Evidence of Fractality in a Pattern of Crystallization of Bovine Cervical Mucus Obtained at Oestrus / Evidencia de Fractalidad en un Patrón de Cristalización de Moco Cervical Bovino Obtenido en Estro

Fractality has emerged as a feature of the organization of some complex natural systems. Several biological secretions show fractal-like patterns for their crystallization phenomena but their presence in crystallizations of bovine cervical mucus (BCM) is yet unknown. In order to assess the fractality of BCM crystallization, samples of this fluid were taken from heifers at oestrus, their crystalline patterns photographed and its morphology analyzed. Among the many images obtained for BCM crystallizations, one of them had a highly symmetrical geometric arrangement, possessing three zones characterized by pine-like, arboriform structures, evidencing a remarkable similarity between them. Moreover, fractal dimensions obtained for these zones were statistically equal when analyzed by using specialized software. In summary, this brief communication shows, for the first time, that a pattern of crystallization of BCM at oestrus possesses a fractal-like organization.

La fractalidad ha surgido como una característica propia de algunos sistemas biológicos complejos. Varias secreciones biológicas presentan patrones de tipo fractal al cristalizar; no obstante, su presencia en las cristalizaciones de moco cervical bovino aún se desconoce. Con el objetivo de investigar la presencia de fractalidad en las cristalizaciones de moco cervical bovino, se obtuvieron muestras de este fluido de vaquillas en estro, fotografiándose los patrones cristalinos observados. Entre las típicas disposiciones similares a frondas de helechos observadas para la cristalización del moco cervical, se encontró una imagen con un arreglo geométrico altamente simétrico, constando de tres zonas caracterizadas por estructuras arborescentes similares a pinos, muy semejantes entre sí. Más aún, las dimensiones fractales obtenidas para esas zonas fueron estadísticamente iguales al ser dichas áreas analizadas con un programa computacional apropiado. En resumen, esta comunicación breve demuestra por primera vez que uno de los patrones de cristalización de moco cervical bovino en estro está caracterizado por una organización de tipo fractal.

Line shapes in infrared absorption by solids and by atomic or molecular species embedded in solids.

When the target is in the solid state, most infrared spectral features are manifestly asymmetric; hence, a line shape function well-grounded in theory is necessary to ascertain the net energy taken by the associated electronic transition. The main sources for spectral line broadening, asymmetry, and shift, no matter the transferred energy, are multiphonon events involving the acoustic vibrational modes. A simple closed-form mathematical expression for the phonon-broadened lineshapes, shown to be valid at low temperatures, and linewidths on the order of the Debye energy of the solid or smaller, giving remarkable agreement with experiment is studied in connection with its utility for analyzing infrared spectral features.