The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimization problem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem; an intuitive picture of how to solve it, based on motion of quasiparticles; and a fast linear optimization method with a reduced memory requirement. The procedure has been tested for N up to 200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript figures, accepted by Phys.Rev.B to be published together with cond-mat/970722

Cylindrically and toroidally symmetric solutions with a cosmological constant

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and Tian. In particular, when the cosmological constant is positive, the spacetimes have toroidal symmetry. One of the two curvature singularities can be removed by matching the Linet-Tian vacuum solution across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. Some other properties and limiting cases of these space-times are also described, together with their generalisation to higher dimensions.Comment: 4 pages, 2 figures. To appear in the Proceedings of The Spanish Relativity Meeting (ERE2010), Journal of Physics: Conference Serie

Ultra-fine beryllium powder by amalgam process Progress report, period ending 31 Oct. 1966

Metallurgical evaluation of beryllium powdered metal, and electron microscope studies of agglomerate particle size

Positionally dependent ^(15)N fraction factors in the UV photolysis of N_2O determined by high resolution FTIR spectroscopy

Positionally dependent fractionation factors for the photolysis of isotopomers of N_2O in natural abundance have been determined by high resolution FTIR spectroscopy at three photolysis wavelengths. Fractionation factors show clear 15N position and photolysis wavelength dependence and are in qualitative agreement with theoretical models but are twice as large. The fractionation factors increase with photolysis wavelength from 193 to 211 nm, with the fractionation factors at 207.6 nm for ^(14)N^(15)N^916)O, ^(15)N^(14)N^(16)O and ^(14)N^(14)N^(18)O equal to −66.5±5‰,−27.1±6‰ and −49±10‰, respectively

Impulsive spherical gravitational waves

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the 2-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary non-linear holomorphic transformation. Using 2-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a world-line with constant acceleration

The VLA Galactic Plane Survey

The VLA Galactic Plane Survey (VGPS) is a survey of HI and 21-cm continuum emission in the Galactic plane between longitude 18 degrees 67 degr. with latitude coverage from |b| < 1.3 degr. to |b| < 2.3 degr. The survey area was observed with the Very Large Array (VLA) in 990 pointings. Short-spacing information for the HI line emission was obtained by additional observations with the Green Bank Telescope (GBT). HI spectral line images are presented with a resolution of 1 arcmin x 1 arcmin x 1.56 km/s (FWHM) and rms noise of 2 K per 0.824 km/s channel. Continuum images made from channels without HI line emission have 1 arcmin (FWHM) resolution. VGPS images are compared with images from the Canadian Galactic Plane Survey (CGPS) and the Southern Galactic Plane Survey (SGPS). In general, the agreement between these surveys is impressive, considering the differences in instrumentation and image processing techniques used for each survey. The differences between VGPS and CGPS images are small, < 6 K (rms) in channels where the mean HI brightness temperature in the field exceeds 80 K. A similar degree of consistency is found between the VGPS and SGPS. The agreement we find between arcminute resolution surveys of the Galactic plane is a crucial step towards combining these surveys into a single uniform dataset which covers 90% of the Galactic disk: the International Galactic Plane Survey (IGPS). The VGPS data will be made available on the World Wide Web through the Canadian Astronomy Data Centre (CADC).Comment: Accepted for publication in The Astronomical Journal. 41 pages, 13 figures. For information on data release, colour images etc. see http://www.ras.ucalgary.ca/VGP

The Paradoxical Forces for the Classical Electromagnetic Lag Associated with the Aharonov-Bohm Phase Shift

The classical electromagnetic lag assocated with the Aharonov-Bohm phase shift is obtained by using a Darwin-Lagrangian analysis similar to that given by Coleman and Van Vleck to identify the puzzling forces of the Shockley-James paradox. The classical forces cause changes in particle velocities and so produce a relative lag leading to the same phase shift as predicted by Aharonov and Bohm and observed in experiments. An experiment is proposed to test for this lag aspect implied by the classical analysis but not present in the currently-accepted quantum topological description of the phase shift.Comment: 8 pages, 3 figure

The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

Exploring a rheonomic system

A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The non-conservative system possess a Lagrangian not explicitly dependent on time and consequently there is a Jacobi's integral. The Lagrange undetermined multiplier method is used as a complement to obtain a few interesting conclusion