Seeing and believing: three episodes in the history of neurophysiology

In this contribution I look at three episodes in the history of neurophysiology that bring out the complex relationship between seeing and believing. I start with Vesalius in the mid-sixteenth century who writes that he can in no way see any cavity in nerves, even in the optic nerves. He thus questions the age-old theory (dating back to the Alexandrians in the third century BC) but, because of the overarching psychophysiology of his time, does not press his case. This conflict between observation and theory persisted for a quarter of a millennium until finally resolved at the beginning of the nineteenth century by the discoveries of Galvani and Volta. The second case is provided by the early history of retinal synaptology. Schultze in 1866 had represented rod spherules and bipolar dendrites in the outer plexiform layer as being separated by a (synaptic) gap, yet in his written account, because of his theoretical commitments, held them to be continuous. Cajal later, 1892, criticized Schultze for this pusillanimity, but his own figure in La Cellule is by no means clear. It was only with the advent of the electron microscopy in the mid-twentieth century that the true complexity of the junction was revealed and it was shown that both investigators were partially right. My final example comes from the Hodgkin-Huxley biophysics of the 1950s. Their theory of the action potential depended on the existence of unseen ion pores with quite complex biophysical characteristics. These were not seen until the Nobel-Prize-winning X-ray diffraction analyses of the early twenty-first century. Seeing, even at several removes, then confirmed Hodgkin and Huxley’s belief. The relation between seeing and believing is by no means straightforward.

The development of a wax layer on the interior wall of a circular pipe transporting heated oil

In this article we develop a simple model to describe the evolution of a depositional wax layer on the inner surface of a circular pipe transporting heated oil, which contains dissolved wax. When the outer pipe surface is cooled sufficiently, the growth of a wax layer is initiated on the inner pipe wall, and this evolves to a saturated steady state thickness. The model proposed is based on fundamental balances of heat flow from the oil, into the wax layer, and across the pipe wall. We present an analysis of the model, examine a relevant asymptotic limit in which the full details of the solution to the model are available and develop an efficient numerical method (based on the method of fundamental solutions) for producing approximations of the model solution. The mathematical structure of the model is that of a free boundary evolution problem of generalised Stefan type. © The Author, 2014.

The development of a wax layer on the interior wall of a circular pipe transporting heated oil

In this article we develop a simple model to describe the evolution of a depositional wax layer on the inner surface of a circular pipe transporting heated oil, which contains dissolved wax. When the outer pipe surface is cooled sufficiently, the growth of a wax layer is initiated on the inner pipe wall, and this evolves to a saturated steady state thickness. The model proposed is based on fundamental balances of heat flow from the oil, into the wax layer, and across the pipe wall. We present an analysis of the model, examine a relevant asymptotic limit in which the full details of the solution to the model are available and develop an efficient numerical method (based on the method of fundamental solutions) for producing approximations of the model solution. The mathematical structure of the model is that of a free boundary evolution problem of generalised Stefan type. © The Author, 2014.