Fulgencio Marín

The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.

Dry friction cannot be understood on a macroscopic scale without knowing what happens at the contact of sliding surfaces on an atomic scale. Tests on this scale are very expensive and very sensitive to the effects of contamination or inaccurate fittings. On the other hand, the sample dimensions are small because of the requirements of the test equipment, which makes it difficult to generalise the conclusions drawn. This work reviews the models used to analyse friction processes, and proposes the application of one of the models, the Frenkel–Kontorova–Tomlinson (FKT) model, to study the dry frictional behaviour of doped surfaces. The study shows that for concreted types of doped pattern, the behaviour can change from chaotic to periodic depending on the stiffness, which in turn are associated with temperature.