After the second recent Paris bombing, close to the Arc de Triomphe on 17 August, new security measures were introduced at all main railway stations. From yesterday, the inspection trains were to be double-manned, with a crew member detailed to watch specifically for obstacles.Officials in the region introduced additional security measures, announcing both mobile and fixed patrols along rail lines, air surveillance, and other measures left undisclosed.The possibility of an attack on a TGV has been at the back of the French authorities’ minds for some time. The device also was not detected by the inspection train that checks the track at the start of each day. But it did not say that such a link had been excluded.
The device was spotted by the driver of a Lyons-Nantes express on Saturday morning, and all traffic on the route was stopped while the bomb was defused and the line checked. A fault in the triggering mechanism was said to have prevented it from exploding.As many as 15 trains were said to have passed the place where the bomb was planted, close to one of the biggest junctions in the TGV network, before it was seen.

Paris – Security precautions were reinforced on French railways yesterday, one of the busiest days for the country’s transport network, after a gas cylinder packed with 25kg of explosives was found on a high- speed train (TGV) line just north of Lyons, writes Mary Dejevsky. The Interior Ministry said no link had been established between the bomb and the two recent explosions in Paris which killed seven people and injured more than 100. He and his second wife Natalia were a joyous couple with many friends from all over the world. He was an exceptional man in another way, being the longest surviving diabetic in Britain, who had regularly injected himself since he was a teenager; indeed he was something of a medical specimen. He was about 6ft tall, moving slowly, smiling slightly, often with a pipe in his mouth, and speaking so that every word counted, with surprisingly strong views on science in all its aspects. Benjamin was a great supporter of scientific and academic communities; he supported the International Centre for Theoretical Physics in Trieste for its work for Third World young scientists; as President of the UK National Conference of University Professors he stimulated public debate in the hope that the government would recognise publicly and materially the value to Britain of its universities; he persuaded those running the annual British Theoretical Mechanics Colloquia to broaden their mathematical appeal and rename them the British Applied Mathematics Colloquia, the first being held in Oxford in 1991; and finally as a Fellow of the Royal Society, he was twice a member of Council and gave the Bakerian Lecture in 1992.Brooke Benjamin had a most attractive aura – wise, sensitive and having a touch of mystery – in fact a bit of a Cheshire cat. He also returned to a number of the hydrodynamic problems he had studied earlier in his career, on vortex breakdown, bubbles and others, but now approaching the problems with more general and powerful mathematical apparatus.He had a number of visiting appointments abroad, but he returned most often to Pennsylvania State University, where he celebrated his 60th birthday at a symposium in his honour.

He took an active interest in the turbulent politics of the Essex campus, as well as conducting the university choir.On his election to the Sedleian chair at the Mathematical Institute in Oxford in 1979, and a Fellowship at Queen’s College, Benjamin continued the fruitful interaction with those experimenting on very sensitive flows, especially his close collaborator Dr T Mullin. There he set up the Fluid Mechanics Research Institute, with a particular aim of showing how more abstract mathematical analysis could really contribute to understanding well-defined but difficult experimental problems; such as why, as concentric cylinders rotate, the flow between them sets up slow eddying motions that have so many and such sensitive flow patterns. Taylor, and winnowed by the ferocious arguments of famous Friday-afternoon seminars.However, despite his brilliance, Benjamin did not find his research easy; he was always focusing on really tough, but well-defined, problems. In the warm summer of 1964 he and his student Jim Feir were struggling to make perfect sinusoidal water waves travel down the new 10m-long wave tank set alongside the brassy old steam engines in the Thermo Lab.Despite ever finer electronic and mechanical control of the harmonic motion of the wave maker, the initially regular wave train would keep spawning higher harmonics along the tank.

The penny dropped – this was the discovery of the fundamental Benjamin-Feir “side-band” instability of all steep waves.Benjamin’s teaching of undergraduates at Cambridge was rather minimal, but no one who attended can forget his slow entry into a lecture-room, the precise wiping of the board, the ceremonial breaking of chalk, the elegant thin writing with serifs on the letters, and his quiet, economical explanations as he led his class through the analysis of water waves.In 1970 he left for a chair in Mathematics at Essex University. He helped set up a new fluid mechanics laboratory there in the old Press Building in 1964 and was appointed a Reader in 1967.During this period he widened his interests in hydrodynamical problems as an active member of the illustrious group of researchers drawn together by G.K Batchelor and G.I. He had already published the first of his papers, on the emerging topic of non-linear effects on steep water waves, with James Lighthill, which led to his appointment to the specially created post of Assistant Director of Research, held jointly between the Engineering Department and the embryonic Department of Applied Mathematics and Theoretical Physics. Benjamin pioneered the way, despite significant scepticism at Cambridge and elsewhere, for applied mathema- ticians to ask and answer more general questions, now that computers can provide more of the numerical answers.On the basis of his thesis he was elected to a Fellowship at King’s College in 1955. One might trace over the years the movement of his mathematics towards more abstractness in relation to the growing capacity of electronic computers to calculate flows with ever greater detail. Benjamin was hooked and stayed to work with Binnie, on a new subject for the laboratory, the formation of the tiny “cavitation” bubbles that form in high-speed water flow and their sudden collapse; they used electronics to trigger the bubbles and to take remarkable high-speed photographs of individual bubbles.A characteristic feature of the elegant theories Benjamin built on these experiments, and on his other studies of “avalanche-like” gravity currents, steep sub-surface “internal” waves in the ocean, and swirling flows, was the use of appropriate averages (in fact integrals of mathematical functions of the velocity and pressure over spatial volumes), to explain the underlying principles of a hydrodynamic problem.His research led him to pose questions about flows in ever more general and abstract terms, beginning with engineering questions such as the total energy or impulse of the flow, and later moving to questions about whether a particular type of flow can exist or not.