La Pointe Saint Mathieu, Brittany, France

The "Pointe Saint Mathieu" is one of the most westerly continental landmarks of France. The promontory is located at the entrance of the "Goulet de la Rade de Brest", that is the entrance channel of the harbour of Brest in Brittany (France). It marks also the Southern end of the "Chenal du Four" that is the main navigation channel between the islands of Ouessant, Molène and Béniquet, and Brittany. The "Chenal du Four" is reputed for its dangers. The tidal range is greater than 7 m in spring tides, and the mid-tide current may exceed 5 knots. The Saint Mathieu promontory is equipped with a lighthouse and a semaphore. The former is located in the ruins of an old monastery, founded during the 6th century AD by Saint Tanguy. The present ruins are the remnants of buildings from the 11th to 15th centuries. The first lighthouse was installed in 1689, although the monks of the monastery used to maintain a signal light since the 1250s. Completed in 1835, the present "Phare de la Pointe Saint-Mathieu" is 37 m high and it reaches 58.8 m above sea level During World War 2, the Pointe Saint Mathieu was defended by a series of concrete fortifications built by the Germans. Some were based upon some earlier French bunker systems, like the coastal battery at the Rospects which included 4 main gun bunkers (4*150 mm, or 2*150 mm & 2*105 mm), an observation bunker on the Western side close to sea, and several smaller structures. There was also the large Kéringar Blockhaus system, near Lochrist, located about 1 km inland and designed for 4 guns of 280 mm. Its command bunker remains a landmark along the main road. All this area was very-heavily bombed between 1943 and 1944, and particularly during the battle of Brest in August-September 1944 ("L'Enfer de Brest").

Exact quantum phase model for mesoscopic Josephson junctions

Starting from the two-mode Bose-Hubbard model, we derive an exact version of the standard Mathieu equation governing the wave function of a Josephson junction. For a finite number of particles N, we find an additional cos 2 phi term in the potential. We also find that the inner product in this representation is nonlocal in phi. Our model exhibits phenomena, such as pi oscillations, which are not found in the standard phase model, but have been predicted from Gross-Pitaevskii mean-field theory.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.