Compartmental epidemiological models are, by far, the most popular in the study of dynamics related with infectious diseases. It is, therefore, not surprising that they are frequently used to study the current COVID-19 pandemic. Taking advantage of the real-time availability of COVID-19 related data, we perform a compartmental model fitting analysis of the portuguese case, using an online open-access platform with the integrated capability of solving systems of differential equations. This analysis enabled the data-driven validation of the used model and was the basis for robust projections of different future scenarios, namely, increasing the detected infected population, reopening schools at different moments, allowing Easter celebrations to take place and population vaccination. The method presented in this work can easily be used to perform the non-trivial task of simultaneously fitting differential equation solutions to different epidemiological data sets, regardless of the model or country that might be considered in the analysis.

Advanced fitting of ordinary differential equations models to experimental results is presented within the context of different academic levels of students and diverse research fields. In many areas, the analysis of experimental results cannot be restricted to cases where particular solutions of the models’ differential equations, valid only for specific limit conditions, apply. In those cases, analytical mathematical equations are not available and a complete description of the systems extends beyond the numerical minimization of statistical estimators, like the chi-square, because it requires solving numerically the models’ differential equations. Dedicated fitting procedures that involve the interdependent processes of solving the ordinary differential equations and fitting the numerical solutions to the experimental results are required to obtain the best fitting sets of parameters with consistent physical meaning. A simple, but powerful, web-based ordinary differential equations solver and fitter is presented, and used to analyse both the complete motion of a rigid pendulum and the dynamics of a viral infection.

Frankfurters are categorised as ready to eat meat products and are prepared by using different meat sources including beef, chicken, turkey or pork or mixtures of them. Due to cost and feasibility, it is very common to adulterate beef-, chicken- and turkey-based frankfurters with pork meat. Since pork is not consumed by some part of the population due to religion, it is important to identify pork frankfurters based on easy quality control methods. In this study, NMR Relaxometry was used to differentiate four different frankfurter types based on their relaxation times. Relaxation measurements were conducted on three permanent field benchtop NMR spectrometers (13.52/20.34/22.35 MHz) and also using an FFC Relaxometer at a frequency range of 40 kHz–8.86 MHz. Physical properties of frankfurters such as moisture and solid fat contents, water activity (a_w) and hardness values were also measured. Results showed that among the permanent field systems, 22.34 MHz was the best to differentiate frankfurters based on both T₁ and T₂ relaxation times. FFC experiments also showed that the dependence of T₁ with respect to frequency follows a well fitted power law behaviour throughout the whole frequency range (R² > 0.97) and the highest difference on T₁ was observed at the lowest frequency of 40 kHz. Thus the results of the study showed that NMR Relaxometry has the potential to discriminate frankfurters of different meat origin. Further studies are needed to detect the authenticity of the type of mixture in frankfurters.

Understanding the behavior of a chemical compound at a molecular level is fundamental, not only to explain its macroscopic properties, but also to enable the control and optimization of these properties. The present work aims to characterize a set of systems based on the ionic liquids [Aliquat][Cl] and [Aliquat][FeCl${}_4$] and on mixtures of these with different concentrations of DMSO by means of ${}^1$H NMR relaxometry, diffusometry and X-ray diffractometry. Without DMSO, the compounds reveal locally ordered domains, which are large enough to induce order fluctuation as a significant relaxation pathway, and present paramagnetic relaxation enhancement for the [Aliquat][Cl] and [Aliquat][FeCl${}_4$] mixture. The addition of DMSO provides a way of tuning both the local order of these systems and the relaxation enhancement produced by the tetrachloroferrate anion. Very small DMSO volume concentrations (at least up to 1%) lead to enhanced paramagnetic relaxation without compromising the locally ordered domains. Larger DMSO concentrations gradually destroy these domains and reduce the effect of paramagnetic relaxation, while solvating the ions present in the mixtures. The paramagnetic relaxation was explained as a correlated combination of inner and outer-sphere mechanisms, in line with the size and structure differences between cation and anion. This study presents a robust method of characterizing paramagnetic ionic systems and obtaining a consistent analysis for a large set of samples having different co-solvent concentrations.