UK Nonlinear News , February 1997.

Professor Peter Gray, FRS

In December 1974 a Faraday Symposium of the Chemical Society was held in London (number 9, to be precise, published with the general discussions that took place, in 1975). The subject was " Physical Chemistry of Oscillatory Phenomena". About 120 Fellows of the Faraday Division and visitors from overseas attended the meeting. Although this was not the first recognition of the generality of non-linear phenomena in science - Prigogine and co-workers had begun to sow those seeds earlier - it was probably the first international gathering of scientists from a number of disciplines to share their knowledge and experience of oscillatory phenomena. Peter Gray was a principal organiser of this meeting and a central participant throughout.

In August 1996 a special issue of Faraday Transactions of the Royal Society of Chemistry was published (Faraday Transactions 92, 2825 - 2996 (1996)), entitled "Chemical Instabilities and Combustion". It comprises a collection of refereed papers written by colleagues and associates throughout the world to celebrate Peter's 70th paper. It also marks Peter's formal retirement as Master of Gonville and Caius College, Cambridge, but definitely not his retirement from academic life and contributions to the learned Societies of which he is a highly respected and valued member.

Only a few of the names are common to both publications, which testifies to the ever expanding influence that Peter has had over more than two decades within the scientific community interested in non-linear dynamics. Peter's contributions evolved from experimental and theoretical studies in gas-phase kinetics and combustion. Seminal work on thermal ignition (the simplest of all criticalities, arising from thermal feedback and the interplay between the heat release and heat loss rates from chemical reactions) were published in the 1960s. There followed a very exciting period of experimental and theoretical investigations of the oscillatory cool flame phenomena associated with gaseous oxidation of hydrocarbons.

The credits here must be shared jointly by "the two Grays". The timely arrival of Brian Gray in Peter's department in Leeds University - hotfoot from California with his remarkable insight into "thermokinetic interactions", which he was developing with Harry Yang - led to a remarkably fruitful and enjoyable association during which the notion of the existence of "unstable oscillatory states" was released upon an unsuspecting and (dare I say it, a rather ill-prepared) chemical kinetic audience. I had the privilege of exposure to those "new" ideas first hand, and together at Leeds, we illustrated how these states could arise in chain branching free radical reactions, when the appropriate thermal interactions also took place. Chemical engineers had already begun to understand the, closely related, chemical reactor theory, stemming largely from the work of Amundsen and Aris, but the lively interactions of combustion chemists and chemical engineers were not as well formed then as they are today

Peter Gray's interest and activity in non-linear dynamics, largely in the context of temporal phenomena in the spatially uniform environment, flourished through the 1970s. Gas-phase kinetics continued to dominate the experimental front with the development of the small-scale, well-stirred flow reactor (CSTR), contemporary with similar work in several other labs. Attention was turned to the H2 + O2 and CO + O2 reactions, from which the understanding of chain branching theory had originally emerged in the 1930s. As quite strongly exothermic reactions, both of these systems exhibit interesting non-isothermal phenomena, and these were studied experimentally and interpreted both analytically and numerically. However, under very carefully controlled conditions the CO + O2 system also displays isothermal oscillations. These phenomena were studied extensively in Leeds in the period 1975 - 85 (Chapter 14, Isothermal oscillations and relaxation ignitions in gas-phase reactions: the oxidation of carbon monoxide and hydrogen, Peter Gray and Stephen Scott, in Oscillations and Travelling Waves in Chemical Systems, eds. R.J. Field and M. Burger, Wiley, New York, 1985).

No doubt the kinetic simplicity of the gas-phase oscillators, certainly relative to that of the isothermal solution phase systems which exhibit such richness of non-linear behaviour, spurred Peter into theoretical investigations of the simplest kinetic structures from which oscillations and other instabilities could emerge. This interest coincided with another very happy, timely and long-standing association, namely that with Stephen Scott. Throughout the 1980s there was an astonishingly prolific period from which came remarkably lucid insights into stability criteria, bifurcation phenomena and the enormously rich patterns of behaviour that are possible through the elegantly simple kinetic interactions of the "Gray and Scott models". Direct interests in spatial structures were born in this period, and the main achievements culminated in publication, in 1990, of the text book Chemical oscillations and Instabilities, by P. Gray and S.K. Scott (Oxford University Press). Although at this point Peter had succumbed to the prestigious distinction of having been invited to leave Leeds and become Master of his Cambridge College, Gonville and Caius, it did not constitute a swansong to scientific interest and endeavour. Peter has extended his exploration of non-linear interactions in simple kinetic systems, especially with spatial structure in mind. He continues to be an active participant at meetings throughout the world.

Throughout his career Peter has been a colleague, mentor and friend to an enormous number of people, and many lives have been enriched by this delightful association. Much of his strength and support came from his wife Barbara, who also befriended so many of the people involved in Peter's life. Barbara's death in 1992 was a great sadness, but the support remains through Peter's family, and added to this most recently has been Peter's remarriage to Rachel, a very long-standing family friend. Many academic distinctions and honours have been bestowed on Peter throughout his career.

The principal themes of the Faraday Discussions in 1974 were A, Inorganic Oscillators; B, Thermokinetic Oscillators; C, Membranes, Heterogeneous and Biological Systems; D, Theory of Excitable Media. Related topics have exercised (different) academic minds in the tributes to Peter Gray in 1996, encapsulated in a diverse range of contributions including reaction-diffusion systems of various kinds, behaviour in CSTRs, excitable media, and combustion processes in solids and gases. Perhaps one of the most striking, common features of these publications, that has always been strongly fostered by Peter, is evidence of the strength of the interaction between experimental and theoretical studies of non-linear dynamical systems.

John Griffiths ( School of Chemistry, University of Leeds.

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