes, free-living nematodes and parasitic nematodes of cattle

In vitro tests were carried out on the pathogenicity of nine isolates of the predatory fungi of the genus Monacrosporium (5 M. sinense isolates, 3 M. appendiculatum and 1 M. thaumasium isolate) for a phytonematode (second stage juveniles from Meloidogyne incognita, race 3), a free-living nematode (Panagrellus spp), and two gastrointestinal parasitic nematodes of cattle (infective larvae of Cooperia punctata and Haemonchus placei). A suspension containing 2,000 nematodes from each species was added to Petri dishes containing fungi and grown on 2% water-agar medium at 25oC in the dark for up to 7 days. The dishes were examined every other day for 7 days and predation-free nematodes were counted. The results showed that the free-living nematodes, Panagrellus spp, were the most susceptible (P<0.05), followed by the phytonematode M. incognita, while the controls were ³98.5% viable. However, a variable susceptibility of the nematodes to different fungi was observed. This indicates that the use of predatory fungi for the environmental control of nematodes will be limited by the multiplicity of nematodes in the environment and their differential susceptibility to fungal isolates of the same genus.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.