Evidence for the impact of global warming on the long-term population dynamics of common birds by Dr R Julliard, Dr F Jiguet and Dr D Couvet
We compared common birds' productivity (proportion of juveniles from standardised samples for 32 species, totalling over 50,000 captured individuals within 60 sites spread over France) between spring 2003, an exceptionally warm spring in France, and previous years. Productivity in 2003 was relatively low for already declining species while it was relatively good for increasing species. This adds evidences that climate warming plays a key role in the long term dynamics of even the commonest species. This further suggests that ability to reproduce in warmer and warmer conditions is a key component of species sensitivity to climate change.
Contact: Dr Romain Julliard, CRBPO-Museum National d'Histoire Nat., 55 rue Buffon, PARIS, F-75005, France
Proceedings of The Royal Society A: Mathematical, Physical and Engineering
On the distribution of elastic forces in disordered structures and materials. I Computer simulation by Dr AHW Ngan
Many engineering materials designed to cushion impacts (eg granular packings and foam materials) have random internal structures. When these materials are subjected to external loading, the internal forces are not uniform but distributed in a particular way because of this structural randomness. Understanding such force distributions is crucial for the prediction of the failure condition of these materials. This study shows that the force distributions can be accurately described by an analogue of the Second Law of Thermodynamics, which governs the directions of changes in thermal systems such as chemical reactions. In thermal systems the balance between the two fundamental driving forces of energy and entropy governs the directions of the changes. The same balance between energy and entropy, which measures disorder, governs the force distributions in random materials; though the linking quantity between energy and entropy in random materials is not the absolute temperature (as in thermal systems), but only an analogue of it. The study's findings demonstrate that the Second Law of Thermodynamics has much wider applications than originally thought.
Contact: Dr Alfonso Ngan, Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
Wiener chaos and the Cox--Ingersoll--Ross model by Professor MR Grasselli and Dr TR Hurd
The Wiener chaos expansion is a general way to specify a model for positive interest rates free from arbitrage opportunities. The increasing orders in the expansion allow for the introduction of randomness in the model in a systematic and controlled manner. In this paper we provide an explicit chaotic representation for the Cox--Ingersoll--Ross model, arguably the most well known model for positive interest rates. We do so by using techniques from infinite dimensional Gaussian integration inspired by quantum field theory. We then derive a new expression for the price of a zero coupon bond which reveals a connection between Gaussian measures and Ricatti differential equations.
Contact: Professor Matheus Grasselli, Dept of Mathematics and Statistics, McMaster University, Hamilton, ONTARIO, L8S 4K1, CANADA
Journal
Proceedings of the Royal Society of London