and 10–9 s, respectively), can provide thermodynamic information on the studied system.
Figure 1.18. Example of calculation at the atomic scale [BEL 17b]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip
COMMENT ON FIGURE 1.18.– The figure represents a molecular structure calculated for the interaction between atrazine and clay. The soil is modeled here by an infinite crystal lattice: in practice, it is a cell, on the edge of which are applied conditions of repetitiveness, reflecting an infinite extension. The calculation shows how the atrazine molecule behaves in this environment and what the associated energies are. The simulation allows us to find the most probable structures after the adsorption of the pesticide on the clay.
“Due to the complexity and size of the models, we used HPC calculation methods. Simulating the desorption of the pesticide in water requires, for example, nearly two million hours of calculation – spread over the thousands of cores of a supercomputer!”
Calculation at the atomic scale is a first step in research: it serves as a reference for validating models that introduce simplifications and lend themselves to faster calculations. The objective is to carry out simulations under environmental conditions, with the data collected in the fields. Calculations using these models, in which accuracy is demonstrated by comparison with the atomic scale calculation, should determine the pesticide partition constants between the liquid and mineral phases – and answer the initial question. It is a wonderful problem, because it is far from simple!
1.5. Plant growth
Vegetation is one of the crucial resources for humanity, providing it with food and energy – and in some cases a place to live. Satellite observations help to consolidate plant occupancy data on the planet’s surface (Figure 1.19). They enable scientists to understand the influence of natural cycles on vegetation (such as droughts or epidemics) or that of human activities (such as deforestation or CO2 emissions).
Figure 1.19. Vegetation map obtained from satellite observations (source: NASA/www.nasa.gouv). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip
COMMENT ON FIGURE 1.19.– The shades of green on the map correspond to values ranging from 0.0 to 1.0, in arbitrary units. Values close to 1.0 (dark green) indicate the presence of abundant vegetation, as in the Amazon rainforest. Values close to 0.0 (beige) indicate areas with little vegetation, such as the oceans or the Arctic continent. Forests cover 30% of the world’s land area, equivalent to just under 40 million km2, while treeless vegetation (tundra, savannah, temperate grasslands) occupies about the same area.
In 1985, English filmmaker John Boorman recounted in The Esmerald Forest how a world disappears, the world of the Amazon rainforest tribes [BOO 85]. The son of an engineer who oversees the construction of a gigantic dam is taken from his parents by a tribe of Forest Men. As the dam’s construction was completed, the father and son found themselves in circumstances that led them both to confront progress and humanity. The dam will eventually give way under the waters of a river doped by torrential rain, engulfed by the songs of frogs calling on the forces of nature. The engineer who wanted to destroy his work to protect the future of his son and that of a tribe wishing to live in peace will not have this power.
The Amazon rainforest is still one of the largest plant communities on the planet today. According to FAO2 estimates, it is now disappearing at an average rate of 25,000 km2 per year (equivalent to half the size of Austria) to make way for new crops. At this rate, it will have completely disappeared by the first half of the next century. It pays the highest price for the consequences of human activities: more than half of the world’s deforestation. The evolution of vegetation as a whole is of particular concern because of its dual importance: it supports a large part of biodiversity and contributes to the absorption of atmospheric CO2. Analyzing satellite observation data, NASA researchers show that in just under 20 years, the planet has re-vegetated with an area equivalent to that of the Amazon, with India and China being among the main contributors to this trend. The observed vegetation corresponds, on the one hand, to the growth of new forests, contributing to the sequestration of carbon from the atmosphere, and, on the other hand, to an extension of agricultural areas, whose natural carbon storage balance is generally neutral [CHE 19].
Understanding the growth mechanisms of species continues to occupy scientists. In the first half of the 20th Century, the British biologist d’Arcy Thompson (1881–1946) became interested in the shape and growth of living organisms, publishing his thoughts in an exciting collection [THO 61]. He looks for invariants and universal principles that govern the evolution of life – for example, fractal structures or particular sequences (Figure 1.20).
Figure 1.20. The Fibonacci spiral: a model (too simple?) to explain plant growth
(source: www.123rf)
COMMENT ON FIGURE 1.20.– Leonardo Fibonacci (1170–1250) was a 13th Century Italian mathematician. The Italy of his time was a region formed by scatterings of merchant cities in strong competition (Venice, Pisa, Genoa). Trade activities needed numbers and calculation to support their economic development. The mathematician developed algebraic methods to contribute to this. In particular, he drew inspiration from Indian and Arab mathematics, while Roman numerals, still widely used in Europe, forced calculation in a rigid numbering system that the invention of zero helped to loosen. The sequence that bears his name is defined from two values, then each term is calculated as the sum of the two previous ones. Thus, starting from 1 and 1, the terms are 2, 3, 5, 8, 13, 21, etc. This sequence, which has properties of interest to mathematicians, is found in some natural growth mechanisms. The Fibonacci sequence hides the famous golden number
Created at the initiative of the Royal Botanical Garden of Edinburgh, the website The Plant List3 aims to provide an exhaustive list of the various plant species: there are currently more than 1 million. Nature is characterized by a great variability of shapes (Figure 1.21): how can we accurately model the development of such diverse plants?
Figure 1.21. Variety of leaf shapes
(source: www.123rf/Liliia Khuzhakhmetova)
Since the late 1960s, scientists have been using a formalism
