A note on non-degenerate umbilics and the path formulation for bifurcation problems

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the ℤ 2-equivariant (general or gradient) problems. Those categories determine an interesting 'Russian doll' type of structure in the universal unfoldings of the umbilic singularities. One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.

Calculated sea level records and deep ocean temperatures from DSDP and ODP sites

During the mid-Pleistocene transition the dominant 41 ka periodicity of glacial cycles transitioned to a quasi-100 ka periodicity for reasons not yet known. This study investigates the potential role of deep ocean hydrography by examining oxygen isotope ratios in benthic foraminifera. Oxygen isotope records from the Atlantic, Pacific and Indian Ocean basins are separated into their ice volume and local temperature/hydrography components using a piece-wise linear transfer function and a temperature calibration. Although our method has certain limitations, the deep ocean hydrography reconstructions show that glacial deep ocean temperatures approached freezing point as the mid-Pleistocene transition progressed. Further analysis suggests that water mass reorganisation could have been responsible for these temperature changes, leading to such stable conditions in the deep ocean that some obliquity cycles were skipped until precessional forcing triggered deglaciation, creating the apparent quasi-100 ka pattern. This study supports previous work that suggests multiples of obliquity cycles dominate the quasi-100 ka glacial cycles with precession components driving deglaciations.

The visual (grating and glass lens) solar spectrum in 1884 /

"From the Transactions of the Royal Society of Edinburgh, vol. XXXII, pt. III."

Internal instability as a possible failure mechanism for layered composites

Funding Financial support of part of this research by The Royal Society, The Royal Society of Edinburgh, The Royal Academy of Engineering and The Carnegie Trust for the Universities of Scotland is gratefully acknowledged.