Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

A hydro-wood net-energy approach to hydro project design

An integrated approach to energy planning, when applied to large hydroelectric projects, requires that the energy-opportunity cost of the land submerged under the reservoir be incorporated into the planning methodology. Biomass energy lost from the submerged land has to be compared to the electrical energy generated, for which we develop four alternative formulations of the net-energy function. The design problem is posed as an LP problem and is solved for two sites in India. Our results show that the proposed designs may not be viable in net-energy terms, whereas a marginal reduction in the generation capacity could lead to an optimal design that gives substantial savings in the submerged area. Allowing seasonal variations in the hydroelectric generation capacity also reduces the reservoir size. A mixed hydro-wood generation system is then examined and is found to be viable.