Using a theory of homogenization that consists in the discretization of the inclusion of a binary phononic crystal in small volumes, in which the material parameters can be expanded in Fourier series, we have determined the dependence of the effective elastic parameters as a function of the frequency. In particular, the frequency dependence of all the elements that constitute the effective tensors of stiffness (moduli of elasticity) and density was analyzed for a 1D phononic crystal conformed of materials whose main characteristic is the high contrast between their elastic properties. In this dynamic case of homogenization, it was found that the effective parameters can reproduce the exact dispersion relations for the acoustic modes that propagate along the periodicity direction of the crystal. Particularly, in the second pass band (high-frequency branch) corresponding to the transverse vibrational modes, the homogenized elastic phononic crystal exhibits a metamaterial behavior because the effective C₄₄-component (shear modulus) and dynamic mass density were found to be both negative. It is noteworthy that the study derived from this homogenization technique can lead to design of double negative metamaterial systems for potential applications.

Computational sciences have been highlighted in the application to any area with good results. One of the primary interests of humanity is water quality because it is a vital resource for the existence of living beings. This research applies a data mining model based on CRISP-DM methodology built to classify water contamination in lotic systems in Puebla City, located in the center of Mexico. The classification was carried out through physicochemical parameters using a water quality evaluation model based on the amount of dissolved oxygen percentage (%DO). Results demonstrate that the application of decision trees and K-NN algorithms, using chemical parameters, are effective in determining the presence of contamination in lotic water bodies and represent a novel way to evaluate water quality in the water system along rivers in Puebla, Mexico.

This paper presents research and theoretical development of a mathematical model that, first, allows us to understand how the positional exactitude of the output link of a four-bar mechanism depends on the manufacturing dimensional tolerances. To find this dependence, the total differentials of the kinematic constraint functions that govern the field of positions must be determined for each kinematic cycle of the mechanism under consideration. These total differentials lead to a system of equations whose solution gives the positional errors of the movable output links as a function of the manufacturing dimensional errors and an incidence matrix that varies with each one of the positions of the input element. On the other hand, the theoretical transmission ratio between the output velocities with respect to the input velocity of the articulated kinematic chain is defined, and for determining the total errors in each ratio, the total differential of each one of them is calculated, showing a clear dependence with respect to the positional errors of the output links (previously defined) of the mechanism. The sum of the theoretical transmission ratio and its respective error provides the real transmission ratio. Furthermore, the described methodology allows for determining the sensitivity (influence coefficients) in the transmission ratios due to errors inherent in the link lengths. Finally, the presented analytical approach is numerically implemented through an example of articulated parallelogram design, principally characterizing in graphic form the transmission ratios in their regions of permitted movements and blocking positions, for a specific IT degree of precision of the bilateral dimensional tolerances of their functional geometric parameters, with the objective of analyzing every aspect related to the performance of the mechanisms. This formalism is validated through three particular design cases using a CAD model in a simulation module of kinematic motion analysis; additionally, the evolution of the transmission angle is discussed. The methods and conclusions proposed in this document also leave open the way as future work to study separately the magnitudes and signs of the positional errors and the transmission ratio, or even the influence coefficients themselves, in order to assign the most convenient degree of IT precision for each link in the mechanism with the purpose of reducing errors in the designs and obtain better efficiency in the transmission ratio.

We have investigated and theoretically developed a mathematical model that, first, allows us to understand how the positional exactitude of the output link of a four-bar mechanism depends on the manufacturing dimensional tolerances (associated with the IT grades, which correspond to the bilateral tolerances specified in the ISO 286-2 norm) of its links and the error of the input coordinate. To find this dependence, the total differentials of the kinematic constraint functions that govern the field of positions must be determined for each kinematic cycle of the mechanism under consideration. These total differentials lead to a system of equations whose solution gives the positional errors of the movable output links as a function of the manufacturing dimensional errors and an incidence matrix that varies with each one of the positions of the input element. On the other hand, the theoretical transmission ratio between the output velocities with respect to the input velocity of the articulated kinematic chain is defined, and for determining the total errors in each ratio, the total differential of each one of them is calculated, showing a clear dependence respect to the positional errors of the output links (previously defined) of the mechanism. The sum of the theoretical transmission ratio and its respective error provides the real transmission ratio. Furthermore, the described methodology allows determining the sensitivity (influence coefficients) in the transmission ratios due to errors inherent in the links lengths. Finally, the presented analytical approach is numerically implemented through an example of articulated parallelogram design, principally characterizing in graphic form the transmission ratios in their regions of permitted movements and blocking positions, for a specific IT degree of precision of the bilateral dimensional tolerances of their functional geometric parameters, with the objective of analyzing every aspect related to the performance of the mechanisms. The methods and conclusions proposed in this document also leave open the way as future work to study separately the magnitudes and signs of the positional errors and the transmission ratio, or even the influence coefficients themselves, in order to assign the most convenient degree of IT precision for each link in the mechanism with the purpose of reducing errors in the designs and obtain better efficiency in the transmission ratio.