A multigrid Waveform Relaxation Method for solving the Pennes bioheat equation Cosmo D. Santiago, Gylles R. Ströher, Marcio A. V. Pinto, and Sebastião R. Franco Informa UK Limited Abstract This work proposes a multigrid Waveform Relaxation Method (WRMG) that uses the finite difference method for the discretization to solve Pennes’ bioheat equation. There is no evidence in the literature of using the WRMG to solve this equation. The proposed algorithm is based on the red-black Gauss-Seidel smoother in space and the line Gauss-Seidel smoother in time. Verification of code is presented. The performance analysis of the multigrid method confirms the convergence and efficiency of the algorithm. The method, which favors parallel architecture, is tested in two-dimensional numerical experiments on an academic problem and for the thermal analysis of human skin.
Generalization of the integral and differential method for analysis of rate data by means of the fractional calculus Gylles Ricardo Ströher and Gisely Luzia Ströher Wiley AbstractThe kinetic study of chemical reactions is usually carried out by means of analysis of experimental rate data obtained during the evolution of a reaction in a batch reactor. The methods for analysis of rate data obtained in a batch reactor include the classical integral methods (CIM) and classical differential methods (CDM), which use temporal derivatives of the unit‐order concentration, dCA/dt, in the mass balance equation. The present study proposes these two methods of analysis in a generalized formulation that makes use of non‐integer order temporal derivatives, dαCA/dtα, 0<α ≤ 1, called generalized integral method (GIM) and generalized differential method (GDM) in the present work. The solutions of the fractional ordinary differential equations (FODE) of GIM are presented using the Laplace transform technique and numerical fractional derivative evaluation methods for GDM application. The proposed generalized methods allow for the determination of the order and the specific reaction rate in the same way as the classical methods, that is, of integer order (α = 1); however, generalized methods have the additional advantage of determining the fractional order of the temporal derivative.
Numerical two-dimensional thermal analysis of the human skin using the multigrid method Gylles Ricardo Stroher and Cosmo Damião Santiago Universidade Estadual de Maringa Heat can be used as an adjuvant treatment of many diseases and also as a powerful tool to help diagnose cancers, with the advantage to be a noninvasive exam. Some tumors may be best diagnosed by evaluating body temperature distribution, for instance, it is observed that local temperatures of the skin over a tumor are higher than the average skin temperature. Certainly, it is expected from medical diagnostics to be, early, fast and very precise. Especially if the health problem is a tumor, it is necessary to know the shape and the size of the cancer. Thermal images can provide further information about the tumor, generally, the thermal diagnostic is made comparing images of the region with a bioheat model. In this context, the present study shows interesting results about the multigrid method applied to solve the Pennes bioheat equation in two dimensions, using a non-stationary and steady state cases for the skin heath and with melanoma. The multigrid method presented itself as an extremely efficient and fast tool to solve the bioheat equation with refined grids that provide good spatial precision.
Explaining trans geometric isomerism through a board game with a focus on food and trans fat
Application of multivariate analysis to assess the incorporation of Omega-3 fatty acid in gluten-free cakes Aline K. Gohara, Aloisio H. P. Souza, Eliza M. Rotta, Gisely L. Stroher, Sandra T. M. Gomes, Jesui V. Visentainer, Nilson E. Souza, and Makoto Matsushita Sociedade Brasileira de Quimica (SBQ) A complete 22 experimental planning (two factors at two levels) with central point in quintuplicate was used to investigate the influence of the factors: chia and azuki flours on fatty acids composition of gluten-free chocolate cake. Both factors were significant, but chia flour presented greater influence on the results. Increased values of both factors contributed to improve contents of polyunsaturated fatty acids (380.96 g kg-1 of product), mainly n-3 series (70.25 g kg-1 of product), and provided more adequate nutritional indices. The principal component analysis and desirability function indicated the sample with higher level of both factors as the optimal region. This sample showed an increase in contents of alpha-linolenic acid (188.03%) and polyunsaturated fatty acids (18.16%) when compared to control formulation. The addition of chia flour can improve nutritional characteristics of food stuffs such as bakery products, especially their lipid composition.
Chemometric methods applied to the mineral content increase in chocolate cakes containing chia and azuki Aline K. Gohara, Aloisio H. P. Souza, Ângela C. Rodrigues, Gisely L. Stroher, Sandra T. M. Gomes, Nilson E. Souza, Jesuí V. Visentainer, and Makoto Matsushita Sociedade Brasileira de Quimica (SBQ) A 22 full factorial design (two factors at two levels) with duplicate was performed to investigate the influence of the percentages of chia and azuki (the two factors) added to gluten-free chocolate cake on the mineral contents (Ca, Cu, Fe, K, Mg , Mn and Zn). In the study, partially defatted chia flour and wholemeal azuki flour were used. The percentage factors of chia and azuki were significant and the increases in these values contributed positively to the responses. The interaction effect was not significant for the Ca, Fe, Mg and Zn responses. The principal component analysis (PCA) distinguished samples with higher content of chia by means of PC1, and PC2 separated the formulations with the highest levels of azuki from the ones with the lowest levels. Using analysis of variance (ANOVA) and response surface analyses, it was possible to conclude that the increase in mineral content was higher with the addition of 20% of both flours.