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Using the transfer matrix method we calculate the frequency dependence of the transmission of longitudinal elastic waves for a layered structure where the specific acoustic impedance of the layers with odd numbering follows a Gaussian distribution, while the inserted even layers have the same impedance as the propagation medium. The structure presents intervals of low-pass, bandstop, and band-pass. The characteristics of the bands depend on the number of layers, on the contrast between the maximum and minimum impedances of the structure, and on the ratio of the width of the inserted layers to the width of the layers with a Gaussian distribution of impedances.

In crop science, tools of non-linear dynamics, fractals, chaos, intermittency and self-organized criticality may be employed and applied to the analysis of spatial variability and temporal behavior of agro-meteorological variables, soil properties, plant attributes, commercial yields, and prices of the agricultural products in order to gain knowledge about underlying complex processes. A search on the occurrence of particular scaling laws in Mexico's normalized yearly mean grain yield anomaly series of maize (Zea mays L.), beans (Phaseolus vulgaris L.), wheat (Triticum aestivum L.) and rice (Oriza sativa L.), using a variography approach is reported in this work. Additionally, power spectrum determination, time-frequency analysis, and estimation of Lyapunov exponent were performed for each profile in order to obtain useful information on the frequency contents and signs at which important frequencies occur as well as to determine their sensitivity to initial conditions. Fractal analysis gives us the order maize < wheat < rice < beans of sensitivity to external forcings, which was the same as that obtained through the Lyapunov exponent values. Results confirm that the final outputs (crop yields) in agricultural systems are affected by the magnetic and sunspot cycles of the Sun, the El Niño Southern Oscillation (ENSO), and the quasi-biannual oscillation, and possibly by the so-called heliospheric mid-term-quasi-periodicities, which act on different time (or spatial and spatial-time) scales. In particular, the maize normalized year anomaly series is clearly correlated with March, April, May and June series of the ENSO index.

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