Climate in the balance

This essay explores how our climate system works, how humans are changing the climate system, and how we might face the challenges of reducing our negative impact on the climate system in the future

A comparison of bearing life in new and refurbished railway axle boxes

A simple linear dynamical model shows that at normal running speeds of freight wagons, forced oscillations due to periodic track compliance are transferred to the overlying unsprung mass and significantly amplified. Due to these oscillations, a small gap opens and closes between the collar of a journal bearing and the axle box many times every second. The forces between these components reach peaks of over 10 tonnes. This is an environment in which wear of the soft spherical graphite iron of the axle box will eventually take place. Due to repeated unloadings of the weight on the bearing during oscillations, the bearing collar may slowly slip against the axle box wall. Although our calculations show that abrasive wear due to this slippage is negligible, the calculation raises general principles that apply to other possible wear mechanisms. If lifetime is proportional to hardness, we can estimate relative lifetimes of refurbished and new boxes. Although the resleeve material is softer than the original, the cost to lifetime ratio would favour refurbishment under this assumption. Important unanswered questions are identified and a specific integrated program of field, laboratory, and theoretical study is suggested

Functional differential equations arising in cell-growth

Non-local differential equations are notoriously difficult to solve. Cell-growth models for population growth of a cohort structured by size, simultaneously growing and dividing, give rise to a class of non-local eigenvalue problems, whose “principal” eigenvalue is the time-constant for growth/decay. These and other novel non-local problems are described and solved in special cases in this paper