A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

The NATO III 5 MHz Distribution System

A high performance 5 MHz distribution system is described which has extremely low phase noise and jitter characteristics and provides multiple buffered outputs. The system is completely redundant with automatic switchover and is self-testing. Since the 5 MHz reference signals distributed by the NATO III distribution system are used for up-conversion and multiplicative functions, a high degree of phase stability and isolation between outputs is necessary. Unique circuit design and packaging concepts insure that the isolation between outputs is sufficient to quarantee a phase perturbation of less than 0.0016 deg when other outputs are open circuited, short circuited or terminated in 50 ohms. Circuit design techniques include high isolation cascode amplifiers. Negative feedback stabilizes system gain and minimizes circuit phase noise contributions. Balanced lines, in lieu of single ended coaxial transmission media, minimize pickup

Ordered and disordered dynamics in monolayers of rolling particles

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles with an offset center of mass and a non-isotropic inertia tensor. The rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface, preventing application of the standard tools of statistical mechanics. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We also investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature

PSP resins, new materials which can be hardened by thermal treatment for use in composite materials resistant to heat and fire

A class of easy-to-prepare heterocyclic-aromatic polymers which can be used for matrices in reinforced laminates is described. These polymers can be cured after B-staging with very little evolution of volatile materials, and they retain a low melt-viscosity which leads to low-void laminates. Resins are stable at temperatures below 150 C. Properties of composites with various reinforcements, in particular carbon-fiber unidirectional laminates, are described, and the fire behavior of PSP-glass laminates is reported