Enrique Castro

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.

Acoustic Emission (AE) is a non-destructive evaluation method that uses transient elastic waves produced by the sudden release of mechanical energy in a material or structure. This method generates multiple AE events during testing; therefore, it is important to develop parameters that capture the characteristics of each event (AE hit). The paper introduces new dimensionless parameters to characterize the waveform of AE signals: Earliness, Transitoriness, and Early Transitoriness. The study shows that these parameters provide an accurate description of AE waveforms, in some respects, better than traditional parameters, which makes them suitable for filtering with simple rules or in combination with machine-learning techniques. Two examples of the application of AE hit filtering from sedimentation and soil compression experiments are provided. In the sedimentation test analysis, the proposed parameters were used with K-means clustering to filter AE hits from outside the zone of interest and to calculate the rate of sedimentation. In the compression test of a sand sample under oedometric conditions, a simple filtering rule was applied to discriminate AE hits from unwanted sources and obtain a clear AE energy cumulative curve. In both cases, the dimensionless parameters have shown the capacity to discriminate between different AE sources and paths and the possibility of filtering hits from unwanted sources.