The growth of demand will limit output growth for food over the next quarter century

The rate of growth of world food demand will be much slower for 1990–2010 than it was for the prior three decades. The major factor determining the increase in food demand is population growth. Income growth has a much smaller effect. From 1960 to 1990, population growth accounted for approximately three fourths of the growth in demand or use of grain. For 1990–2010, it is anticipated that population growth will account for nearly all of the increase in world demand for grain. The rate of population growth from 1990 to 2020 is projected to be at an annual rate of 1.3% compared with 1.9% for 1960 to 1990—a decline of more than 30%. World per capita use of grain will increase very little—perhaps by 4%. The increase in grain use is projected to be 40% less than in 1960–1990. It is anticipated that real grain prices will decline during the period, although not nearly as much as the 40% decline in the previous three decades. Concern has been expressed concerning the deterioration of the quality and productivity of the world’s farmland. A study for China and Indonesia indicates that there has been no significant change in the productive capacity of the land over the past 50 years. Contrary to numerous claims, the depth of the topsoil has not changed, indicating that erosion has had little or no impact.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.