PT symmetry and large-N models

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.Comment: 15 pages, to be published in J. Phys. A special issue on Pseudo Hermitian Hamiltonians in Quantum Physic

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 4: Satellite-1P program for STARS-2P digital computer program

A special data debugging package called SAT-1P created for the STARS-2P computer program is described. The program was written exclusively in FORTRAN 4 for the IBM 370-165 computer, and then converted to the UNIVAC 1108

Modal analysis and dynamic stresses for acoustically excited shuttle insulation tiles

Improvements and extensions to the RESIST computer program developed for determining the normalized modal stress response of shuttle insulation tiles are described. The new version of RESIST can accommodate primary structure panels with closed-cell stringers, in addition to the capability for treating open-cell stringers. In addition, the present version of RESIST numerically solves vibration problems several times faster than its predecessor. A new digital computer program, titled ARREST (Acoustic Response of Reusable Shuttle Tiles) is also described. Starting with modal information contained on output tapes from RESIST computer runs, ARREST determines RMS stresses, deflections and accelerations of shuttle panels with reusable surface insulation tiles. Both programs are applicable to stringer stiffened structural panels with or without reusable surface insulation titles

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 3: Engineer's program manual for STARS-2P digital computer program

Engineering programming information is presented for the STARS-2P (shell theory automated for rotational structures-2P (plasticity)) digital computer program, and FORTRAN 4 was used in writing the various subroutines. The execution of this program requires the use of thirteen temporary storage units. The program was initially written and debugged on the IBM 370-165 computer and converted to the UNIVAC 1108 computer, where it utilizes approximately 60,000 words of core. Only basic FORTRAN library routines are required by the program: sine, cosine, absolute value, and square root

Implementation of elastic-plastic structural analysis into NASTRAN

Elastic-plastic analytic capabilities were incorporated into the NASTRAN program. The present implementation includes a general rigid format and additional bulk data cards as well as to two new modules. The modules are specialized to include only perfect plasticity of the CTRMEN and CROD elements but can easily be expanded to include other plasticity theories and elements. The practical problem of an elastic-plastic analysis of a ship's bracket connection is demonstrated and compared to an equivalent analysis using Grumman's PLANS program. The present work demonstrates the feasibility of incorporating general elastic-plastic capabilities into NASTRAN

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors

Non-axisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow

We study the stability of cylindrical Taylor-Couette flow in the presence of azimuthal magnetic fields, and show that one obtains non-axisymmetric magnetorotational instabilities, having azimuthal wavenumber m=1. For Omega_o/Omega_i only slightly greater than the Rayleigh value (r_i/r_o)^2, the critical Reynolds and Hartmann numbers are Re_c ~ 10^3 and Ha_c ~ 10^2, independent of the magnetic Prandtl number Pm. These values are sufficiently small that it should be possible to obtain these instabilities in the PROMISE experimental facility.Comment: final version as accepted by Phys Rev Let

Arrested development-A comparative analysis of multilayer corona textures in high-grade metamorphic rocks

Coronas, including symplectites, provide vital clues to the presence of arrested reaction and preservation of partial equilibrium in metamorphic and igneous rocks. Compositional zonation across such coronas is common, indicating the persistence of chemical potential gradients and incomplete equilibration. Major controls on corona mineralogy include prevailing pressure (P), temperature (T ) and water activity (aH2O) during formation, reaction duration (t ) single-stage or sequential corona layer growth; reactant bulk compositions (X) and the extent of metasomatic exchange with the surrounding rock; relative diffusion rates for major components; and/or contemporaneous deformation and strain. High-variance local equilibria in a corona and disequilibrium across the corona as a whole preclude the application of conventional thermobarometry when determining P-T conditions of corona formation, and zonation in phase composition across a corona should not be interpreted as a record of discrete P-T conditions during successive layer growth along the P-T path. Rather, the local equilibria between mineral pairs in corona layers more likely reflect compositional partitioning of the corona domain during steadystate growth at constant P and T . Corona formation in pelitic and mafic rocks requires relatively dry, residual bulk rock compositions. Since most melt is lost along the high-T prograde to peak segment of the P-T path, only a small fraction of melt is generally retained in the residual post-peak assemblage. Reduced melt volumes with cooling limit length scales of diffusion to the extent that diffusion-controlled corona growth occurs. On the prograde path, the low melt (or melt-absent) volumes required for diffusion-controlled corona growth are only commonly realized in mafic igneous rocks, owing to their intrinsic anhydrous bulk composition, and in dry, residual pelitic compositions that have lost melt in an earlier metamorphic event. Experimental work characterizing rate-limiting reaction mechanisms and their petrogenetic signatures in increasingly complex, higher-variance systems has facilitated the refinement of chemical fractionation and partial equilibration diffusion models necessary to more fully understand corona development. Through the application of quantitative physical diffusion models of coronas coupled with phase equilibria modelling utilizing calculated chemical potential gradients, it is possible to model the evolution of a corona through P-T-X-t space by continuous, steady-state and/or sequential, episodic reaction mechanisms. Most coronas in granulites form through a combination of these endmember reaction mechanisms, each characterized by distinct textural and chemical potential signatures with very different petrogenetic implications. An understanding of the inherent petrogenetic limitations of a reaction mechanism model is critical if an appropriate interpretation of P-T evolution is to be inferred from a corona. Since corona modelling employing calculated chemical potential gradients assumes nothing about the sequence in which the layers form and is directly constrained by phase compositional variation within a layer, it allows far more nuanced and robust understanding of corona evolution and its implications for the path of a rock in P-T-X space.EM201

Solar wind observations with the ion composition instrument aboard the ISEE-3 ICE spacecraft

The principal observations obtained by the Ion Composition Instrument (ICI) flown on the ISEE-3/ICE spacecraft, which was in the solar wind from September 1978 to the end of 1982, before being directed to the far magnetotail of the Earth are discussed. Almost continuous observations were made of the abundances of 3He++, 4He++, O6+, O7+, Ne, Si and Fe in various charge states, and of their bulk speeds and temperatures. The results show that there is a strong tendency in the collisionless solar wind for the ionic temperatures to be proportional to the masses. For heavier ions these temperatures exceed typical coronal electron temperatures. 4He++, especially in high speed streams, moves faster than H+, and travels at the same speed as heavier ions. The mechanism leading to this heating and rapid streaming is still not entirely clear

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review