Diversity of Soils

The earth’s surface is heterogeneous in nature. This feature of the earth’s crust implies that the distribution in space of its natural resources is also varied. Most natural resources vary in a continuum rather than in a discrete way. However, our cognitive system works better in discretely classifying the world that surrounds us. Therefore, we divide all the observed features in nature into non-overlapping categories, through a process called “categorization.” Then we order, name, and group objects previously created in our minds in such categories, producing classifications, either consciously or unconsciously. Most of these classifications are hierarchical (splitting the natural continua in discernible classes by using nested classifications of increasing refinement). A scientific universal taxonomy is a mental construct that inventories the diversity of the universe studied at the global level by experts, such as living organisms, rocks, and soils, conforming to explicit rules. The diversity of a natural resource is based on these grounds. Therefore, the quantification of any diversity always depends on the number of classes and categories of the taxonomy used. As a corollary, the inventory of diversities will always suffer biases and limitations, being provisionally from a historical perspective. At first instance, the notion of diversity of a given natural resource is clear and intuitive. All naturalists recognize that some territories are more diverse than others, regardless of whether they are interested in species, soils, landforms, rocks, etc. Therefore, it is impossible to consider a particular naturalist as the founder of the analysis of diversity. In ecology, the first patterns and theories in biodiversity date back to the first decades of the 20th century. In contrast, the interest of the scientific community in the diversity of the abiotic natural resources began in the last decade of the 20th century, although it is possible to find some exceptional publications before that date. The starting point of this article goes back to the first attempts to operationalize the concept and the first indexes for its estimation.

THE THUE-MORSE APERIODIC CRYSTAL, A LINK BETWEEN THE FIBONACCI QUASICRYSTAL AND THE PERIODIC CRYSTAL

The electronic spectrum and eigenstates of a one-dimensional aperiodic Thue-Morse crystal isstudied with an on-site tight-binding model. The relation between the constructing elements andthe hierarchical splitting of the bands into subbands is analysed. The eigenstates are shown to be much more similar to those of a periodic crystal than those of a Fibonacci quasicrystal. We thus claim that the Thue-Morse aperiodic crystal is a link between the Fibonacci quasicrystal and theperiodic crystal, and that the study of non-Fibonaccian aperiodic crystals is a promising steptowards the desired unified theory of disordered, aperiodic and periodic systems. Since the experimentally studied MBE-grown aperiodic crystals typically has 5% fluctuation in layer thickness, we also investigate the density of states and eigenstates for a model system withfluctuating site-energies.