Piles of piles: An inter-country comparison of nuclear pile development during World War II

Between the time of the discovery of nuclear fission in early 1939 and the end of 1946, approximately 90 nuclear piles were constructed in six countries. These devices ranged from simple graphite columns containing neutron sources but no uranium to others as complex as the water-cooled 250-megawatt plutonium production reactors built at Hanford, Washington. This paper summarizes and compares the properties of these piles.Comment: 45 pages, 9 figure

Numerically Integrating Irregularly-spaced (x, y) Data

This article describes a computer program for numerically integrating under a y(x) curve of experimental data where the abscissa values are not equally-spaced. This technique is based on fitting parabolas to successive groups of three data points, and may be regarded as a generalization of Simpson’s rule

Rigorous Real-Time Feynman Path Integral for Vector Potentials

we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the $L^2$ transition probability amplitude via improper Riemann integrals. Our formulation will hold for vector potential Hamiltonian for which its potential and vector potential each carries at most a finite number of singularities and discontinuities

Quantum Spin Dynamics VIII. The Master Constraint

Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the non -- Lie -- algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the Master Constraint Operator was derived. In this paper we close this gap and prove that the quadratic form is closable and thus stems from a unique self -- adjoint Master Constraint Operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.Comment: 19p, no figure

Natural boundaries for the Smoluchowski equation and affiliated diffusion processes

The Schr\"{o}dinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994

Characterizing K2 planet discoveries : a super-Earth transiting the bright K dwarf HIP 116454

We report the first planet discovery from the two-wheeled Kepler (K2) mission: HIP 116454 b. The host star HIP 116454 is a bright (V = 10.1, K = 8.0) K1 dwarf with high proper motion and a parallax-based distance of 55.2 ± 5.4 pc. Based on high-resolution optical spectroscopy, we find that the host star is metal-poor with [Fe/H] =–0.16 ± 0.08 and has a radius R = 0.716 ± 0.024 R ☉ and mass M = 0.775 ± 0.027 M ☉. The star was observed by the Kepler spacecraft during its Two-Wheeled Concept Engineering Test in 2014 February. During the 9 days of observations, K2 observed a single transit event. Using a new K2 photometric analysis technique, we are able to correct small telescope drifts and recover the observed transit at high confidence, corresponding to a planetary radius of pR = 2.53 ± 0.18 R ⊕. Radial velocity observations with the HARPS-N spectrograph reveal a 11.82 ± 1.33 M ⊕ planet in a 9.1 day orbit, consistent with the transit depth, duration, and ephemeris. Follow-up photometric measurements from the MOST satellite confirm the transit observed in the K2 photometry and provide a refined ephemeris, making HIP 116454 b amenable for future follow-up observations of this latest addition to the growing population of transiting super-Earths around nearby, bright stars.Publisher PDFPeer reviewe