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The chapter introduces some of the basic concepts of ecology to characterize the biosphere of the earth, its ecosystems and their components of biotic and abiotic environment. It describes the organic and inorganic substances and climate conditions as constituents of the ecosystems which determine their structure and function and the conditions of supply of various natural resources and eco-services to the human economy. The chapter also explains the solar energy flow and the hydrological and bio-geochemical cycles to further elaborate the functions of eco-services of regeneration of resources and absorption of wastes for the economy. It characterizes the energetics of the ecosystems and its modification due to human intervention, pointing to the need for a holistic view of energy analysis taking account of its flows and uses in both the ecological and the economic processes for our better understanding of the physical conditions of sustainable development.

There are many relationships between ecosystem properties and species (Jones and Lawton, 1995) with the potential links described by five hypotheses: 1. The null hypothesis claims that there is no effect of species diversity on ecosystem processes. The following hypotheses imply biological mechanisms. 2. The diversity–stability hypothesis predicts that ecosystem productivity and recovery increase as the number of species increases (Johnson et al. 1996). 3. The rivet hypothesis predicts a threshold in species richness, below which ecosystem function declines steadily and above which changes in species richness are not reflected by changes in ecosystem function (Ehrlich and Ehrlich 1981; Vitousek and Hooper 1993). 4. The redundant species hypothesis states that species loss has little effect on ecosystem processes if the losses are within the same functional group (Walker 1992) 5. The idiosyncratic response hypothesis suggests that as diversity changes so do ecocosystem processes (Lawton 1994, Lawton and Brown 1994). There have been both field and laboratory attempts to test these hypotheses, (Naeem and Li 1998), however, the interpretation and the generality of the results remain contentious (Tilman 1999). A fundamental reason for such uncertainty is that the hypotheses are not driven by a comprehensive theory of the relationship between species properties and ecosystem processes (Tilman et al., 1997). We propose that the foundations for the necessary theory are in models of the distribution of resources and their utilization by organisms. This is because ecosystem processes such as primary production, decomposition, mineralization, and evapotranspiration are dependent on the processing of resources by the species that are producers, consumers, and decomposers. A theory that links the direct participation of species in ecosystem processes may resolve differences among the various hypotheses or identify how they complement each other. From a community perspective, a theory of resource utilization is based on two alternative assumptions: 1. The rate of ecosystem processes is determined by the few species that are most efficient in using and converting resources. For example, in a desert system, dominant species are those that are proficient in using water for biomass production or in converting inorganic matter into organic materials.

Belowground organisms are key components of the trophic structure and they mediate the dynamics of nutrients of all terrestrial ecosystems. The interactions among assemblages of belowground microorganisms and their consumers mediate the cycling of plant-limiting nutrients, influence aboveground plant productivity, affect the course of plant community development, and affect the dynamic stability of aboveground communities following natural and anthropogenic disturbances (Clarholm, 1985; Ingham et al., 1985; Laakso and Setälä, 1999; Naeem et al., 1994; Tilman et al., 1996; Wall and Moore, 1999). The influence of belowground organisms on the aboveground plant community is heightened in systems such as the shortgrass steppe (Blair et al., 2000), given the relatively high percentage of plant production that is diverted belowground through plant roots. Many of the human-induced changes that the shortgrass steppe has been subjected to during the past 150 years fall outside the scope of the natural variations in climate and grazing. This conflict between the natural history of the shortgrass steppe and the more recent human legacy forms the backdrop of this chapter. First we present a detailed description of the belowground food web for the native shortgrass steppe and present its structure in terms of the patterns of trophic interactions, the distribution of biomass, the flow of energy, and the strengths of interactions. Second, we explore how three disturbances—managed grazing, agricultural practices, and climate change (altered precipitation and temperature, and elevated CO2)—have altered the structure of the belowground community. We conclude with a synthesis of the common patterns that we observed in the grassland’s response to these disturbances, and speculate on their consequences. Aboveground plant parts provide from 20% to 40% cover with exposed soil between them (Lauenroth and Milchunas, 1991). Much of the aboveground production remains in place as standing dead, rather than falling to the soil surface as litter. The ratio of shoot production to root production is roughly 1:1, contrasting sharply with forests, where far more production is allocated aboveground (Jackson et al., 1996; Milchunas and Lauenroth, 1993, 2000). Hence, in the shortgrass steppe, plant roots provide the major input of carbon to soil. As such, plant roots are the focal point of biological activity in soils (Coleman et al., 1983).

In this chapter, we provide a brief introduction to ultrasonic wave propagation in unbounded anisotropic solids with emphases on examples suitable for ultrasonics of composites. Many excellent books are relevant to the subject addressed in this chapter. Some of them broadly discuss elastic waves in anisotropic solids, including waves in layered anisotropic media. In-depth theoretical description of elastic waves in anisotropic media is given in classical texts, which have influenced and provided guidance to our treatment of some aspects of the theory. Beautiful visualization of ultrasonic waves in crystals (often obtained by laser excitation) is given in reference. The equations of motion for the vibration of an elastic medium are extensions of Newton’s second law for particles. Treating the elastic continuum as a collection of particles, each of which is assumed to obey Newton’s laws, leads to a particularly straightforward argument. We begin by considering a short segment of a bar with length Δx and cross-sectional area S0 as is illustrated in Fig. 2.1. The material is assumed to be linear and elastic, and its deformations can be described by constitutive equations derived in the previous chapter. For simplicity, we assume only uniaxial stress in the x-direction of the continuum.

On large spatial scales, species diversity is typically correlated positively with productivity or energy supply (Wright et al. 1993, Huston 1994, Waide et al. 1999). In line with this general pattern, deserts are assumed to have relatively few species for two main reasons. First, relatively few plants and animals have acquired the physiological capabilities to withstand the stresses exerted by the high temperatures and shortage of water found in deserts (reviewed by Noy-Meir 1974, Evenari 1985, Shmida et al. 1986). A second, more ecological mechanism is resource limitation. In deserts, the low and highly variable precipitation levels, high temperatures and high evapotranspiration ratios limit both plant abundance and productivity to very low levels (Noy-Meir 1973, 1985, Polis 1991d). This lack of material at the primary producer level should exacerbate the harsh abiotic conditions and reduce the abundance of animals at higher trophic levels by limiting the types of resources and their availability. Animal abundance should be even further reduced because primary productivity is not only low, but also tends to be sporadic in time and space (MacMahon 1981, Crawford 1981, Ludwig 1986). Herbivores should have difficulties tracking these variations (e.g., Ayal 1994) and efficiently using the available food resources. Hence, herbivore populations in deserts have low densities relative to other biomes (Wisdom 1991) and most of the primary productivity remains unused (Crawford 1981, Noy-Meir 1985). This low abundance of herbivores should propagate through the food web and result as well in lower abundance of higher trophic levels. The number of individuals and the number of species are not always positively correlated; in particular, some examples of low diversity at high productivity with high densities are well documented (e.g., salt marshes, reviewed by Waide et al. 1999). However, several distinct mechanisms have led to the expectation that when productivity and the number of individuals are low, the number of species is also likely to be low. First, within trophic levels, the “statistical mechanics” model of Wright et al. (1993) may operate. In this model, the amount of energy present determines the probability distribution of population sizes for the members of the species pool in a region.

In this chapter we treat plane waves specified by a wave normal and a particle motion vector . Two types of waves, longitudinal waves and shear waves, are observed in solids. For low symmetry directions, there are generally three different waves with the same wave normal, a longitudinal wave and two shear waves. The particle motions in the three waves are perpendicular to one another. Only longitudinal waves are present in liquids because of their inability to support shear stresses. The transverse waves are strongly absorbed. Acoustic wave velocities (v) are controlled by elastic constants (c) and density (ρ). For a stiff ceramic (c ∼ 5 × 1011 N/m2) and density (ρ ∼ 5 g/cm3 = 5000 kg/m3), the wave velocity is about 104 m/s. For low frequency vibrations near 1 kHz the wavelength λ is about 10 m. The shortest wavelengths are around 1 nm and correspond to infrared vibrations of 1013 Hz. Acoustic wave velocities for polycrystalline alkali metals are plotted in Fig. 23.2. Longitudinal waves travel at about twice the speed of transverse shear waves since c11 > c44. Sound is transmitted faster in light metals like Li which have shorter, stronger bonds and lower density than heavy alkali atoms like Cs. The tensor relation between velocity and elastic constants is derived using Newton’s Laws and the differential volume element shown in Fig. 23.3(a). The volume is equal to (δZ1) (δZ2) (δZ3). Acoustic waves are characterized by regions of compression and rarefaction because of the periodic particle displacements associated with the wave. These displacements are caused by the inhomogeneous stresses emanating from the source of the sound. In tensor form the components of the stress gradient are ∂Xij/∂Zk and will include both tensile stress gradients and shear stress gradients, as pictured in Fig. 23.3(b). The force F acting on the volume element is calculated by multiplying the stress components by the area of the faces on which the force acts.