Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Metabolic profiling and classification of propolis samples from Southern Brazil: an NMR-based platform coupled with machine learning

The chemical composition of propolis is affected by environmental factors and harvest season, making it difficult to standardize its extracts for medicinal usage. By detecting a typical chemical profile associated with propolis from a specific production region or season, certain types of propolis may be used to obtain a specific pharmacological activity. In this study, propolis from three agroecological regions (plain, plateau, and highlands) from southern Brazil, collected over the four seasons of 2010, were investigated through a novel NMR-based metabolomics data analysis workflow. Chemometrics and machine learning algorithms (PLS-DA and RF), including methods to estimate variable importance in classification, were used in this study. The machine learning and feature selection methods permitted construction of models for propolis sample classification with high accuracy (>75%, reaching 90% in the best case), better discriminating samples regarding their collection seasons comparatively to the harvest regions. PLS-DA and RF allowed the identification of biomarkers for sample discrimination, expanding the set of discriminating features and adding relevant information for the identification of the class-determining metabolites. The NMR-based metabolomics analytical platform, coupled to bioinformatic tools, allowed characterization and classification of Brazilian propolis samples regarding the metabolite signature of important compounds, i.e., chemical fingerprint, harvest seasons, and production regions.

Separation by thermal diffusion in a rotary column

A rotary thermal diffusion column with the inner cylinder rotating and the outer cylinder static was used to separate n-heptane-benzene mixtures at different speeds of rotation. The results show that the column efficiency depends on the speed of rotation. For the optimum speed the increase in efficiency relative to the static column was of the order of 8%. The role of the geometric irregularities in the annulus width on performance of the rotary column is also discussed.

Nonsymmetrical separations in thermal diffusion columns

The influence of the feed composition upon the actual degrees of separation attained at the top and bottom sections of a thermogravitational column is discussed using the classical phenomenological theory of Furry, Jones, and Onsager. It is shown that, except for a feed composition of C 0 = 0.5 (mass fraction), the separation profile is nonsymmetric, i.e., the separations in the top and bottom sections of the column are nonsymmetric with respect to the feed composition, the asymmetry increasing as the feed composition moves away from C 0 = 0.5. An equation for the determination of the optimum feed location as a function of the feed composition is derived.

Some observations on asymmetrical separation in thermal diffusion columns

Data have been obtained in steady-state batch operated thermogravitational separation columns using different binary mixtures to test the theory recently published by Morgado et al. The experimental results confirm that separations by thermal diffusion are asymmetrical except when the initial concentration is 0.5 and that the asymmetry is larger as the initial concentration deviates from 0.5 and as the separation potential increases.

The application of the equivalent annulus width concept in thermal diffusion separations

The equivalent annulus width concept is used to characterize a small commercial thermogravitational hermal diffusion column and its validity checked experimentally by separating batchwise in the column mixtures of n-heptanebenzene with different initial concentrations. The equation of Ruppell and Coull was used to analyse the data in the short separation times range and determine the equivalent annulus width. Good agreement was obtained between the experimental and predicted time-separation curves when using the equivalent annulus width value and on averaged value of the thermal diffusion constant. A new method is presented for the simultaneous determination of the equivalent annulus width and the thermal diffusion constant of a binary mixture from a single set of experimental data.

Single molecule simulation of diffusion and enzyme kinetics

This work presents a molecular-scale agent-based model for the simulation of enzymatic reactions at experimentally measured concentrations. The model incorporates stochasticity and spatial dependence, using diffusing and reacting particles with physical dimensions. We developed strategies to adjust and validate the enzymatic rates and diffusion coefficients to the information required by the computational agents, i.e., collision efficiency, interaction logic between agents, the time scale associated with interactions (e.g., kinetics), and agent velocity. Also, we tested the impact of molecular location (a source of biological noise) in the speed at which the reactions take place. Simulations were conducted for experimental data on the 2-hydroxymuconate tautomerase (EC 5.3.2.6, UniProt ID Q01468) and the Steroid Delta-isomerase (EC 5.3.3.1, UniProt ID P07445). Obtained results demonstrate that our approach is in accordance to existing experimental data and long-term biophysical and biochemical assumptions.