Narrow Results

We extend to higher dimensions a recent work of Bonnor, which generalizes the Einstein–Straus model utilizing the inhomogeneous Tolman–Bondi universe in place of the homogeneous Friedmann one. Following Israel's junction conditions, the criteria of matching between the higher dimensional Schwarzschild-like interior and the Tolman–Bondi-like exterior is obtained. We also give a new exact solution for a five-dimensional TB type of metric and use it to study the dynamical behavior of the vacuole boundary. Furthermore the transformation relations which transform the inhomogeneous TB metric to the homogeneous Friedmann model are explicitly given for any arbitrary dimensions. The frequency shift of radiation coming from the boundary surface is calculated and it is found that, depending on initial conditions both redshift and blue-shift are possible for an expanding vacuole. This is at variance with Bonnor's result where only redshift is possible under similar situation. It is also observed that higher dimensional models are less stable against perturbation than the usual 4D ones.

Water uptake and nutritious mineral utilisation via roots from the soil are the critical requirements for terrestrial plants that have evolved as the major host organisms on the grove of Earth, autotrophically nourishing animals, fungi and many other heterotrophic organisms and continuing to play a crucial role in forming the landscapes of the planet’s biosphere. Minerals taken up from the ground return to the earth via food chains and biome networks through the actions of consumers and decomposers. Through the cyclic usage of inorganic and organic resources, plants and their associates sustain and develop as whole communities. In this chapter, based on such a co-association, or co-evolution, concept, the important interactions between autotrophic plants and the coordinative or competitional fungi and microbes are discussed and emphasised, especially in relation to plant stresses caused by excess levels of Li⁺ and Ni²⁺ ions in land environments.

Li and Ni are gathering more attention, as well as cobalt (Co), because of their importance as very useful elements in industrial activities and sustainable energy for people in the future; however, their use is also accompanied by the incidental threat and concern about their possible increases through release and contamination into land and other environments. Li belongs to the group of relatively abundant alkaline metals (light metals), and Ni is one of the rare and micro-elementary heavy metals. Although their differential and unique impacts on plants and fungi are known, their combinational effects are not well known, so it will be necessary to address the increasing risks in the near future. In this chapter, the existing evidence will be substantiated with details about their bindings and localisations with different bioligands and polymers in the cells of plants or fungi. Taken together, we discuss the importance of complex binding and detoxification systems in plants and the symbiotic associates under combined stresses caused by the two metals as well as others.