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Sample records for axisymmetric geometry ii

  1. Buckling of a thin, viscous film in an axisymmetric geometry

    NASA Astrophysics Data System (ADS)

    Bhattacharya, S.; Craster, R. V.; Flynn, M. R.

    2013-04-01

    By adapting the Föppl-von Kàrmàn equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wave-number, m⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech. 694, 5-28 (2012)], 10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experiments reveal a limited range of angular velocities wherein waves of either small or large amplitude may be excited. Transition from one to the other regime does not appear to be associated with a notable change in m⋆.

  2. Optimal geometry of an axisymmetric wave energy converter

    NASA Astrophysics Data System (ADS)

    Edwards, Emma; Yue, Dick K. P.; Vortical Flow Research Laboratory Team

    2015-11-01

    There have been a number of theoretical, experimental and pilot-scale studies on wave energy converters with varying shapes and designs, but due to the complex nature of wave-body hydrodynamics, as yet there is not one single three-dimensional shape that is agreed-upon to be optimal for wave power extraction. Our objective is to determine the optimal geometry to maximize power uptake over a spectrum of incident waves. As an initial investigation, we consider an axisymmetric floating wave power extraction device operating in heave. We assume linear wave conditions. The body geometry is described by smooth polynomial basis functions and is allowed to be completely general, subject to simple constraints. We consider a linear power uptake with a fixed damping coefficient (which could be optimized). For each frequency in the spectrum, hydrodynamic coefficients are calculated using a linear frequency-domain panel method. Then, for a specific incident wave spectrum, maximal extractable power is integrated over the entire spectrum. We will discuss the optimal geometry and associated maximum power for different geometrical constraints and wave conditions.

  3. Axisymmetric curvature-driven instability in a model divertor geometry

    SciTech Connect

    Farmer, W. A.; Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California 94550 ; Ryutov, D. D.

    2013-09-15

    A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.

  4. Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry

    SciTech Connect

    Brizard, Alain J.; Duthoit, François-Xavier

    2014-05-15

    The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.

  5. Transient unsteadiness of SWBLI in an axisymmetric geometry

    NASA Astrophysics Data System (ADS)

    Baars, Woutijn J.; Tinney, Charles E.

    2013-11-01

    Shock wave boundary layer interactions (SWBLIs) inside an axisymmetric large area ratio nozzle (Me = 5 . 58) are studied by way of unsteady wall pressure measurements. First, a case of non-transient SWBLI is considered by operating at a nozzle pressure ratio of 28.7, at which a RSS structure forms with trapped annular separation bubbles [Baars et al. AIAA J. 50:1, 2012]. Conditional selection of the data [Erengil and Dolling, AIAA J. 29:5, 1991] resemble similar unsteady features as encountered in nominally 2D interactions. That is, 1) pressures increase in the separated regions as the incipient separation shock translates downstream, and vice versa, which indicates a breathing behavior, and 2) the PDF of the time between shock crossings in the intermittent region is highly skewed, e.g. the shock zero frequency is 33% of the most probable frequency. Secondly, ramping the pressure ratio sweeps the shock system over the transducers and allows the study of transient SWBLI. Time-frequency analyses reveal global features of the unsteady wall signatures, such as low-frequency oscillations in separated regions, and it is identified that nozzle shut-downs are more energetic than start-ups. Post Doctoral Research Fellow.

  6. Statistical mechanics of Beltrami flows in axisymmetric geometry: theory reexamined.

    PubMed

    Naso, Aurore; Monchaux, Romain; Chavanis, Pierre-Henri; Dubrulle, Bérengère

    2010-06-01

    A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation. The fluctuations are found to be Gaussian, while the mean flow is in a Beltrami state. Furthermore, we show that the maximization of entropy at fixed helicity, angular momentum, and microscopic energy is equivalent to the minimization of macroscopic energy at fixed helicity and angular momentum. This provides a justification of this selective decay principle from statistical mechanics. These theoretical predictions are in good agreement with experiments of a von Kármán turbulent flow and provide a way to measure the temperature of turbulence and check fluctuation-dissipation relations. Relaxation equations are derived that could provide an effective description of the dynamics toward the Beltrami state and the progressive emergence of a Gaussian distribution. They can also provide a numerical algorithm to determine maximum entropy states or minimum energy states. PMID:20866533

  7. Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry

    SciTech Connect

    Duthoit, F.-X.; Brizard, A. J.; Hahm, T. S.

    2014-12-15

    Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)] accurately.

  8. On the prediction of swirling flowfields found in axisymmetric combustor geometries

    NASA Technical Reports Server (NTRS)

    Rhode, D. L.; Lilley, D. G.; Mclaughlin, D. K.

    1981-01-01

    The paper reports research restricted to steady turbulence flow in axisymmetric geometries under low speed and nonreacting conditions. Numerical computations are performed for a basic two-dimensional axisymmetrical flow field similar to that found in a conventional gas turbine combustor. Calculations include a stairstep boundary representation of the expansion flow, a conventional k-epsilon turbulence model and realistic accomodation of swirl effects. A preliminary evaluation of the accuracy of computed flowfields is accomplished by comparisons with flow visualizations using neutrally-buoyant helium-filled soap bubbles as tracer particles. Comparisons of calculated results show good agreement, and it is found that a problem in swirling flows is the accuracy with which the sizes and shapes of the recirculation zones may be predicted, which may be attributed to the quality of the turbulence model.

  9. Predictions and measurements of isothermal flowfields in axisymmetric combustor geometries. Ph.D. Thesis. Final Report

    NASA Technical Reports Server (NTRS)

    Rhodes, D. L.; Lilley, D. G.

    1985-01-01

    Numerical predictions, flow visualization experiments and time-mean velocity measurements were obtained for six basic nonreacting flowfields (with inlet swirl vane angles of 0 (swirler removed), 45 and 70 degrees and sidewall expansion angles of 90 and 45 degrees) in an idealized axisymmetric combustor geometry. A flowfield prediction computer program was developed which solves appropriate finite difference equations including a conventional two equation k-epsilon eddy viscosity turbulence model. The wall functions employed were derived from previous swirling flow measurements, and the stairstep approximation was employed to represent the sloping wall at the inlet to the test chamber. Recirculation region boundaries have been sketched from the entire flow visualization photograph collection. Tufts, smoke, and neutrally buoyant helium filled soap bubbles were employed as flow tracers. A five hole pitot probe was utilized to measure the axial, radial, and swirl time mean velocity components.

  10. A 'turbulent spot' in an axisymmetric free shear layer. II

    NASA Astrophysics Data System (ADS)

    Hussain, A. K. M. F.; Kleis, S. J.; Sokolov, M.

    1980-05-01

    The paper considers a turbulent spot in an axisymmetric free shear layer induced by a spark triggered in the boundary layer. The spot was educed by the method of iterative alignment of individual realizations through maximization of cross-relation between individual realizations and ensemble average. The dynamics of the turbulent mixing-layer spot, whose signature is buried in the large-amplitude random fluctuations, is much more complicated than that of the boundary layer spot. The spacing between sparks was so chosen that at a measurement station the passage time of a spot was less than 4% of the interval between the spots; thus, there was no interaction between two induced spots, and on the front or the back of the spot, the phase-average properties approach the constant time-mean values. It is shown that the spot structure plays a dominant role in entrainment and vorticity transport, and that the coherent (spot) structure vorticity is not significantly larger than the mixing-layer mean vorticity.

  11. FACET: a radiation view factor computer code for axisymmetric, 2D planar, and 3D geometries with shadowing

    SciTech Connect

    Shapiro, A.B.

    1983-08-01

    The computer code FACET calculates the radiation geometric view factor (alternatively called shape factor, angle factor, or configuration factor) between surfaces for axisymmetric, two-dimensional planar and three-dimensional geometries with interposed third surface obstructions. FACET was developed to calculate view factors for input to finite-element heat-transfer analysis codes. The first section of this report is a brief review of previous radiation-view-factor computer codes. The second section presents the defining integral equation for the geometric view factor between two surfaces and the assumptions made in its derivation. Also in this section are the numerical algorithms used to integrate this equation for the various geometries. The third section presents the algorithms used to detect self-shadowing and third-surface shadowing between the two surfaces for which a view factor is being calculated. The fourth section provides a user's input guide followed by several example problems.

  12. A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries

    NASA Technical Reports Server (NTRS)

    Lilley, D. G.; Rhode, D. L.

    1982-01-01

    A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.

  13. A PC-based package for interactive assessment of MHD equilibrium and poloidal field coil design in axisymmetric toroidal geometry

    SciTech Connect

    Kelleher, W.; Steiner, D.

    1989-03-01

    A personal computer system was developed for use in the assessment of magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement in toroidal axisymmetric geometry. This system involves two steps: first MHD equilibrium is calculated with the program PCEQ, then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment using the program PFDESIGN. The PCEQ/PFDESIGN system was used to examine equilibrium for the STARFIRE reactor concept, including the design of two different PFC arrangements. The MHD/PFC calculations agree to within a few percent of mainframe code results, demonstrating the utility and accuracy of PCEQ/PFDESIGN, proving it to be an ideal tool for scoping studies.

  14. Global axisymmetric simulations of two-fluid reconnection in an experimentally relevant geometry

    SciTech Connect

    Murphy, N. A.; Sovinec, C. R.

    2008-04-15

    To address the interplay between local and global effects in magnetic reconnection, axisymmetric numerical simulations for the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)] are performed using the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. The 'pull' and 'push' modes of the device are simulated both with and without two-fluid effects in the generalized Ohm's law. As in experiment, the pull reconnection rate is slowed due to the presence of downstream pressure associated with the outflow. Effects induced by toroidicity include a radially inward drift of the current sheet during pull reconnection and a radially outward displacement of the X-point during push reconnection. These effects result from the inboard side of the current sheet having less volume than the outboard side, facilitating the formation of large scale pressure gradients since the inboard side is more susceptible to a buildup or depletion of density. Toroidicity also leads to asymmetry of the quadrupole field during two-fluid simulations. During pull reconnection, the outboard lobes of the quadrupole typically peak close to the X-point, whereas the inboard quadrupole lobes peak near the flux core surfaces. At experimentally relevant parameters, the reconnection rate is found to depend more on the mode of operation than on the inclusion of two-fluid effects. The current sheet in two-fluid co-helicity simulations tilts due to a Lorentz force associated with the guide field and the outflowing electrons, resulting in asymmetric flow patterns for both ions and electrons. In two-fluid counter-helicity simulations, the Hall effect leads to a radial shift in position of the X-point and an asymmetric outflow pattern, which is examined in terms of separate force-density contributions. In general, asymmetry due to toroidicity or the Hall effect often leads to uneven outflow, which then feeds back on the reconnection process through large scale

  15. PC-based package for interactive assessment of MHD equilibrium and poloidal field coil design in axisymmetric toroidal geometry

    SciTech Connect

    Kelleher, W.P.

    1987-01-01

    In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field.

  16. A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

    NASA Astrophysics Data System (ADS)

    Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

    2013-03-01

    A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

  17. Geometry, Student's Text, Part II, Unit 14.

    ERIC Educational Resources Information Center

    Allen, Frank B.; And Others

    Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…

  18. A panel method study of vortex sheets with special emphasis on sheets of axisymmetric geometry. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Sugioka, I.; Widnall, S. E.

    1985-01-01

    The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report.

  19. Experimental and analytical investigation of axisymmetric supersonic cruise nozzle geometry at Mach numbers from 0.60 to 1.30

    NASA Technical Reports Server (NTRS)

    Carson, G. T., Jr.; Lee, E. E., Jr.

    1981-01-01

    Quantitative pressure and force data for five axisymmetric boattail nozzle configurations were examined. These configurations simulate the variable-geometry feature of a single nozzle design operating over a range of engine operating conditions. Five nozzles were tested in the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.60 to 1.30. The experimental data were also compared with theoretical predictions.

  20. Supersymmetric geometries of IIA supergravity II

    NASA Astrophysics Data System (ADS)

    Gran, Ulf; Papadopoulos, George; von Schultz, Christian

    2015-12-01

    We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor equations impose some mild constraints on the geometry of the spacetime which include the existence of a time-like Killing vector field which leaves the fields and the Killing spinor invariant.

  1. Supermassive Black Holes in Galactic Nuclei with Tidal Disruption of Stars. II. Axisymmetric Nuclei

    NASA Astrophysics Data System (ADS)

    Zhong, Shiyan; Berczik, Peter; Spurzem, Rainer

    2015-09-01

    The tidal disruption (TD) of stars by supermassive central black holes from dense rotating star clusters is modeled by high-accuracy direct N-body simulations. As in a previous paper on spherical star clusters, we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, which are now accorded to several classes of orbits that only occur in axisymmetric systems (short-axis tube and saucer orbits). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss cone in phase space that stems from the fact that the total angular momentum {\\boldsymbol{J}} is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted stars has a conspicuous bimodal structure with a local minimum near the equatorial plane. Outside of the influence radius this dependence is weak. We show that the bimodal structure of orbital parameters can be explained by the presence of two families of regular orbits, namely short-axis tube and saucer orbits. Also, we present the consequences of our results for the loss cone in axisymmetric galactic nuclei.

  2. Absorption of acoustic waves by sunspots. II - Resonance absorption in axisymmetric fibril models

    NASA Technical Reports Server (NTRS)

    Rosenthal, C. S.

    1992-01-01

    Analytical calculations of acoustic waves scattered by sunspots which concentrate on the absorption at the magnetohydrodynamic Alfven resonance are extended to the case of a flux-tube embedded in a uniform atmosphere. The model is based on a flux-tubes of varying radius that are highly structured, translationally invariant, and axisymmetric. The absorbed fractional energy is determined for different flux-densities and subphotospheric locations with attention given to the effects of twist. When the flux is highly concentrated into annuli efficient absorption is possible even when the mean magnetic flux density is low. The model demonstrates low absorption at low azimuthal orders even in the presence of twist which generally increases the range of wave numbers over which efficient absorption can occur. Resonance absorption is concluded to be an efficient mechanism in monolithic sunspots, fibril sunspots, and plage fields.

  3. Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development

    NASA Astrophysics Data System (ADS)

    Mehring, C.; Sirignano, W. A.

    2000-06-01

    The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle") solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup.

  4. Differential geometry based solvation model II: Lagrangian formulation.

    PubMed

    Chen, Zhan; Baker, Nathan A; Wei, G W

    2011-12-01

    Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of

  5. Differential geometry based solvation model II: Lagrangian formulation

    PubMed Central

    Chen, Zhan; Baker, Nathan A.; Wei, G. W.

    2010-01-01

    Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for

  6. Sound generated by instability waves of supersonic flows. I Two-dimensional mixing layers. II - Axisymmetric jets

    NASA Technical Reports Server (NTRS)

    Tam, C. K. W.; Burton, D. E.

    1984-01-01

    An investigation is conducted of the phenomenon of sound generation by spatially growing instability waves in high-speed flows. It is pointed out that this process of noise generation is most effective when the flow is supersonic relative to the ambient speed of sound. The inner and outer asymptotic expansions corresponding to an excited instability wave in a two-dimensional mixing layer and its associated acoustic fields are constructed in terms of the inner and outer spatial variables. In matching the solutions, the intermediate matching principle of Van Dyke and Cole is followed. The validity of the theory is tested by applying it to an axisymmetric supersonic jet and comparing the calculated results with experimental measurements. Very favorable agreements are found both in the calculated instability-wave amplitude distribution (the inner solution) and the near pressure field level contours (the outer solution) in each case.

  7. Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy

    NASA Astrophysics Data System (ADS)

    Pfefferlé, D.; Graves, J. P.; Cooper, W. A.

    2015-05-01

    To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).

  8. XAFS study of copper(II) diethylenetriamine complexes having different coordination geometries

    NASA Astrophysics Data System (ADS)

    Gaur, A.; Klysubun, W.; Joshi, S. K.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.

    2016-05-01

    XAFS of three Cu(II) diethylenetriamine complexes (in crystalline form) having different coordination geometries have been investigated. First complex has distorted tetragonal pyramidal, second has distorted square planar and third has distorted square pyramidal geometry. The difference in coordination geometries has been inferred from the differences in pre-edge peak, rising part of edge and in shape of white line, which are seen clearly in the derivative XANES spectra. The distortion in geometry has been correlated with the intensity of peaks in derivative spectra. These inferences have been corroborated from EXAFS analysis where the different paths have been used in the theoretical fits in R space to show contributions of different scatterers at different distances.

  9. Detailed Decomposition of Galaxy Images II: Fitting Spiral Arms, Bars, and Non-axisymmetric Structures in GALFIT 3.0

    NASA Astrophysics Data System (ADS)

    Peng, Chien Y.; Ho, L. C.; Impey, C. D.; Rix, H. W.

    2007-12-01

    The technique of fitting galaxy light profiles with analytic functions (e.g. de Vaucouleurs, exponential), also known as parametric fitting, has been a useful tool for studying galaxy structure and evolution. It is often used to quantify global properties of galaxies such as luminosity, size, ellipticity, and profile shape in a self-consistent manner. It also allows one to deblend multiple components of a galaxy, e.g. bulge/disk/bar/AGN, or to separate overlapping galaxies in a rigorous and robust way. However, the traditional method of fitting galaxies relies on using ellipsoid models, which is sometimes criticized to argue in favor of non-parametric techniques. In this study, we show that two dimensional image fitting is not fundamentally restricted to using axisymmetric ellipsoid shapes. By breaking from axisymmetry parametrically through the use of Fourier modes, one can better quantify the degree of galaxy irregularity in an intuitive and well-motivated manner. We also introduce a technique that allows one to fit spiral structures in late-type galaxies through the use of coordinate rotation. By comparing with more realistic models now possible, we find that the traditional use of simple ellipsoid models is robust even on irregular and spiral galaxies, because single component fits are by nature large scale averages. However, when it comes to quantifying sub-components of a galaxy, sometimes it is necessary to model structures in detail, such as when performing bulge-to-disk decomposition of galaxies with strong spiral arms, or quantifying the symmetry due to bright (e.g. bulge) and faint (e.g. disk) galaxy sub-components separately. These new techniques are implemented in GALFIT 3.0 (http://www.ociw.edu/ peng/work/galfit/galfit.html ). CYP gratefully acknowledges support from the Plaskett Fellowship (NRC-HIA) and the Institute/Giacconi Fellowship (STScI) programs.

  10. Cobalt(II) complex with new terpyridine ligand: An ab initio geometry optimization investigation

    NASA Astrophysics Data System (ADS)

    Ciesielski, Artur; Gorczyński, Adam; Jankowski, Piotr; Kubicki, Maciej; Patroniak, Violetta

    2010-06-01

    Structural parameters of a complex formed between Co(II), and a terpyridine ligand were investigated using the unrestricted Becke three-parameter hybrid exchange functional combined with the Lee-Yang-Parr correlation functional (B3LYP) with the LANL2DZ, 6-31G(d,p), and 6-31G++(d,p) basis sets applied for geometry optimizations. The computations reveal that frequently used methods, which take into consideration primary and secondary interactions, can often be efficient in optimizing structural geometries of systems based on organic molecules and transition-metal ions.

  11. THREE-DIMENSIONAL GEOMETRIES AND THE ANALYSIS OF H II REGIONS

    SciTech Connect

    Wood, Kenneth; Barnes, J. E.; Ercolano, Barbara; Haffner, L. M.; Reynolds, R. J.; Dale, J.

    2013-06-20

    We compare emission line intensities from photoionization models of smooth and fractal shell geometries for low density H II regions, with particular focus on the low-ionization diagnostic diagram [N II]/H{alpha} versus H{alpha}. Building on previously published models and observations of Barnard's Loop, we show that the observed range of intensities and variations in the line intensity ratios may be reproduced with a three-dimensional shell geometry. Our models adopt solar abundances throughout the model nebula, in contrast with previous one-dimensional modeling which suggested the variations in line intensity ratios could only be reproduced if the heavy element abundances were increased by a factor of {approx}1.4. For spatially resolved H II regions, the multiple sightlines that pierce and sample different ionization and temperature conditions within smooth and fractal shells produce a range of line intensities that are easily overlooked if only the total integrated intensities from the entire nebula model are computed. Our conclusion is that inference of H II region properties, such as elemental abundances, via photoionization models of one-dimensional geometries must be treated with caution and further tested through three-dimensional modeling.

  12. Zn(II) and Hg(II) binding to a designed peptide that accommodates different coordination geometries.

    PubMed

    Szunyogh, Dániel; Gyurcsik, Béla; Larsen, Flemming H; Stachura, Monika; Thulstrup, Peter W; Hemmingsen, Lars; Jancsó, Attila

    2015-07-28

    Designed metal ion binding peptides offer a variety of applications in both basic science as model systems of more complex metalloproteins, and in biotechnology, e.g. in bioremediation of toxic metal ions, biomining or as artificial enzymes. In this work a peptide (HS: Ac-SCHGDQGSDCSI-NH2) has been specifically designed for binding of both Zn(II) and Hg(II), i.e. metal ions with different preferences in terms of coordination number, coordination geometry, and to some extent ligand composition. It is demonstrated that HS accommodates both metal ions, and the first coordination sphere, metal ion exchange between peptides, and speciation are characterized as a function of pH using UV-absorption-, synchrotron radiation CD-, (1)H-NMR-, and PAC-spectroscopy as well as potentiometry. Hg(II) binds to the peptide with very high affinity in a {HgS2} coordination geometry, bringing together the two cysteinates close to each end of the peptide in a loop structure. Despite the high affinity, Hg(II) is kinetically labile, exchanging between peptides on the subsecond timescale, as indicated by line broadening in (1)H-NMR. The Zn(II)-HS system displays more complex speciation, involving monomeric species with coordinating cysteinates, histidine, and a solvent water molecule, as well as HS-Zn(II)-HS complexes. In summary, the HS peptide displays conformational flexibility, contains many typical metal ion binding groups, and is able to accommodate metal ions with different structural and ligand preferences with high affinity. As such, the HS peptide may be a scaffold offering binding of a variety of metal ions, and potentially serve for metal ion sequestration in biotechnological applications. PMID:26040991

  13. Catalytically active lead(ii)-imidazolium coordination assemblies with diversified lead(ii) coordination geometries.

    PubMed

    Naga Babu, Chatla; Suresh, Paladugu; Srinivas, Katam; Sathyanarayana, Arruri; Sampath, Natarajan; Prabusankar, Ganesan

    2016-05-10

    Five Pb(ii)-imidazolium carboxylate coordination assemblies with novel structural motifs were derived from the reaction between the corresponding flexible, semi flexible or rigid imidazolium carboxylic acid ligands and lead nitrate. The imidazolium linker present in these molecules likely plays a triple role such as the counter ion to balance the metal charge, the ligand being an integral part of the final product and the catalyst facilitating carbon-carbon bond formation reaction. These lead-imidazolium coordination assemblies exhibit, variable chemical and thermal stabilities, as well as catalytic activity. These newly prepared catalysts are highly active towards benzoin condensation reactions with good functional group tolerance. PMID:27093629

  14. Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology

    SciTech Connect

    Llorens, J. M.; Wewior, L.; Cardozo de Oliveira, E. R.; Alén, B.; Ulloa, J. M.; Utrilla, A. D.; Guzmán, A.; Hierro, A.

    2015-11-02

    External control over the electron and hole wavefunctions geometry and topology is investigated in a p-i-n diode embedding a dot-in-a-well InAs/GaAsSb quantum structure with type II band alignment. We find highly tunable exciton dipole moments and largely decoupled exciton recombination and ionization dynamics. We also predicted a bias regime where the hole wavefunction topology changes continuously from quantum dot-like to quantum ring-like as a function of the external bias. All these properties have great potential in advanced electro-optical applications and in the investigation of fundamental spin-orbit phenomena.

  15. XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries

    NASA Astrophysics Data System (ADS)

    Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.

    2016-08-01

    X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.

  16. Discretizations of axisymmetric systems

    NASA Astrophysics Data System (ADS)

    Frauendiener, Jörg

    2002-11-01

    In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.

  17. The axisymmetric stellar wind of AG Carinae

    NASA Technical Reports Server (NTRS)

    Schulte-Ladbeck, Regina E.; Clayton, Geoffrey C.; Hillier, D. John; Harries, Tim J.; Howarth, Ian D.

    1994-01-01

    We present optical linear spectropolarimetry of the Luminous Blue Variable AG Carinae obtained after a recent visual brightness increase. The absence of He II lambda 4686 emission, together with the weakening of the He I spectrum and the appearance of Fe lines in the region around 5300 A, confirm that AG Car has started a new excursion across the HR diagram. The H alpha line profile exhibits very extended line wings that are polarized differently in both amount and position angle from either the continuum or the line core. The polarization changes across H alpha, together with variable continuum polarization, indicate the presence of intrinsic polarization. Coexistence of the line-wing polarization with extended flux-line wings evidences that both are formed by electron scattering in a dense wind. The position angle rotates across the line profiles, in a way that presently available models suggest is due to rotation and expansion of the scattering material. AG Car displays very large variations of its linear polarization with time, Delta P approximately 1.2%, indicating significant variations in envelope opacity. We find that the polarization varies along a preferred position angle of approximately 145 deg (with a scatter of +/- 10 deg) which we interpret as a symmetry axis of the stellar wind (with an ambiguity of 90 deg). This position angle is co-aligned with the major axis of the AG Car ring nebula and perpendicular to the AG Car jet. Our observations thus suggest that the axisymmetric geometry seen in the resolved circumstellar environment at various distances already exists within a few stellar radii of AG Car. From the H alpha polarization profile we deduce an interstellar polarization of Q = 0.31%, U = -1.15% at H alpha. The inferred interstellar polarization implies that the intrinsic polarization is not always of the same sign. This indicates either significant temporal changes in the envelope geometry, or it may arise from effects of multiple scattering

  18. Axisymmetric single shear element combustion instability experiment

    NASA Astrophysics Data System (ADS)

    Breisacher, Kevin J.

    1993-06-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.

  19. Axisymmetric single shear element combustion instability experiment

    NASA Technical Reports Server (NTRS)

    Breisacher, Kevin J.

    1993-01-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.

  20. Axisymmetric single shear element combustion instability experiment

    NASA Technical Reports Server (NTRS)

    Breisacher, Kevin J.

    1993-01-01

    The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.

  1. Galaxies, Axisymmetric Systems and Relativity

    NASA Astrophysics Data System (ADS)

    MacCallum, M. A. H.

    2011-06-01

    List of contributors; Preface; Prof. W. B. Bonnor: a biological sketch; Part I. Galaxies and Cosmology: 1. The origin of large scale cosmic structure B. J. T. Jones and P. L. Palmer; 2. The problem of origin of the primordial pertubations and the modern cosmology V. N. Lukash and I. D. Novikov; 3. The automorphism group and field equations for Bianchi universes W. L. Rogue and G. F. R. Ellis; 4. New perspectives on galaxy formation J. Silk; Part II. Axisymmetric Systems: 5. On exact radiative solutions representing finite sources J. Bicak; 6. Proof of a generalized Geroch conjecture I. Hauser and F. J. Ernst; 7. Limits of the double Kerr solution C. Hoenselaers; 8. Non-inheritance of static symmetry by Maxwell fields M. A. H. MacCallum and N. Van den Bergh; 9. Stationary axisymmetric electrovacuum fields in general relativity G. Neugebauer and D. Kramer; 10. An almost conformal approach to axial symmetry Z. Perjes; 11. Conformally stationary axisymmetric space-times J. Winicour; Part III. Relativity: 12. A family of conformally flat space-times having the same curvature tensor in a given co-ordinate frame C. D. Collinson; 13. On the Bell-Szekeres solution for colliding electromagnetic waves J. B. Griffiths; 14. A remark on the Hauser metric A. Held; 15. Numerical relativity by power series R. Penrose; 16. Projective relativity and the equation of motion E. Schmutzer; 17. On generalized equations of goedesic deviation B. F. Schutz; 18. Lobatchevski plane gravitational waves S. T. C. Siklos; 19. Perfect fluid and vacuum solutions of Einstein's field equations with flat 3-dimensional slices H. Stephani and Th. Wolf; 20. Self-similar solutions of Einstein's equations J. Wainwright.

  2. Lagrangian aspects of the axisymmetric Euler equation

    NASA Astrophysics Data System (ADS)

    Preston, Stephen C.; Sarria, Alejandro

    2016-03-01

    In this paper we are interested in geometric aspects of blowup in the axisymmetric three-dimensional (3D) Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and imposing oddness on the vertical component of the flow, we extend some blowup criteria due to Chae, Constantin and Wu related to assumptions on the sign of the pressure Hessian. In addition. we give a geometric interpretation of the results, both in terms of the local geometry along trajectories and in terms of the Riemannian geometry of the volume-preserving diffeomorphism group.

  3. Geometry with Coordinates, Student's Text, Part II, Unit 48. Revised Edition.

    ERIC Educational Resources Information Center

    Allen, Frank B.; And Others

    This is part two of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development…

  4. Axisymmetric flows from fluid injection into a confined porous medium

    NASA Astrophysics Data System (ADS)

    Guo, Bo; Zheng, Zhong; Celia, Michael A.; Stone, Howard A.

    2016-02-01

    We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime

  5. Study of thermoviscous dissipation on axisymmetric wave propagating in a shear pipeline flow confined by rigid wall. Part II. Numerical study

    NASA Astrophysics Data System (ADS)

    Chen, Xiaoqian; Chen, Yong; Huang, Yiyong; Bai, Yuzhu; Hu, Dengpeng; Fei, Shaoming

    2016-03-01

    Axisymmetric acoustic wave propagating in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear mean flow. In Part 2 of this paper, comprehensive analysis of the effects of shear mean flow and acoustic frequency on the features (relative phase velocity and attenuation coefficient) of the acoustic wave are numerically addressed in cases of water and perfect gas respectively. Comparisons between the non-isentropic and isentropic models are provided in details. Meanwhile, discussions of the thermoviscous effects on the acoustic wave between water and perfect gas are given.

  6. Axisymmetric Plume Simulations with NASA's DSMC Analysis Code

    NASA Technical Reports Server (NTRS)

    Stewart, B. D.; Lumpkin, F. E., III

    2012-01-01

    A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.

  7. OD(X/sup 2/II) and SD(X/sup 2/II) from reactions of D atoms with OCS under bulk and precursor geometry limited conditions

    SciTech Connect

    Haeusler, D.; Rice, J.; Wittig, C.

    1987-10-08

    Reactions of D atoms with OCS were studied by 193-nm pulsed laser photolysis of DBr as a nearly monoenergetic D-atom source. Nascent OD(X/sup 2/II) and SD(X/sup 2/II) rotational, vibrational, spin-orbit, and ..lambda..-doublet populations were obtained under single-collision bulk conditions at 300 K. The SD channel is favored energetically (..delta.. H = -43 +/- 13 and 230 +/- 13 kJ mol/sup -1/ for the SD and OD channels, respectively) and is the dominant pathway ((SD)/(OD) = 5 +/- 2). Nascent OD(X/sup 2/II) products were also obtained from a precursor geometry limited (PGL) reaction by using the weakly bound van der Waals complex SCO-DBr. The OD(X/sup 2/II) rotational distributions are the same for both bulk and PGL conditions and can be reproduced by using a statistical model. Due to experimental difficulties, SD(X/sup 2/II) distributions could not be obtained under PGL conditions. The SD(X/sup 2/II) distribution obtained under bulk conditions is very nonstatistical, suggesting that this species is not formed via a long-lived DSCO intermediate complex in which vibrational energy is randomized.

  8. Axisymmetric multiwormholes revisited

    NASA Astrophysics Data System (ADS)

    Clément, Gérard

    2016-06-01

    The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.

  9. Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature

    NASA Astrophysics Data System (ADS)

    Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

    2016-08-01

    We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.

  10. Axisymmetric Coanda-assisted vectoring

    NASA Astrophysics Data System (ADS)

    Allen, Dustin; Smith, Barton L.

    2009-01-01

    An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.

  11. Studies in Mathematics, Volume II. Euclidean Geometry Based on Ruler and Protractor Axioms. Second Revised Edition.

    ERIC Educational Resources Information Center

    Curtis, Charles W.; And Others

    These materials were developed to help high school teachers to become familiar with the approach to tenth-grade Euclidean geometry which was adopted by the School Mathematics Study Group (SMSG). It is emphasized that the materials are unsuitable as a high school textbook. Each document contains material too difficult for most high school students.…

  12. Surface complexation and precipitate geometry for aqueous Zn(II) sorption on ferrihydrite: II. XANES analysis and simulation

    USGS Publications Warehouse

    Waychunas, G.A.; Fuller, C.C.; Davis, J.A.; Rehr, J.J.

    2003-01-01

    X-ray absorption near-edge spectroscopy (XANES) analysis of sorption complexes has the advantages of high sensitivity (10- to 20-fold greater than extended X-ray absorption fine structure [EXAFS] analysis) and relative ease and speed of data collection (because of the short k-space range). It is thus a potentially powerful tool for characterization of environmentally significant surface complexes and precipitates at very low surface coverages. However, quantitative analysis has been limited largely to "fingerprint" comparison with model spectra because of the difficulty of obtaining accurate multiple-scattering amplitudes for small clusters with high confidence. In the present work, calculations of the XANES for 50- to 200-atom clusters of structure from Zn model compounds using the full multiple-scattering code Feff 8.0 accurately replicate experimental spectra and display features characteristic of specific first-neighbor anion coordination geometry and second-neighbor cation geometry and number. Analogous calculations of the XANES for small molecular clusters indicative of precipitation and sorption geometries for aqueous Zn on ferrihydrite, and suggested by EXAFS analysis, are in good agreement with observed spectral trends with sample composition, with Zn-oxygen coordination and with changes in second-neighbor cation coordination as a function of sorption coverage. Empirical analysis of experimental XANES features further verifies the validity of the calculations. The findings agree well with a complete EXAFS analysis previously reported for the same sample set, namely, that octahedrally coordinated aqueous Zn2+ species sorb as a tetrahedral complex on ferrihydrite with varying local geometry depending on sorption density. At significantly higher densities but below those at which Zn hydroxide is expected to precipitate, a mainly octahedral coordinated Zn2+ precipitate is observed. An analysis of the multiple scattering paths contributing to the XANES

  13. The Influence of Environment Geometry on Injury Outcome: II. Lumbosacral Spine

    NASA Astrophysics Data System (ADS)

    Shaibani, Saami J.

    2006-03-01

    It is widely agreed that the type of motor vehicle in which an occupant is situated can sometimes make a noticeable difference in injury potential even when the insult suffered is the same. A simple example might be the same occupant being in a sports car as opposed to a minivan, but such anecdotal experience does not usually help to distinguish the effect of particular features within the same category of vehicle. Other research has addressed the role of environment geometry in neck injury,[1] and this paper adopts the same methodology for the low back. The heights, lengths and angles of the seat cushion and seat back (including head rest) are all examined as descriptors of passenger compartment geometry, and any changes caused by these are determined. Useful results are feasible with the large patient population available even if clear patterns in these are not always present. As in earlier work, there is still the option of finding individual outcomes on a case-by-case basis. [1] The influence of environment geometry on injury outcome: I. Cervical spine, Bull Am Phys Soc, in press (2006).

  14. Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas

    SciTech Connect

    Predebon, I.; Xanthopoulos, P.

    2015-05-15

    Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.

  15. Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas

    NASA Astrophysics Data System (ADS)

    Predebon, I.; Xanthopoulos, P.

    2015-05-01

    Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.

  16. Axisymmetric magnetic gauges

    SciTech Connect

    Wright, B.L.; Alrick, K.R.; Fritz, J.N.

    1994-05-01

    Axisymmetric magnetic (ASM) gauges are useful diagnostic tools in the study of the conversion of energy from underground explosions to distant seismic signals. Requiring no external power, they measure the strength (particle velocity) of the emerging shock wave under conditions that would destroy most instrumentation. Shock pins are included with each gauge to determine the angle of the shock front. For the Non-Proliferation Experiment, two ASM gauges were installed in the ANFO mixture to monitor the detonation wave and 10 were grouted into boreholes at various ranges in the surrounding rock (10 to 64 m from the center of explosion). These gauges were of a standard 3.8-inch-diameter design. In addition, two unique Jumbo ASM gauges (3-ft by 3-ft in cross section) were grouted to the wall of a drift at a range of 65 m. We discuss issues encountered in data analysis, present the results of our measurements, and compare these results with those of model simulations of the experiment.

  17. Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

    NASA Astrophysics Data System (ADS)

    Basovník, M.; Semerák, O.

    2016-08-01

    We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.

  18. Geometry of river networks. II. Distributions of component size and number

    SciTech Connect

    Dodds, Peter Sheridan; Rothman, Daniel H.

    2001-01-01

    The structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon, and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power-law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.

  19. Axisymmetric Liquid Hanging Drops

    ERIC Educational Resources Information Center

    Meister, Erich C.; Latychevskaia, Tatiana Yu

    2006-01-01

    The geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…

  20. Twisted versus braided magnetic flux ropes in coronal geometry. II. Comparative behaviour

    NASA Astrophysics Data System (ADS)

    Prior, C.; Yeates, A. R.

    2016-06-01

    Aims: Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods: A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided topologies. These embedded flux ropes are then evolved using a 3D MHD code. Results: Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality - a phenomenon previously observed in cylindrical configurations. Conclusions: Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a

  1. Axisymmetric annular curtain stability

    NASA Astrophysics Data System (ADS)

    Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian

    2012-06-01

    A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect.

  2. Classification of Stellar Orbits in Axisymmetric Galaxies

    NASA Astrophysics Data System (ADS)

    Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood

    2015-09-01

    It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.

  3. EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY

    SciTech Connect

    Liu, Guilin; Calzetti, Daniela; Hong, Sungryong; Whitmore, Bradley; Chandar, Rupali; O'Connell, Robert W.; Blair, William P.; Cohen, Seth H.; Kim, Hwihyun; Frogel, Jay A.

    2013-12-01

    We present Hubble Space Telescope/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (Hβ, Hα, and Paβ), which we use to investigate the dust extinction in the H II regions. We derive extinction maps with 6 pc spatial resolution from two combinations of hydrogen lines (Hα/Hβ and Hα/Paβ), and show that the longer wavelengths probe larger optical depths, with A{sub V} values larger by ≳1 mag than those derived from the shorter wavelengths. This difference leads to a factor ≳2 discrepancy in the extinction-corrected Hα luminosity, a significant effect when studying extragalactic H II regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground ''dust screen'' assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large (≳100-200 pc) scales, the extinction becomes consistent with a ''dust screen'', suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center (≲2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.

  4. Axi-symmetric patterns of active polar filaments on spherical and composite surfaces

    NASA Astrophysics Data System (ADS)

    Srivastava, Pragya; Rao, Madan

    2014-03-01

    Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.

  5. Non-axisymmetric flow characteristics in centrifugal compressor

    NASA Astrophysics Data System (ADS)

    Wang, Leilei; Lao, Dazhong; Liu, Yixiong; Yang, Ce

    2015-06-01

    The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute. The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions. The results show that the pressure distributionin volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream, which results in the non-axisymmetric flow inside the compressor. The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition, its effect on the upstream flow field is also stronger. Additionally, the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet. In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different. Meanwhile, the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow. The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel, while the low static pressure zone of the volute corresponds to the increase of the mass flow. In small flow condition, the mass flow difference in the blade channel is bigger than that in the large flow condition.

  6. Axisymmetric inlet minimum weight design method

    NASA Technical Reports Server (NTRS)

    Nadell, Shari-Beth

    1995-01-01

    An analytical method for determining the minimum weight design of an axisymmetric supersonic inlet has been developed. The goal of this method development project was to improve the ability to predict the weight of high-speed inlets in conceptual and preliminary design. The initial model was developed using information that was available from inlet conceptual design tools (e.g., the inlet internal and external geometries and pressure distributions). Stiffened shell construction was assumed. Mass properties were computed by analyzing a parametric cubic curve representation of the inlet geometry. Design loads and stresses were developed at analysis stations along the length of the inlet. The equivalent minimum structural thicknesses for both shell and frame structures required to support the maximum loads produced by various load conditions were then determined. Preliminary results indicated that inlet hammershock pressures produced the critical design load condition for a significant portion of the inlet. By improving the accuracy of inlet weight predictions, the method will improve the fidelity of propulsion and vehicle design studies and increase the accuracy of weight versus cost studies.

  7. Modeling the Orion nebula as an axisymmetric blister

    NASA Technical Reports Server (NTRS)

    Rubin, R. H.; Simpson, J. P.; Haas, M. R.; Erickson, E. F.

    1991-01-01

    The ionized gas in the Orion nebula is examined by means of axisymmetric modeling that is based on observational data from the ionized, neutral, and molecular regions. Nonsymmetrical features are omitted, radial dependence from the Trapezium is assumed, and azimuthal symmetry in the plane of the sky is used. Stellar properties and abundances of certain elements are described, and these data are used to compare the present axisymmetric-blister model to a previous spherical model. Strong singly-ionized emission that are visible near the Trapezium are found to originate in the ionization-bounded region in the dense Trapezium zone. The model can be more tightly constrained by adding near-IR data on noncentral zones for (Ar II), (AR III), (Ne II), and (S IV). The quadrant with the 'bar' creates an nonsymmetry that influences the observational data, and the model can therefore be improved with the additional data.

  8. Stability of axisymmetric liquid bridges

    NASA Astrophysics Data System (ADS)

    Fel, Leonid G.; Rubinstein, Boris Y.

    2015-12-01

    Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.

  9. Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.

    PubMed

    Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A

    2016-06-01

    A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. PMID:27345204

  10. Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry

    NASA Astrophysics Data System (ADS)

    Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

    2016-06-01

    A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.

  11. Experiments in axisymmetric supersonic jets

    NASA Astrophysics Data System (ADS)

    Moore, Cyrille Dennis

    An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric

  12. Multi-objective optimization of weld geometry in hybrid fiber laser-arc butt welding using Kriging model and NSGA-II

    NASA Astrophysics Data System (ADS)

    Gao, Zhongmei; Shao, Xinyu; Jiang, Ping; Wang, Chunming; Zhou, Qi; Cao, Longchao; Wang, Yilin

    2016-06-01

    An integrated multi-objective optimization approach combining Kriging model and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to predict and optimize weld geometry in hybrid fiber laser-arc welding on 316L stainless steel in this paper. A four-factor, five-level experiment using Taguchi L25 orthogonal array is conducted considering laser power ( P), welding current ( I), distance between laser and arc ( D) and traveling speed ( V). Kriging models are adopted to approximate the relationship between process parameters and weld geometry, namely depth of penetration (DP), bead width (BW) and bead reinforcement (BR). NSGA-II is used for multi-objective optimization taking the constructed Kriging models as objective functions and generates a set of optimal solutions with pareto-optimal front for outputs. Meanwhile, the main effects and the first-order interactions between process parameters are analyzed. Microstructure is also discussed. Verification experiments demonstrate that the optimum values obtained by the proposed integrated Kriging model and NSGA-II approach are in good agreement with experimental results.

  13. A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

    NASA Astrophysics Data System (ADS)

    Jiang, J.; Wang, J. X.

    2007-05-01

    More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric α2-Ω dynamo model is derived to explore the characteristics of the axisymmetric (m = 0) and the first non-axisymmetric (m = 1) modes and to provide a theoretical basis with which to explain the `active longitude', `flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the α2-Ω and the α-Ω models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.

  14. Non-axisymmetric annular curtain stability

    NASA Astrophysics Data System (ADS)

    Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian

    2013-08-01

    A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a

  15. Axisymmetric model of the ionized gas in the Orion Nebula

    NASA Technical Reports Server (NTRS)

    Rubin, R. H.; Simpson, J. P.; Haas, M. R.; Erickson, E. F.

    1991-01-01

    New ionization and thermal equilibrium models for the ionized gas in the Orion Nebula with an axisymmetric two-dimensional 'blister' geometry/density distribution are presented. The HII region is represented more realistically than in previous models, while the physical detail of the microphysics and radiative transfer of the earlier spherical modeling is maintained. The predicted surface brightnesses are compared with observations for a large set of lines at different positions to determine the best-fitting physical parameters. The model explains the strong singly ionized line emission along the lines of sight near the Trapezium.

  16. Transition and mixing in axisymmetric jets and vortex rings

    NASA Technical Reports Server (NTRS)

    Allen, G. A., Jr.; Cantwell, B. J.

    1986-01-01

    A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.

  17. Two-dimensional axisymmetric Child-Langmuir scaling law

    SciTech Connect

    Ragan-Kelley, Benjamin; Verboncoeur, John; Feng Yang

    2009-10-15

    The classical one-dimensional (1D) Child-Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit J{sub CL2} to the theoretical 1D value J{sub CL1} is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results.

  18. Local stability of axisymmetric plumes

    NASA Astrophysics Data System (ADS)

    R. v. K., Chakravarthy; Lesshafft, Lutz; Huerre, Patrick

    2014-11-01

    A linear stability analysis of a forced plume with non-zero momentum at the inlet is performed for Pr = 1 , Re = 100 and Ri near 1. The steady base flow is obtained as a laminar solution of the steady Navier Stokes equations. The base flow asymptotes to a self-similar solution as it evolves downstream. In the non-self-similar regime close to the inlet, both axisymmetric mode (m = 0) and the helical mode (m = 1) are convectively unstable at sufficiently low Richardson number. In the self-similar regime, only the helical mode is absolutely unstable and the axisymmetric mode is stable. Higher helical modes (m >= 2) are seen to be convectively unstable very close to the inlet and become stable as the flow evolves downstream. The transition from convective to absolute instability makes the flow a good candidate for observing steep nonlinear global modes associated with buoyancy. This work is supported by a PhD scholarship from Ecole polytechnique.

  19. Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer

    NASA Astrophysics Data System (ADS)

    Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo

    2015-05-01

    The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.

  20. Geometry matters: inverse cytotoxic relationship for cis/trans-Ru(ii) polypyridyl complexes from cis/trans-[PtCl2(NH3)2].

    PubMed

    Wachter, Erin; Zamora, Ana; Heidary, David K; Ruiz, José; Glazer, Edith C

    2016-08-01

    Two thermally activated ruthenium(ii) polypyridyl complexes, cis-Ru(bpy)2Cl2 and trans-Ru(qpy)Cl2 were investigated to determine the impact of the geometric arrangement of the exchangable ligands on the potential of the compounds to act as chemotherapeutics. In contrast to the geometry requirements for cisplatin, trans-Ru(qpy)Cl2 was 7.1-9.5× more cytotoxic than cis-Ru(bpy)2Cl2. This discovery could open up a new area of metal-based chemotherapeutic research. PMID:27352966

  1. Modeling and simulation of axisymmetric coating growth on nanofibers

    SciTech Connect

    Moore, K.; Clemons, C. B.; Kreider, K. L.; Young, G. W.

    2007-03-15

    This work is a modeling and simulation extension of an integrated experimental/modeling investigation of a procedure to coat nanofibers and core-clad nanostructures with thin film materials using plasma enhanced physical vapor deposition. In the experimental effort, electrospun polymer nanofibers are coated with metallic materials under different operating conditions to observe changes in the coating morphology. The modeling effort focuses on linking simple models at the reactor level, nanofiber level, and atomic level to form a comprehensive model. The comprehensive model leads to the definition of an evolution equation for the coating free surface. This equation was previously derived and solved under a single-valued assumption in a polar geometry to determine the coating morphology as a function of operating conditions. The present work considers the axisymmetric geometry and solves the evolution equation without the single-valued assumption and under less restrictive assumptions on the concentration field than the previous work.

  2. On the existence of certain axisymmetric interior metrics

    SciTech Connect

    Angulo Santacruz, C.; Batic, D.; Nowakowski, M.

    2010-08-15

    One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner-Nordstroem solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g., Gaussian), we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.

  3. MHD Simulations of Plasma Dynamics with Non-Axisymmetric Boundaries

    NASA Astrophysics Data System (ADS)

    Hansen, Chris; Levesque, Jeffrey; Morgan, Kyle; Jarboe, Thomas

    2015-11-01

    The arbitrary geometry, 3D extended MHD code PSI-TET is applied to linear and non-linear simulations of MCF plasmas with non-axisymmetric boundaries. Progress and results from simulations on two experiments will be presented: 1) Detailed validation studies of the HIT-SI experiment with self-consistent modeling of plasma dynamics in the helicity injectors. Results will be compared to experimental data and NIMROD simulations that model the effect of the helicity injectors through boundary conditions on an axisymmetric domain. 2) Linear studies of HBT-EP with different wall configurations focusing on toroidal asymmetries in the adjustable conducting wall. HBT-EP studies the effect of active/passive stabilization with an adjustable ferritic wall. Results from linear verification and benchmark studies of ideal mode growth with and without toroidal asymmetries will be presented and compared to DCON predictions. Simulations of detailed experimental geometries are enabled by use of the PSI-TET code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-TET will also be presented including work to support resistive wall regions within extended MHD simulations. Work supported by DoE.

  4. Strategic guidelines for street canyon geometry to achieve sustainable street air quality—part II: multiple canopies and canyons

    NASA Astrophysics Data System (ADS)

    Chan, Andy T.; Au, William T. W.; So, Ellen S. P.

    The flow field and pollutant dispersion characteristics in a three-dimensional urban street canyon are investigated for various building array geometries. The street canyon in consideration is located in a multi-canopy building array that is similar to realistic estate situations. The pollutant dispersion characteristics are studied for various canopy aspect ratios, namely: the canyon height to width ratio, canyon length to height ratio, canyon breadth ratio and crossroad locations are studied. A three-dimensional field-size canyon has been analysed through numerical simulations using k- ɛ turbulence model. As expected, the wind flow and mode of pollutant dispersion is strongly dependent on the various flow geometric configurations and that the results can be different from that of a single canyon system. For example, it is found that the pollutant retention value is minimum when the canyon height-to-width ratio is approximately 0.8, or that the building height ratio is 0.5. Various rules of thumbs on urban canyon geometry have been established for good pollutant dispersion.

  5. Precision absolute frequency laser spectroscopy of argon II in parallel and antiparallel geometry using a frequency comb for calibration

    NASA Astrophysics Data System (ADS)

    Lioubimov, Vladimir

    A collinear fast ion beam laser apparatus was constructed and tested. It will be used on-line to the SLOW RI radioactive beam facility in RIKEN (Japan) and as in the present experiment for precision absolute frequency measurements of astrophysically important reference lines. In the current work we conducted absolute measurements of spectral lines of Ar+ ions using parallel and antiparallel geometries. To provide a reference for the laser wavelength iodine saturation spectroscopy was used. The precision of this reference was enhanced by simultaneously observing the beat node between the spectroscopy laser and the corresponding mode of a femtosecond laser frequency comb. When performing collinear and anticollinear measurements simultaneously for the laser induced fluorescence, the exact relativistic formula for the transition frequency n0=ncoll˙n anticoll can be applied. In this geometry ion source instabilities due to pressure and anode voltage fluctuation are minimized. The procedure of fluorescence lineshapes fitting is discussed and the errors in the measurements are estimated. The result is n0 = 485, 573, 619.7 +/- 0.3MHz corresponding to Dnn = 6 x 10-10 and is an improvement of two orders of magnitude over the NIST published value.

  6. Internal performance of a hybrid axisymmetric/nonaxisymmetric convergent-divergent nozzle

    NASA Technical Reports Server (NTRS)

    Taylor, John G.

    1991-01-01

    An investigation was conducted in the static test facility of the Langley 16-foot transonic tunnel to determine the internal performance of a hybrid axisymmetric/nonaxisymmetric nozzle in forward-thrust mode. Nozzle cross-sections in the spherical convergent section were axisymmetric whereas cross-sections in the divergent flap area nonaxisymmetric (two-dimensional). Nozzle concepts simulating dry and afterburning power settings were investigated. Both subsonic cruise and supersonic cruise expansion ratios were tested for the dry power nozzle concepts. Afterburning power configurations were tested at an expansion ratio typical for subsonic acceleration. The spherical convergent flaps were designed in such a way that the transition from axisymmetric to nonaxisymmetric cross-section occurred in the region of the nozzle throat. Three different nozzle throat geometries were tested for each nozzle power setting. High-pressure air was used to simulate jet exhaust at nozzle pressure ratios up to 12.0.

  7. A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction

    NASA Technical Reports Server (NTRS)

    Hood, Caroline; Frendi, Abdelkader

    2006-01-01

    This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.

  8. Radiation from Axisymmetric Waveguide Fed Horns

    NASA Technical Reports Server (NTRS)

    Chinn, G. C.; Hoppe, D. J.; Epp, L. W.

    1995-01-01

    Return losses and radiation patterns for axisymmetric waveguide fed horns are calculated with the finite element method (FEM) in conjunction with the method of moments (MoM) and the mode matching technique (MM).

  9. Stability of perturbed geodesics in nD axisymmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Coimbra-Araújo, C. H.; Anjos, R. C.

    2016-09-01

    The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall–Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto–Nagai and Chazy–Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS–Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.

  10. Lie algebra automorphisms as Lie-point symmetries and the solution space for Bianchi type I, II, IV, V vacuum geometries

    NASA Astrophysics Data System (ADS)

    Terzis, Petros A.; Christodoulakis, T.

    2012-12-01

    Lie-group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein’s field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi type IV. The result is the acquisition of the general solution of type IV in terms of sixth Painlevé transcendent PVI, along with the known pp-wave solution. For Bianchi types I, II, V the known entire solution space is attained and very briefly listed, along with two new type V solutions of Euclidean and neutral signature and a type I pp-wave metric.

  11. Variation in DNA binding constants with a change in geometry of ternary copper(II) complexes with N2O donor Schiff base and cyanate or dicyanamide

    NASA Astrophysics Data System (ADS)

    Jana, Subrata; Santra, Ramesh Chandra; Das, Saurabh; Chattopadhyay, Shouvik

    2014-09-01

    Two new copper(II) complexes, [Cu(L)(OCN)] (1) and [CuL(dca)]n (2), where HL = 2-(-(2-(diethylamino)ethylimino)methyl)naphthalen-1-ol, dca = N(CN)2-, have been synthesized and characterized by elemental analysis, IR, UV-VIS spectroscopy and single crystal X-ray diffraction studies. Complex 1 has square planar and complex 2 square pyramidal geometries in solid state around metal centre. Interactions of the complexes with calf thymus DNA (CT DNA) were studied by UV-VIS spectroscopy. Binding constant and site size of interaction were determined. Binding site size and intrinsic binding constant K revealed complex 1 interacted with calf thymus DNA better than complex 2.

  12. Material laws and related uncommon phenomena in the electromagnetic response of type-II superconductors in longitudinal geometry

    NASA Astrophysics Data System (ADS)

    Ruiz, H. S.; Badía-Majós, A.; López, C.

    2011-11-01

    Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component J_{ {c} \\parallel } ) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.

  13. Two field-induced slow magnetic relaxation processes in a mononuclear Co(ii) complex with a distorted octahedral geometry.

    PubMed

    Li, Jing; Han, Yuan; Cao, Fan; Wei, Rong-Min; Zhang, Yi-Quan; Song, You

    2016-05-31

    A distorted octahedral Co(II) complex is reported with homoscorpionate ligands. This complex comprised a field-induced single-molecule magnet, showing two slow relaxation processes under a low dc field (<800 Oe) and only one process under a high dc field (≥800 Oe), which was an unusually discovery for 3d metal ions. On the basis of the ac magnetic data, we show for the first time that one of the slow relaxation processes in the low dc field originates from intermolecular dipolar interactions. Interestingly, the Raman process is predominant in the spin reversal relaxation process. The origin of the behaviours of the complex was elucidated by ab initio calculations. PMID:27180637

  14. Bianisotropic-critical-state model to study flux cutting in type-II superconductors at parallel geometry

    NASA Astrophysics Data System (ADS)

    Romero-Salazar, C.

    2016-04-01

    A critical-state model is postulated that incorporates, for the first time, the structural anisotropy and flux-line cutting effect in a type-II superconductor. The model is constructed starting from the theoretical scheme of Romero-Salazar and Pérez-Rodríguez to study the anisotropy induced by flux cutting. Here, numerical calculations of the magnetic induction and static magnetization are presented for samples under an alternating magnetic field, orthogonal to a static dc-bias one. The interplay of the two anisotropies is analysed by comparing the numerical results with available experimental data for an yttrium barium copper oxide (YBCO) plate, and a vanadium-titanium (VTi) strip, subjected to a slowly oscillating field {H}y({H}z) in the presence of a static field {H}z({H}y).

  15. Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. II. Electrically charged gravitational collapse

    NASA Astrophysics Data System (ADS)

    Nakonieczna, Anna; Yeom, Dong-han

    2016-05-01

    Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.

  16. Colliding Winds in Symbiotic Binary Systems. II. Colliding Winds Geometries and Orbital Motion in the Symbiotic Nova AG Pegasi

    NASA Astrophysics Data System (ADS)

    Kenny, H. T.; Taylor, A. R.

    2007-06-01

    AG Pegasi has been observed at high angular resolution and sensitivity at the Very Large Array (VLA) at 5 GHz in four epochs between 1984 and 1991. Analysis of the radio visibilities indicate that a mass of 4.0+/-0.5×10-5 Msolar is concentrated in the inner nebula and is moving outward at a velocity of 53+/-4 km s-1 (D=600 pc assumed). In order to explain the observed morphology of the inner nebula, a new colliding winds model is derived, which includes the effects of orbital motion (CWo model). Orbital effects cannot be ignored in AG Pegasi since the orbital timescale (2.25 yr; Meinunger 1981) is short compared to the likely timescale of wind collision (symbiotic nova eruption beginning ~1850 Merrill 1959). When these effects are considered, the interaction front between binary stellar winds is wrapped into spiral walls whose density decreases outward with 1/r2. Distinctive geometries are found to arise depending on which wind dominates the interaction, the late-type wind from the symbiotic ``cool component,'' or the high-velocity wind from the ``hot component.'' Application of the CWo model to AG Peg suggests that the observed transient lobe enhancements of the inner nebula arise due to changes in the mass-loss rate from the hot component. Hot component mass-loss rates ranging between 2.1 and 6.0×10-8 Msolar yr-1 are derived. The model is also successful in reproducing the radio spectrum of the central unresolved object of the system. A position angle of -15deg+/-10deg is inferred for the orbital pole as projected on the plane of the sky.

  17. Axisymmetric and three dimensional flow modeling within thermal vapor compressors

    NASA Astrophysics Data System (ADS)

    Sharifi, Navid

    2013-10-01

    Thermal vapor compressor (TVC) is a device for compressing vapor in water-steam cycles and frequently used in desalination systems. Large amounts of useless vapor can be compressed by this device and the efficiency of a desalination unit is effectively enhanced through this process. Motive steam is injected into the TVC through a convergent-divergent nozzle and accelerated to supersonic velocities. The low pressure steam is entrained at the upstream zone and mixed with this highly compressible motive flow within the TVC. In the current study, the flow field of an experimental TVC is scrutinized in both axisymmetric and three-dimensional approaches and compared with experimental measurements. Since the steam collector at the suction surface of the TVC has a curved shape and may undermine the symmetry of the flow on either side of the central axis, the second objective of this study is to reveal the deviation of the symmetric assumption from the real non-symmetric condition of entering steam flow into the TVC. Results show that the presence of a bending at the inlet side has approximately negligible effects on the mixing phenomenon and the flow remains symmetric around the central axis. Hence, there is no need to consider the collector geometry in further simulations and the performance parameters of the TVC would be sufficiently obtained through an axisymmetric method with a substantial reduction in the computational cost and time.

  18. SEAWAT-based simulation of axisymmetric heat transport.

    PubMed

    Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele

    2014-01-01

    Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. PMID:24571415

  19. Radiative transfer in arbitrarily-shaped axisymmetric bodies

    NASA Astrophysics Data System (ADS)

    Nunes, Edmundo Miguel

    2001-08-01

    A mathematical model for evaluating thermal radiative transport in axisymmetric enclosures is presented. Based on the Discrete Exchange Factor (DEF) method, exchange factors between arbitrarily-oriented differential surface/volume ring elements are systematically calculated. The formulation is capable of treating geometrically complex systems including enclosures with shadowing effects ensuing from inner and/or outer obstructing bodies. The model is developed for isotropically scattering participating media. The solutions to several cylindrical media benchmark problems are found to be in excellent agreement with existing solutions in the literature. The solutions to several rocket-nozzle and plug-chamber geometries are presented for a host of geometric conditions and optical thicknesses. In addition, two variants of the DEF method are presented for anisotropically scattering media. The N-bounce method approximates total exchange factors by summing direct and user-designated higher order terms representative of multiple reflections/scattering. The source function approach is an intensity-based method relating the source function (gas leaving intensity) to the surface leaving intensity. The results obtained via these methods are found to be in good agreement with the existing solutions to several axisymmetric benchmark problems. A mathematical formulation is additionally proposed for addressing the effects of nonhomogeneous property distributions. Several nonhomogeneous benchmark problems are solved in an effort to validate the model.

  20. Fast optimization of static axisymmetric shell structures

    NASA Astrophysics Data System (ADS)

    Jacoby, Jeffrey

    An axisymmetric shell optimization procedure is developed which is a fast, user-friendly and practical tool for design use in disciplines including aerospace, mechanical and civil engineering. The shape and thickness of a shell can be optimized to minimize shell mass, mass/volume ratio or stress with constraints imposed on von Mises stress and local buckling. The procedure was created with the aid of the GENOPT optimization development system (Dr. D. Bushnell, Lockheed Missiles and Space Co) and uses the FAST1 shell analysis program (Prof. C. R. Steele, Stanford University) to perform the constraint analysis. The optimization method used is the modified method of feasible directions. The procedure is fast because exact analysis methods allow complex shells to be modelled with only a few large shell elements and still retain a sufficiently accurate solution. This is of particular advantage near shell boundaries and intersections which can have small regions of very detailed variation in the solution. Finite element methods would require many small elements to capture accurately this detail with a resulting increase in computation time and model complexity. Reducing the complexity of the model also reduces the size of the required input and contributes to the simplicity of the procedure. Optimization design variables are the radial and axial coordinates of nodes and the shape parameters and thicknesses of the elements. Thickness distribution within an element can be optimized by specifying the thickness at evenly spaced control points. Spline interpolation is used to provide a smooth thickness variation between the control points. An effective method is developed for reducing the number of required stress constraint equations. Various shells have been optimized and include models for comparison with published results. Shape, thickness and shape/thickness optimization has been performed on examples including a simple aerobrake, sphere-nozzle intersections, ring

  1. Induced stresses due to fluid extraction from axisymmetric reservoirs

    USGS Publications Warehouse

    Segall, P.

    1992-01-01

    Earthquakes can be induced by fluid extraction, as well as by fluid injection. Segall (1989) proposed that poroelastic stresses are responsible for inducing earthquakes associated with fluid extraction. Here, I present methods for computing poroelastic stress changes due to fluid extraction for general axisymmetric reservoir geometries. The results of Geertsma (1973) for a thin disk reservoir with uniform pressure drop are recovered as a special case. Predicted surface subsidence agrees very well with measured leveling changes over the deep Lacq gas field in southwestern France. The induced stresses are finite if the reservoir pressure changes are continuous. Computed stress changes are on the order of several bars, suggesting that the preexisting stress states in regions of extraction induced seismicity are very close to frictional instability prior to production. ?? 1992 Birkha??user Verlag.

  2. Integral-Field Spectroscopy of the Post-Red Supergiant IRC +10420: Evidence for an Axisymmetric Wind

    NASA Astrophysics Data System (ADS)

    Davies, Ben; Oudmaijer, René D.; Sahu, Kailash C.

    2007-12-01

    We present NAOMI/OASIS adaptive-optics-assisted integral-field spectroscopy of the transitional massive hypergiant IRC +10420, an extreme mass-losing star apparently in the process of evolving from a red supergiant toward the Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the star, we study the appearance of the line emission from the inner wind as viewed when reflected off the surrounding nebula. We find that, contrary to previous work, there is strong evidence for wind axisymmetry, based on the equivalent width and velocity variations of Hα and Fe II λ6516. We attribute this behavior to the appearance of the complex line profiles when viewed from different angles. We also speculate that the Ti II emission originates in the outer nebula in a region analogous to the strontium filament of η Carinae, based on the morphology of the line emission. Finally, we suggest that the present-day axisymmetric wind of IRC +10420, combined with its continued blueward evolution, is evidence that the star is evolving toward the B[e] supergiant phase.

  3. Supersonic quasi-axisymmetric vortex breakdown

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

    1991-01-01

    An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

  4. Static internal performance characteristics of two thrust reverser concepts for axisymmetric nozzles

    NASA Technical Reports Server (NTRS)

    Leavitt, L. D.; Re, R. J.

    1982-01-01

    The statis performance of two axisymmetric nozzle thrust reverser concepts was investigated. A rotating vane thrust reverser represented a concept in which reversing is accomplished upstream of the nozzle throat, and a three door reverser concept provided reversing downstream of the nozzle throat. Nozzle pressure ratio was varied from 2.0 to approximately 6.0. The results of this investigation indicate that both the rotating vane and three door reverser concepts were effective static thrust spoilers with the landing approach nozzle geometry and were capable of providing at least a 50 percent reversal of static thrust when fully deployed with the ground roll nozzle geometry.

  5. Kinetically Stabilized Axisymmetric Tandem Mirrors: Summary of Studies

    SciTech Connect

    Post, R F

    2005-02-08

    The path to practical fusion power through plasma confinement in magnetic fields, if it is solely based on the present front-runner, the tokamak, is clearly long, expensive, and arduous. The root causes for this situation lie in the effects of endemic plasma turbulence and in the complexity the tokamak's ''closed'' field geometry. The studies carried out in the investigations described in the attached reports are aimed at finding an approach that does not suffer from these problems. This goal is to be achieved by employing an axisymmetric ''open'' magnetic field geometry, i.e. one generated by a linear array of circular magnet coils, and employing the magnetic mirror effect in accomplishing the plugging of end leakage. More specifically, the studies were aimed at utilizing the tandem-mirror concept in an axisymmetric configuration to achieve performance superior to the tokamak, and in a far simpler system, one for which the cost and development time could be much lower than that for the tokamak, as exemplified by ITER and its follow-ons. An important stimulus for investigating axisymmetric versions of the tandem mirror is the fact that, beginning from early days in fusion research there have been examples of axisymmetric mirror experiments where the plasma exhibited crossfield transport far below the turbulence-enhanced rates characteristic of tokamaks, in specific cases approaching the ''classical'' rate. From the standpoint of theory, axisymmetric mirror-based systems have special characteristics that help explain the low levels of turbulence that have been observed. Among these are the facts that there are no parallel currents in the equilibrium state, and that the drift surfaces of all of the trapped particles are closed surfaces, as shown early on by Teller and Northrop. In addition, in such systems it is possible to arrange that the radial boundary of the confined plasma terminates without contact with the chamber wall. This possibility reduces the

  6. Magneto-hydrodynamically stable axisymmetric mirrorsa)

    NASA Astrophysics Data System (ADS)

    Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.

    2011-09-01

    Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.

  7. Fabrication of Submillimeter Axisymmetric Optical Components

    NASA Technical Reports Server (NTRS)

    Grudinin, Ivan; Savchenkov, Anatoliy; Strekalov, Dmitry

    2007-01-01

    It is now possible to fashion transparent crystalline materials into axisymmetric optical components having diameters ranging from hundreds down to tens of micrometers, whereas previously, the smallest attainable diameter was 500 m. A major step in the fabrication process that makes this possible can be characterized as diamond turning or computer numerically controlled machining on an ultrahigh-precision lathe.

  8. Axisymmetric ideal MHD stellar wind flow

    NASA Technical Reports Server (NTRS)

    Heinemann, M.; Olbert, S.

    1978-01-01

    The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

  9. Optimizing a neutron-beam focusing device for the direct geometry time-of-flight spectrometer TOFTOF at the FRM II reactor source

    NASA Astrophysics Data System (ADS)

    Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.

    2016-04-01

    A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the "chromatic" displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.

  10. Approach to universality in axisymmetric bubble pinch-off

    NASA Astrophysics Data System (ADS)

    Gekle, Stephan; Snoeijer, Jacco H.; Lohse, Detlef; van der Meer, Devaraj

    2009-09-01

    The pinch-off of an axisymmetric air bubble surrounded by an inviscid fluid is compared in four physical realizations: (i) cavity collapse in the wake of an impacting disk, (ii) gas bubbles injected through a small orifice, (iii) bubble rupture in a straining flow, and (iv) a bubble with an initially necked shape. Our boundary-integral simulations suggest that all systems eventually follow the universal behavior characterized by slowly varying exponents predicted by J. Eggers [Phys. Rev. Lett. 98, 094502 (2007)]. However, the time scale for the onset of this final regime is found to vary by orders of magnitude depending on the system in question. While for the impacting disk it is well in the millisecond range, for the gas injection needle universal behavior sets in only a few microseconds before pinch-off. These findings reconcile the different views expressed in recent literature about the universal nature of bubble pinch-off.

  11. Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

    NASA Astrophysics Data System (ADS)

    Stacey, W. M.; Bae, C.

    2015-06-01

    A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ω τ -ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric "neoclassical toroidal viscosity" mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

  12. Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

    SciTech Connect

    Stacey, W. M.; Bae, C.

    2015-06-15

    A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

  13. A simple model of axisymmetric turbulent boundary layers along long thin circular cylinders

    NASA Astrophysics Data System (ADS)

    Jordan, Stephen A.

    2014-08-01

    Useful empirical and semi-empirical models of the turbulent boundary layer (TBL) and skin friction evolution along planar geometries are not applicable for axisymmetric thin cylinder flows. Their dissimilarity is readily detectable once the TBL thickness exceeds the cylinder radius (a). Although several recent empirically based axisymmetric models recognize this fact, their acceptable fidelity is either restrictive or deficient for general applicability. Herein, we correct this deficit by building a simple model for the specific canonical class of axisymmetric turbulent flows along long thin cylinders with a zero streamwise pressure gradient. Streamwise growth of the TBL thickness (δ/a), integral scales [displacement (δ*/a) and momentum thicknesses (θ/a)] and skin friction coefficient (Cf) can be estimated along the cylinder length via the respective axial mean velocity profile in wall units. This profile is given by Spalding's formula with algebraic expressions for the two input parameters (κ, κβ) that cover all turbulent Reynolds numbers. The necessary database for empirically tuning Spalding's parameters entails both experimental measurements and new numerical computations. Our present-day understanding of the axisymmetric TBL is replicated by the simple model where δ/a, δ*/a, and θ/a grow slower than the planar-type flow with Cf comparatively elevating once δ/a > O(1). These differences manifest themselves in the radial impact imposed by the thin cylinder transverse curvature. Interestingly, the axial-based Reynolds numbers Rea ≈ 7500 and a+ ≈ 350 at δ/a ≈ 21 mark earliest signs of a homogeneous streamwise state (constant Cf) near the cylinder wall. Owning a simple model of axisymmetric turbulent flows along thin cylinders eliminates expensive and timely experiments and/or computations. Its practicality targets both the Naval and oceanographic communities.

  14. Axisymmetric, Nonstationary Black Hole Magnetospheres: Revisited

    NASA Astrophysics Data System (ADS)

    Song, Yoo Geun; Park, Seok Jae

    2015-10-01

    An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park & Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.

  15. Attitude stability criteria of axisymmetric solar sail

    NASA Astrophysics Data System (ADS)

    Hu, Xiaosai; Gong, Shengping; Li, Junfeng

    2014-07-01

    Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.

  16. Nonlinear axisymmetric flexural vibration of spherical shells

    NASA Technical Reports Server (NTRS)

    Kunieda, H.

    1972-01-01

    Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.

  17. Magneto-hydrodynamically stable axisymmetric mirrors

    NASA Astrophysics Data System (ADS)

    Ryutov, Dmitri

    2010-11-01

    The achievement of high beta (60%) plasma with near classical confinement in a linear axisymmetric magnetic configuration has sparked interest in the Gas Dynamic Trap concept. The significance of these results is that they can be projected directly to a neutron source for materials testing. The possibility of axisymmetric mirrors (AM) being magneto-hydrodynamically (MHD) stable is also of interest from a general physics standpoint (as it seemingly contradicts to well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a brief summary of classical results (in particular of the Rosenbluth-Longmire theory and of the energy principle as applied to AM) several approaches towards achieving MHD stabilization of the AM will be considered: 1) Employing the favorable field-line curvature in the end tanks; 2) Using the line-tying effect; 3) Setting the plasma in a slow or fast differential rotation; 4) Imposing a divertor configuration on the solenoidal magnetic field; 5) Controlling the plasma dynamics by the ponderomotive force; 6) Other techniques. Several of these approaches go beyond pure MHD and require accounting for finite Larmor radius effects and trapped particle modes. Some illuminative theoretical approaches for understanding axisymmetric mirror stability will be described. Wherever possible comparison of theoretical and experimental results on AM will be provided. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors will be discussed and the constraints on the plasma parameters will be formulated. Prepared by LLNL under Contract DE-AC52-07NA27344.

  18. A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers

    NASA Astrophysics Data System (ADS)

    Fournier, Alexandre; Bunge, Hans-Peter; Hollerbach, Rainer; Vilotte, Jean-Pierre

    2005-04-01

    We present a Fourier-spectral element approach for modeling thermal convection in a rotating axisymmetric container. Following the theory detailed in Bernardi et al. [C. Bernardi, M. Dauge, Y. Maday, Spectral Methods for Axisymmetric Domains, Gauthier-Villars, Paris, 1999], a Fourier expansion of the field variables is performed in the periodic direction, and the resulting collection of meridional problems is discretized by means of a parallel spectral element method. A Gauss-Lobatto-Jacobi (0,1) quadrature, which incorporates the cylindrical radius in its weight, is introduced to avoid a potential degeneracy of the discrete set of equations, due to those nodes located on the axis of symmetry. A second-order timestepping scheme is presented, which treats the Coriolis and viscous forces implicitly. Numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties.

  19. Pinch-off of axisymmetric vortex pairs in the limit of vanishing vortex line curvature

    NASA Astrophysics Data System (ADS)

    Sadri, V.; Krueger, P. S.

    2016-07-01

    Pinch-off of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation ΔR was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing ΔR. The flow was simulated at a jet Reynolds number of 1000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio ( /L Δ R ) in the range 10-20, and gap-to-outer radius ratio ( /Δ R R o ) in the range 0.01-0.1. Contrary to investigations of strictly planar flows, vortex pinch-off was observed for all gap sizes investigated. This difference was attributed to the less constrained geometry considered, suggesting that even very small amounts of vortex line curvature and/or vortex stretching may disrupt the absence of pinch-off observed in strictly planar vortex dipoles.

  20. Solves Poisson's Equation in Axizymmetric Geometry on a Rectangular Mesh

    Energy Science and Technology Software Center (ESTSC)

    1996-09-10

    DATHETA4.0 computes the magnetostatic field produced by multiple point current sources in the presence of perfect conductors in axisymmetric geometry. DATHETA4.0 has an interactive user interface and solves Poisson''s equation using the ADI method on a rectangular finite-difference mesh. DATHETA4.0 uncludes models specific to applied-B ion diodes.

  1. Stabilization of the vertical instability by non-axisymmetric coils

    NASA Astrophysics Data System (ADS)

    Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.

    2016-08-01

    In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10‑3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.

  2. Molecular Geometry.

    ERIC Educational Resources Information Center

    Desseyn, H. O.; And Others

    1985-01-01

    Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…

  3. Non-axisymmetric ultrasonic guided waves for tubing inspection

    NASA Astrophysics Data System (ADS)

    Shin, Hyeon Jae

    1997-11-01

    The purpose of this study is to understand the physical phenomena of wave propagation in hollow cylinders and also to investigate the utility of ultrasonic guided waves in hollow cylinders for nondestructive evaluation purposes. In this document, a theoretical and experimental study of axisymmetric and non-axisymmetric ultrasonic guided wave modes is carried out. Guided wave modes in hollow cylinders are calculated and are represented in phase and group velocity dispersion diagrams based on wave mechanics and the theory of elasticity. Guided wave propagation characteristics and proper mode selection concepts are discussed by analyzing the acoustic fields. Excellent inspection results of using axisymmetric modes for programmed flaws are given. Designs of a bore probe and specifications of a high power tone burst system are given for practical implementation. The work also focuses on an experimental study on the utilization of non-axisymmetric guided waves generated by a non-axisymmetric oblique incident partial loading transducer setup. For complete coverage in tubing inspection with non-axisymmetric guided waves, three dimensional tuning concepts are developed. An experimental study on the relationship between the circumferential loading angle and the generated guided waves was carried out. It is found that a 180 degree partial loading comb transducer set up could generate strong axisymmetric modes. The expected non-axisymmetric guided wave fields are studied by normal mode expansion. The non-axisymmetric source design parameters are discussed for partial uniform pressure loading on the outer boundary of a sample tube.

  4. Preferential axisymmetric field growth in kinematic geodynamo models

    NASA Astrophysics Data System (ADS)

    Livermore, Philip W.; Jackson, Andrew

    2004-11-01

    Earth's magnetic field, generated by fluid motion and inductive processes in Earth's core, has a predominantly axisymmetric dipolar component. Yet indefinite self-excitation of purely axisymmetric fields through any dynamo mechanism is specifically disallowed, begging the question of why the geodynamo sustains this dominant axisymmetric component. By considering a number of different fluid flow models modified from existing studies, we show that axisymmetric fields are consistently the most easily regenerated magnetic fields on short timescales, despite the fact that on long timescales they must die away. We argue that this transient field generation may play an important role in generating Earth's magnetic field, especially in the recovery after reversals.

  5. Axisymmetric instability in a thinning electrified jet

    NASA Astrophysics Data System (ADS)

    Dharmansh; Chokshi, Paresh

    2016-04-01

    The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.

  6. The breaking of axisymmetric slender liquid bridges

    NASA Astrophysics Data System (ADS)

    Meseguer, J.

    1983-05-01

    Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems.

  7. Isodynamic axisymmetric equilibrium near the magnetic axis

    SciTech Connect

    Arsenin, V. V.

    2013-08-15

    Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration)

  8. Isodynamic axisymmetric equilibrium near the magnetic axis

    NASA Astrophysics Data System (ADS)

    Arsenin, V. V.

    2013-08-01

    Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo's configuration).

  9. Mach disk from underexpanded axisymmetric nozzle flow

    NASA Technical Reports Server (NTRS)

    Chang, I.-S.; Chow, W. L.

    1974-01-01

    The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.

  10. Calculation of rf fields in axisymmetric cavities

    SciTech Connect

    Iwashita, Y.

    1985-01-01

    A new code, PISCES, has been developed for calculating a complete set of rf electromagnetic modes in an axisymmetric cavity. The finite-element method is used with up to third-order shape functions. Although two components are enough to express these modes, three components are used as unknown variables to take advantage of the symmetry of the element matrix. The unknowns are taken to be either the electric field components or the magnetic field components. The zero-divergence condition will be satisfied by the shape function within each element.

  11. Axisymmetric scrape-off plasma transport

    SciTech Connect

    Singer, C.E.; Langer, W.D.

    1983-05-01

    The two-dimensional flow of a collision dominated hydrogen scrape-off plasma in an axisymmetric tokamak is examined. This flow is described by a set of equations which contain the dominant terms in a maximal ordering appropriate to high density experimental divertors and reactor scrape-off plasmas. Comparison of the theory to estimates of scrape-off parameters in the Doublet III expanded boundary plasmas suggests that analysis of classical and neoclassical processes alone may be sufficient to predict plasma transport in high density scrape-off plasmas of practical importance.

  12. Minimal energy damping in an axisymmetric flow

    NASA Astrophysics Data System (ADS)

    Sachs, Alexander

    2008-05-01

    The method of Lagrange's undetermined multipliers is used to find the velocity field which minimizes the energy damping for a viscous incompressible fluid described by the Navier- Stoke equation. The vorticity of this velocity field obeys a Helmholtz equation with an undetermined parameter. This Helmholtz equation is used to determine the axisymmetric velocity field in a cylinder. This velocity field is slightly different from the Poiseuille velocity field. The rate of energy damping per unit energy is calculated as a function of the parameter. It is a minimum when the parameter is equal to the root of a Bessel function.

  13. DETAILED DECOMPOSITION OF GALAXY IMAGES. II. BEYOND AXISYMMETRIC MODELS

    SciTech Connect

    Peng, Chien Y.; Ho, Luis C.; Impey, Chris D.; Rix, Hans-Walter E-mail: lho@obs.carnegiescience.ed E-mail: rix@mpia-hd.mpg.d

    2010-06-15

    We present a two-dimensional (2D) fitting algorithm (GALFIT, ver. 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2D fitting algorithms by allowing for irregular, curved, logarithmic and power-law spirals, ring, and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, and apply them to an arbitrary number of model components of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius, or luminosity remains intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and beyond luminous galaxies, to allow more realistic decompositions of galaxy subcomponents in the presence of strong rings and spiral arms, and to enable ways to gauge the uncertainties when decomposing galaxy subcomponents. We illustrate these new features by way of several case studies that display various levels of complexity.

  14. Refraction and Shielding of Noise in Non-Axisymmetric Jets

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas

    1996-01-01

    This paper examines the shielding effect of the mean flow and refraction of sound in non-axisymmetric jets. A general three-dimensional ray-acoustic approach is applied. The methodology is independent of the exit geometry and may account for jet spreading and transverse as well as streamwise flow gradients. We assume that noise is dominated by small-scale turbulence. The source correlation terms, as described by the acoustic analogy approach, are simplified and a model is proposed that relates the source strength to 7/2 power of turbulence kinetic energy. Local characteristics of the source such as its strength, time- or length-scale, convection velocity and characteristic frequency are inferred from the mean flow considerations. Compressible Navier Stokes equations are solved with a k-e turbulence model. Numerical predictions are presented for a Mach 1.5, aspect ratio 2:1 elliptic jet. The predicted sound pressure level directivity demonstrates favorable agreement with reported data, indicating a relative quiet zone on the side of the major axis of the elliptic jet.

  15. Computing Axisymmetric Jet Screech Tones Using Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Loh, Ching Y.

    2002-01-01

    The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

  16. Low-dimensional azimuthal characteristics of suddenly expanding axisymmetric flows

    NASA Astrophysics Data System (ADS)

    Tinney, C. E.; Glauser, M. N.; Eaton, E. L.; Taylor, J. A.

    2006-11-01

    Two rakes of cross-wire probes were used to capture the two-point velocity statistics in a flow through an axisymmetric sudden expansion. The expansion ratio of the facility is 3, and has a constant geometry. Measurements were acquired at a Reynolds number equal to 54 000, based on centreline velocity and inlet pipe diameter. The two-point velocity correlations were obtained along a plane normal to the flow (r,theta), at eleven downstream step-height positions spanning from the recirculating region, through reattachment, and into the redeveloping region of the flow. Measurements were acquired by means of a flying-hot-wire technique to overcome rectification errors near the outer wall of the pipe where flow recirculations were greatest. A mixed application of proper orthogonal (in radius) and Fourier decomposition (in azimuth) was performed at each streamwise location to provide insight into the dynamics of the most energetic modes in all regions of the flow. This multi-point analysis reveals that the flow evolves from the Fourier-azimuthal mode m {=} 2 (containing the largest amount of turbulent kinetic energy) in the recirculating region, to m {=} 1 in the reattachment and redeveloping regions of the flow. An eigenvector reconstruction of the kernel, using the most energetic modes from the decomposition, displays the spatial dependence of the Fourier-azimuthal modes and the characteristics that govern the turbulent shear layer and recirculating regions of the flow.

  17. Using curvature extrema to track the evolution of axisymmetric interfaces

    NASA Astrophysics Data System (ADS)

    Vogel, M. J.; Nitsche, M.; Steen, P. H.

    2003-11-01

    The temporal evolution of the shape of an interface can exhibit phenomena such as break-up or pinch-off, which are fundamental events that must be controlled in many capillary systems of technological importance. For an axisymmetric surface, lemmas rooted in differential geometry dictate that curvature extrema coincide with curvature crossings or profile extrema. These features provide a convenient means to characterize the profiles of interfaces and to track their evolution even up to singularities, such as occurs at pinch-off. Being solely geometric in nature, this characterization is not limited by the physical properties of the system, e.g., Newtonian versus non-Newtonian behavior, viscous versus inviscid etc. We illustrate by tracking images from evolving soap-films (passive) and polymeric films (non-Newtonian), both observed in experiment, and a deforming mathematical surface predicted by the inviscid vortex-sheet model in simulation. We will discuss extensions of this approach that bring in some model of the flow (e.g. inviscid) and thereby lead to a dynamical system for the motion of the extrema.

  18. Geometry of PDE's. IV

    NASA Astrophysics Data System (ADS)

    Prástaro, Agostino

    2008-02-01

    Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.

  19. Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data

    NASA Technical Reports Server (NTRS)

    Riley, B. R.; Fuhrman, S. J.; Penko, P. F.

    1993-01-01

    A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate.

  20. Dark Geometry

    NASA Astrophysics Data System (ADS)

    Cembranos, J. A. R.; Dobado, A.; Maroto, A. L.

    Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space-time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

  1. Turbulent dynamo action in axisymmetric linear machine

    NASA Astrophysics Data System (ADS)

    Kabantsev, A. A.; Reva, V. B.; Sokolov, V. G.

    1997-11-01

    Generation of large-scale magnetic fields by turbulent motion of an electrically conducting fluids plays an important role not only for astrophysical applications, but also for magnetic fusion confinement phenomena. The well-studied turbulent dynamo α-effect comes from helical properties of turbulent motion. Under this dynamo the mean electric current is produced in the direction parallel or antiparallel to the mean magnetic field. In particular, the α-effect leads to the generation of plasma current along the magnetic field in reversed field pinches. We have shown that the α-effect takes place also in axisymmetric linear machines. In axisymmetric mirror traps AMBAL-M and MAL (BINP) the electrostatic turbulence, having mean helicity h≈ 6\\cdot 10^6 m/s^2, caused as a result of unstable differential rotation of plasma column in crossed E×B fields. By manipulating the trap's magnetic and plasma conditions, we can obtain both the parallel and the antiparallel B electric current to the order of 100 A/cm^2 (total current up to 6 kA) in the plasma. The measured mean electromotive force F_em= has linear growth with turbulent diffusion coefficient DT and reaches up to 50 V/m.

  2. Vortexons in axisymmetric Poiseuille pipe flows

    NASA Astrophysics Data System (ADS)

    Fedele, F.; Dutykh, D.

    2013-02-01

    We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (Fluid Dyn. Res., 44 (2012) 45509). The KdV dynamics of a perturbation is also investigated by means of a high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (Plysica D, 237 (2008) 1956). The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.

  3. Linear lateral vibration of axisymmetric liquid briges

    NASA Astrophysics Data System (ADS)

    Ferrera, C.; Montanero, J. M.; Cabezas, M. G.

    A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid

  4. A skin friction model for axisymmetric turbulent boundary layers along long thin circular cylinders

    NASA Astrophysics Data System (ADS)

    Jordan, Stephen A.

    2013-07-01

    Only a few engineering design models are presently available that adequately depict the axisymmetric skin friction (Cf) maturity along long thin turbulent cylinders. This deficit rests essentially on the experimental and numerical difficulties of measuring (or computing) the spatial evolution of the thin cylinder turbulence. Consequently, the present axisymmetric Cf models have questionable accuracy. Herein, we attempt to formulate a more robust Cf model that owns acceptable error. The formulation is founded on triple integration of the governing equation system that represents a thin cylinder turbulent boundary layer (TBL) at statistical steady-state in appropriate dimensionless units. The final model requires only the radius-based Reynolds number (Rea) and transverse curvature (δ/a) as input parameters. We tuned the accompanying coefficients empirically via an expanded statistical database (over 60 data points) that house new Cf values from large-eddy simulations (LES). The LES computations employed a turbulence inflow generation procedure that permits spatial resolution of the TBL at low-high Reynolds numbers and transverse curvatures. Compared to the new skin friction database, the Cf model revealed averaged predictive errors under 5% with a 3.5% standard deviation. Apart from owning higher values than the flat plate TBL, the most distinguishing characteristic of the axisymmetric skin friction is its rising levels when the boundary layer thickness exceeds the cylinder radius. All Cf levels diminish with increasing Reynolds number. These unique features differentiate the axisymmetric TBL along thin cylinders as a separate canonical flow when compared to the turbulent wall shear-layers of channels, pipes, and planar-type geometries.

  5. Impingement of supersonic jets on an axisymmetric deflector

    NASA Astrophysics Data System (ADS)

    Prasad, J. K.; Mehta, R. C.; Sreekanth, A. K.

    1994-07-01

    Experimental and numerical studies are carried out to investigate impingement flowfield produced on a typical axisymmetric jet deflector. The experiments consisted of schlieren flow visualization and measurements of pressure. The present study will be useful for the design of a typical axisymmetric jet deflector during the liftoff phase of a rocket.

  6. An Analysis of Saturn's Non-Axisymmetric Planetary Magnetic Field

    NASA Astrophysics Data System (ADS)

    Roy, M.; Burton, M. E.; Dougherty, M. K.

    2013-12-01

    Planetary magnetic field models based on Pioneer and Voyager data [Davis and Smith, 1990], [Connerney et al., 1984], [Giampieri and Dougherty, 2004] as well as initial models based on Cassini data [Dougherty et al., 2005] were necessarily axisymmetric since they were based on a rotation period now thought to be incorrect by several minutes [Galopeau and Lecacheux, 2000]. Subsequent models were constrained to be strictly axisymmetric because of this lack of knowledge [Burton et al., 2009], yet the periodic character of the magnetic field in Saturn's inner magetosphere is evident [Southwood and Kivelson, 2007], [Andrews et al., 2008]. For Jupiter, the substantial contribution by the non-axial field, a direct method of determining the rate of rotation, is possible by examining the periodic variation in the tilt of the magnetic dipole axis. Saturn's magnetic field with a negligible dipole tilt, makes this direct determination difficult. Attempts to quantify the degree of non-axisymmetry based on Cassini data obtained on thrity-seven orbits during the prime mission were inconclusive [Burton et al., 2010]. Without accurate knowledge of Saturn's rotation rate, it is not possible to derive an internal magnetic field model that includes non-axial terms. Given the high degree of symmetry, less direct methods have been used to estimate Saturn's rotation rate [Anderson and Schubert, 2007] and[ Read et al., 2009]. Since the beginning of the Cassini mission in July 2004 until the present, the spacecraft has completed more than 194 orbits in a wide variety of geometries in Saturn's magnetosphere. Seventy-four of those orbits have come closer than the L-shell of Enceladus at 3.95 Rs. In this analysis we use magnetic field measurements obtained on more then seventy orbits to attempt to quantify the degree of non-axisymmetry of Saturn's magnetic field. Because of the significant effect of Enceladus on Saturn's magnetosphere [Kivelson, 2006], only data obtained on orbits well inside

  7. Compact neutron imaging system using axisymmetric mirrors

    SciTech Connect

    Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E

    2014-05-27

    A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.

  8. A Compact Quasi-axisymmetric Stellarator Reactor

    SciTech Connect

    L.P. Ku; the ARIES-CS Team

    2003-10-20

    We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils.

  9. Axisymmetric supersonic flow in rotating impellers

    NASA Technical Reports Server (NTRS)

    Goldstein, Arthur W

    1952-01-01

    General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.

  10. Ideal ballooning modes in axisymmetric mirror machines

    SciTech Connect

    Baldwin, D.E.; McNamara, B.; Willmann, P.

    1980-12-15

    A simple code is described that finds marginally stable (..omega../sup 2/ = 0) ballooning-type MHD modes, localized about a field line in an axisymmetric, open-ended, plasma confinement device. The equations are based on a lower bound for the perturbed energy delta W, derived by W. Newcomb from the ideal MHD energy principle, and are cast in the form of a Ricatti equation for the first derivative of the eigenfunction, with the open boundary conditions that this derivative vanish at the plasma boundary down each field line. The input to the code is the two-dimensional shape of a field line, the field strength B(s), and parameters to define pressure profiles throughout the system. The objective is to find the highest plasma pressures for which the given line is MHD-stable.

  11. The evolution of swirling axisymmetric vortex rings

    NASA Astrophysics Data System (ADS)

    Gargan-Shingles, C.; Rudman, M.; Ryan, K.

    2015-08-01

    Swirling vortex rings form in any turbulent flow where a swirling component is present, such as in combustion chambers or the downwash of helicopter blades. Instabilities on initially non-swirling vortex rings result in a localized swirl velocity being generated within the core. The presence of a swirl component of velocity in a vortex ring modifies the relaxation and evolution of numerical Gaussian cores in a manner that is currently unknown. The evolution of Gaussian axisymmetric vortex rings of size 0.2 < Λ < 0.5, with Gaussian swirls of magnitude 0.0 < W < 0.5, is analyzed with reference to the governing equations. A relaxation time, at which the initial Gaussian approximation has minimal influence on the subsequent evolution, has been estimated for each case. An axial vortex forms along the axis of the ring and is responsible for the growth of a shear layer that is found to form at the leading edge. The circulation based Reynolds number is set at 10 000 to encourage the growth of shear layer instabilities from within this region. Secondary vortex rings are subsequently shown to evolve from the Kelvin-Helmholtz instability for shear layers of sufficient strength and are convected around the original ring and shed from the system. It is shown that complete settling of the strain rate within the core does not occur until all sheddings have ceased. Increasing the swirl magnitude past that considered in this paper is expected to result in the original ring losing its structure before the instability can occur. The evolution is found to be qualitatively similar to that of a piston generated axisymmetric vortex ring with swirl, with both cases eventually reaching a similar quasi-steady state.

  12. Analytical and experimental study of axisymmetric truncated plug nozzle flow fields

    NASA Technical Reports Server (NTRS)

    Muller, T. J.; Sule, W. P.; Fanning, A. E.; Giel, T. V.; Galanga, F. L.

    1972-01-01

    Experimental and analytical investigation of the flow field and base pressure of internal-external-expansion truncated plug nozzles are discussed. Experimental results for two axisymmetric, conical plug-cylindrical shroud, truncated plug nozzles are presented for both open and closed wake operations. These results include extensive optical and pressure data covering nozzle flow field and base pressure characteristics, diffuser effects, lip shock strength, Mach disc behaviour, and the recompression and reverse flow regions. Transonic experiments for a special planar transonic section are presented. An extension of the analytical method of Hall and Mueller to include the internal shock wave from the shroud exit is presented for closed wake operation. Results of this analysis include effects on the flow field and base pressure of ambient pressure ratio, nozzle geometry, and the ratio of specific heats. Static thrust is presented as a function of ambient pressure ratio and nozzle geometry. A new transonic solution method is also presented.

  13. The field lines of an axisymmetric magnetic field

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.

  14. Non-Axisymmetric Wave Focusing in Pipe Inspection

    NASA Astrophysics Data System (ADS)

    Sun, Zongqi; Rose, Joseph L.; Song, Won-Joon; Hayashi, Takahiro

    2003-03-01

    Non-axisymmetric guided waves have been applied to pipe inspection recently. Due to the non-axisymmetric characteristics of the waves, the circumferential displacement distribution is non-axisymmetric. It shows a natural focusing phenomenon. With the aid of a circumferential transducer array, we developed an algorithm to focus wave energy at arbitrary locations. The algorithm is based on applying different amplitude and time delay to each of the excitation elements. A series of experiments were carried out to show the focusing effect.

  15. Axisymmetric Numerical Modeling of Pulse Detonation Rocket Engines

    NASA Technical Reports Server (NTRS)

    Morris, Christopher I.

    2005-01-01

    Pulse detonation rocket engines (PDREs) have generated research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred considerable interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the progress that has been made in comparing the available experimental measurements with analytical and numerical models. In recent work by the author, a quasi-one-dimensional, finite rate chemistry CFD model was utilized to study the gasdynamics and performance characteristics of PDREs over a range of blowdown pressure ratios from 1-1000. Models of this type are computationally inexpensive, and enable first-order parametric studies of the effect of several nozzle and extension geometries on PDRE performance over a wide range of conditions. However, the quasi-one-dimensional approach is limited in that it cannot properly capture the multidimensional blast wave and flow expansion downstream of the PDRE, nor can it resolve nozzle flow separation if present. Moreover, the previous work was limited to single-pulse calculations. In this paper, an axisymmetric finite rate chemistry model is described and utilized to study these issues in greater detail. Example Mach number contour plots showing the multidimensional blast wave and nozzle exhaust plume are shown. The performance results are compared with the quasi-one-dimensional results from the previous paper. Both Euler and Navier-Stokes solutions are calculated in order to determine the effect of viscous

  16. Extension to an analysis of turbulent swirling compressible flow for application to axisymmetric small gas turbine ducts

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B.; Edwards, D. E.

    1981-01-01

    An existing computer program, the Axisymmetric Diffuser Duct Code (ADD code), which calculates compressible turbulent swirling flow through axisymmetric ducts was modified to permit calculation of flows through small gas turbine ducts with struts, guide vanes and large degrees of turning. The improvements include a coordinate generator, an end-wall loss model, and a generalized geometry capability to describe struts and guide vanes in ducts which turn more than 90 degrees. An improved output format was developed to provide the solution on any arbitrary plane in the duct and an extensive literature survey of calculation procedures used in gas turbine technology was completed which suggests improvements in the computer code. Calculations are presented for the flow through the AGT101 small gas turbine inlet duct and turbine exhaust diffuser which demonstrate the ADD code modifications implemented in the investigation. The computed results compare favorably with experimental results.

  17. Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach

    NASA Astrophysics Data System (ADS)

    Cervone, A.; Manservisi, S.; Scardovelli, R.

    2010-09-01

    A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

  18. Numerical simulations of rotating axisymmetric sunspots

    NASA Astrophysics Data System (ADS)

    Botha, G. J. J.; Busse, F. H.; Hurlburt, N. E.; Rucklidge, A. M.

    2008-07-01

    A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.

  19. Axisymmetric, Ventilated Supercavitation in Unsteady, Horizontal Flow

    NASA Astrophysics Data System (ADS)

    Kawakami, Ellison; Lee, Seung-Jae; Arndt, Roger

    2012-11-01

    Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, an artificial supercavity is required until the vehicle can reach conditions at which a natural supercavity can be sustained. Previous studies at Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling under waves. A study has been carried out at SAFL to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity tracking script has been developed. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number and a possible relationship between the two is being explored. (Supported by ONR)

  20. Four motional invariants in axisymmetric tori equilibria

    SciTech Connect

    A ring gren, O.; Moiseenko, V.E.

    2006-05-15

    In addition to the standard set ({epsilon},{mu},p{sub {phi}}) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I{sub r}. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I{sub r}= of the gyro center radial Clebsch coordinate is constant. To lowest order in the banana width, the radial invariant is the gyro center radial coordinate r{sub 0}(x,v), and to this order the gyro center moves on a magnetic flux surface. The gyro center orbit projected on the (r,z) plane determines the radial invariant and first order banana width corrections to I{sub r} are calculated. The radial drift invariant exists for trapped as well as passing particles. The new invariant is applied to construct Vlasov equilibria, where the magnetic field satisfies a generalized Grad-Shafranov equation with a poloidal plasma current and a bridge to ideal magnetohydrodynamic equilibria is found. For equilibria with sufficiently small banana widths and radial drift excursions, the approximation I{sub r}{approx_equal}r{sub 0}(x,v) can be used for the equilibrium state.

  1. Transient, hypervelocity flow in an axisymmetric nozzle

    NASA Technical Reports Server (NTRS)

    Jacobs, P. A.

    1991-01-01

    The performance of an axisymmetric nozzle was examined which was designed to produce uniform, parallel flow with a nominal Mach number of 8. A free-piston driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzle and, over the range of operating conditions examined, the nozzle produced satisfactory test flows. However, there were flow disturbances that persisted for significant times after flow initiation. The detailed starting process of the nozzle was also investigated by performing numerical simulations at several nominal test conditions. The classical description of the starting process, based on a quasi-one-dimensional model, provided a reasonable approximation and was used to demonstrate that the starting process could consume a significant fraction of the otherwise usable test gas. This was especially important at high operating enthalpies where nozzle supply conditions were maintained for shorter times. Multidimensional simulations illustrated a mechanism by which the starting process in the actual nozzle could take longer than that predicted by the quasi-one-dimensional analysis. However, the cause of the persistent disturbances observed in the experimental calibration was not identified.

  2. Design of swirled axisymmetric turbulent jets

    NASA Astrophysics Data System (ADS)

    Zhumayev, Z. S.; Abramov, A. A.; Fayziyev, R. A.

    1984-10-01

    The problem of swirling a jet for such applications as turbulization of the flame from burners in industrial furnaces or combustion chambers is treated on the basis of steady state turbulent straight axisymmetric flow of an incompressible fluid with the addition of a tangential velocity component. In the corresponding system of four partial differential equations there appears an exchange coefficient proportional to the mixing half width squared. After reduction to dimensionless form, this system of nonlinear equations is solved for the appropriate boundary conditions with constant momentum flow and constant moment of momentum. Radial profiles of both axial and tangential velocity components at various distances from the nozzle throat have been calculated numerically by the method of finite differences with an implicit scheme. The maxima of both velocity components are found to decrease and to shift toward the jet axis with increasing distance from the nozzle. A sharp swirl can give rise to a positive pressure gradient sufficiently large to produce a backcurrent. The results agree qualitatively with experimental data.

  3. EXACT VECTORIAL LAW FOR AXISYMMETRIC MAGNETOHYDRODYNAMICS TURBULENCE

    SciTech Connect

    Galtier, S.

    2009-10-20

    Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B{sub 0} . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich and Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B{sub 0} are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.

  4. Magnetic surfaces in an axisymmetric torus

    SciTech Connect

    Skovoroda, A. A.

    2013-04-15

    A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = B{sub s}({theta}) and the gradient of the poloidal flux vertical bar vertical bar {nabla}{Psi} vertical bar = vertical bar {nabla}{Psi} vertical bar {sub s}({theta}) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/d{Psi}) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n {center_dot} {nabla} ln B and the local shear s) and all constants (including the toroidal current J and the shear d{mu}/d{Psi}) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.

  5. Logo Activities in Elementary Geometry.

    ERIC Educational Resources Information Center

    Libeskind, Shlomo; And Others

    These activities were designed for use at the University of Montana, where they were tested for four quarters in a mathematics for elementary teachers course on informal geometry. They are for use with Apple II-Plus computers with 64K memory or Apple IIe computers and MIT Logo. (Modifications are necessary if the activities are to be used with…

  6. Investigations of flowfields found in typical combustor geometries

    NASA Technical Reports Server (NTRS)

    Lilley, D. G.

    1982-01-01

    Experimental and theoretical research undertaken on 2-D axisymmetric geometries under low speed, nonreacting, turbulent, swirling flow conditions is reported. The flow enters the test section and proceeds into a larger chamber (the expansion ratio D/d = 2) via a sudden or gradual expansion (sidewall angle alpha = 90 and 45 degrees). Inlet swirl vanes are adjustable to a variety of vane angles with values of phi = 0, 38, 45, 60 and 70 degrees being emphasized.

  7. The motion of axisymmetric satellite with drag and radiation pressure

    NASA Astrophysics Data System (ADS)

    Elshaboury, S. M.; Mostafa, A.

    2014-08-01

    The axisymmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. The energy-like and Laplace-like invariants of motion have been derived for a general drag force function of the polar angle, and the Laplace-like invariant is used to find the orbit equation in the case of a spherical satellite. Then using the small parameter, the orbit of the satellite is determined for an axisymmetric satellite.

  8. Complex image method for RF antenna-plasma inductive coupling calculation in planar geometry. Part II: measurements on a resonant network

    NASA Astrophysics Data System (ADS)

    Guittienne, Ph; Jacquier, R.; Howling, A. A.; Furno, I.

    2015-12-01

    Measurements and analysis of a radio-frequency planar antenna are presented for applications in inductively-coupled plasma processing. The network of inductive and capacitive elements exhibits high currents under resonance which are efficient for plasma generation. Mode frequencies and impedances are accurately calculated by accounting for the mutual partial inductances using the impedance matrix. The effect of plasma inductive coupling on mode frequency shift and mode impedance is estimated using the complex image method, giving good agreement with experiment. It is proposed that the complex image method combined with the partial inductance concept (see the accompanying paper, Part I (Howling et al 2015 Plasma Sources Sci. Technol. 24 065014)) offers a general way to calculate the impedance characteristics of inductively-coupled plasma sources in planar geometry.

  9. Transport of Colloids along Corners: Visualization of Evaporation-Induced Flows beyond the Axisymmetric Condition.

    PubMed

    Vélez-Cordero, J Rodrigo; Yáñez Soto, Bernardo; Arauz-Lara, José L

    2016-08-16

    Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness. PMID:27437865

  10. Assembly multi-dimensional CdII coordination architectures based on flexible bis(benzimidazole) ligands: Diversity of their coordination geometries and fluorescent properties

    NASA Astrophysics Data System (ADS)

    Jiao, Cui-huan; Geng, Jian-chen; He, Cui-hong; Cui, Guang-hua

    2012-08-01

    Based on three structurally related flexible bis(5,6-dimethylbenzimidazole) ligand, five novel metal-organic CdII coordination architectures: from 0D to 3D structures CdII complexes have been hydrothermally synthesized and structurally characterized, namely, Cd2I4(L1)2 (1), [CdCl2(L1)]n (2), [CdCl2(L2)]n (3), {[Cd(chdc)(L2)0.5]·H2O}n (4), {[Cd(pydca)(L3)0.5(H2O)2]·H2O}n (5) (where L1 = 1,2-bis(5,6-dimethylbenzimidazole)ethane, L2 = 1,3-bis(5,6-dimethylbenzimidazole)propane, L3 = 1,4-bis(5,6-dimethylbenzimidazole)butane, H2chdc = 1,4-cyclohexanedicarboxylic acid, H2pydca = pyridine-2,6-dicarboxylic acid). A discrete binuclear [2 + 2] metallomacrocycles cadmium(II) complex of 1 is 0D, 3 and 5 exhibit one-dimensional helical and zigzag chain structures, respectively. 4 Forms a 2D layer with sql net topology bridged by carboxylate anion and L2, while 2 is an overall 3D array with the diamond topology (dia). In these complexes, the influences of anions coordination on the framework formation were observed and discussed. These results indicate the spacer length of the ligands and anions play important roles in controlling the diversity structural topologies of such metal-organic coordination architectures. The thermogravimetric analyses, X-ray powder diffraction and solid-state luminescent properties of the complexes have also been investigated.

  11. Axisymmetric Control in Alcator C-Mod

    NASA Astrophysics Data System (ADS)

    Tinios, Gerasimos

    1995-01-01

    This thesis investigates the degree to which linear axisymmetric modeling of the response of a tokamak plasma can reproduce observed experimental behavior. The emphasis is on the vertical instability. The motivation for this work lies in the fact that, once dependable models have been developed, modern control theory methods can be used to design feedback laws for more effective and efficient tokamak control. The models are tested against experimental data from the Alcator C-Mod tokamak. A linear model for each subsystem of the closed-loop system constituting an Alcator C-Mod discharge under feedback control has been constructed. A non-rigid, approximately flux-conserving, perturbed equilibrium plasma response model is used in the comparison to experiment. A detailed toroidally symmetric model of the vacuum vessel and the supporting superstructure is used. Modeling of the power supplies feeding the active coils has been included. Experiments have been conducted with vertically unstable plasmas where the feedback was turned off and the plasma response was observed in an open -loop configuration. The closed-loop behavior has been examined by injecting step perturbations into the desired vertical position of the plasma. The agreement between theory and experiment in the open-loop configuration was very satisfactory, proving that the perturbed equilibrium plasma response model and a toroidally symmetric electromagnetic model of the vacuum vessel and the structure can be trusted for the purpose of calculations for control law design. When the power supplies and the feedback computer hardware are added to the system, however, as they are in the closed-loop configuration, they introduce nonlinearities that make it difficult to explain observed behavior with linear theory. Nonlinear simulation of the time evolution of the closed-loop experiments was able to account for the discrepancies between linear theory and experiment. (Copies available exclusively from MIT Libraries

  12. Methanethiol Binding Strengths and Deprotonation Energies in Zn(II)-Imidazole Complexes from M05-2X and MP2 Theories: Coordination Number and Geometry Influences Relevant to Zinc Enzymes.

    PubMed

    Linder, Douglas P; Rodgers, Kenton R

    2015-09-17

    Zn(II) is used in nature as a biocatalyst in hundreds of enzymes, and the structure and dynamics of its catalytic activity are subjects of considerable interest. Many of the Zn(II)-based enzymes are classified as hydrolytic enzymes, in which the Lewis acidic Zn(II) center facilitates proton transfer(s) to a Lewis base, from proton donors such as water or thiol. This report presents the results of a quantum computational study quantifying the dynamic relationship between the zinc coordination number (CN), its coordination geometry, and the thermodynamic driving force behind these proton transfers originating from a charge-neutral methylthiol ligand. Specifically, density functional theory (DFT) and second-order perturbation theory (MP2) calculations have been performed on a series of [(imidazole)nZn-S(H)CH3](2+) and [(imidazole)nZn-SCH3](+) complexes with the CN varied from 1 to 6, n = 0-5. As the number of imidazole ligands coordinated to zinc increases, the S-H proton dissociation energy also increases, (i.e., -S(H)CH3 becomes less acidic), and the Zn-S bond energy decreases. Furthermore, at a constant CN, the S-H proton dissociation energy decreases as the S-Zn-(ImH)n angles increase about their equilibrium position. The zinc-coordinated thiol can become more or less acidic depending upon the position of the coordinated imidazole ligands. The bonding and thermodynamic relationships discussed may apply to larger systems that utilize the [(His)3Zn(II)-L] complex as the catalytic site, including carbonic anhydrase, carboxypeptidase, β-lactamase, the tumor necrosis factor-α-converting enzyme, and the matrix metalloproteinases. PMID:26317178

  13. Physics of a magnetic filter for negative ion sources. II. E Ö- B drift through the filter in a real geometry

    NASA Astrophysics Data System (ADS)

    Boeuf, J. P.; Claustre, J.; Chaudhury, B.; Fubiani, G.

    2012-11-01

    The physics of a magnetic filter under conditions similar to those of the negative ion source for the ITER neutral beam injector is analyzed with the help of a two-dimensional particle-in-cell Monte Carlo Collisions model. A detailed analysis of the different terms of the electron momentum equations shows how diamagnetic and drift currents can be dominant in different regions of the filter. Electron transport through the filter is due to an E × B drift current on one side of the chamber induced by the presence of the chamber walls perpendicular to the electron diamagnetic current. The filter design of the ITER negative ion source, which does not allow a closed electron diamagnetic current, induces an asymmetry of the plasma that is analyzed with the particle model. It is shown that electron transport through the filter in this geometry is very different from the transport in an ideal, one-dimensional magnetic filter often considered in the literature and described in detail in the companion paper [Boeuf et al., Phys. Plasmas 19, 113509 (2012)].

  14. Physics of a magnetic filter for negative ion sources. II. E Multiplication-Sign B drift through the filter in a real geometry

    SciTech Connect

    Boeuf, J. P.; Claustre, J.; Chaudhury, B.; Fubiani, G.

    2012-11-15

    The physics of a magnetic filter under conditions similar to those of the negative ion source for the ITER neutral beam injector is analyzed with the help of a two-dimensional particle-in-cell Monte Carlo Collisions model. A detailed analysis of the different terms of the electron momentum equations shows how diamagnetic and drift currents can be dominant in different regions of the filter. Electron transport through the filter is due to an E Multiplication-Sign B drift current on one side of the chamber induced by the presence of the chamber walls perpendicular to the electron diamagnetic current. The filter design of the ITER negative ion source, which does not allow a closed electron diamagnetic current, induces an asymmetry of the plasma that is analyzed with the particle model. It is shown that electron transport through the filter in this geometry is very different from the transport in an ideal, one-dimensional magnetic filter often considered in the literature and described in detail in the companion paper [Boeuf et al., Phys. Plasmas 19, 113509 (2012)].

  15. Experimental study on the effects of nose geometry on drag over axisymmetric bodies in supersonic flow

    NASA Astrophysics Data System (ADS)

    Brooker, B. Tyler

    A new nose shape that was determined using the penetration mechanics to have the least penetration drag has been tested in the supersonic wind tunnel of the University of Alabama to determine the aerodynamic characteristics of this nose shape. The aerodynamic drag measured on the new nose shape and on four additional nose shapes are compared to each other. The results show that the new nose shape has the least aerodynamic drag. The measurements were made at Mach numbers ranging from 1.85 to 3.1. This study also required the maintenance of several components of the University of Alabama's 6-inch by 6-inch supersonic wind tunnel and modification of the existing data acquisition programs. These repairs and modifications included the repair and recalibration of the supersonic wind tunnel, repair of the four component force balance, and the modification of the tunnel's control program.

  16. Pressure limits of an axisymmetric torus

    SciTech Connect

    Yoshikawa, S.

    1986-03-01

    In order to clarify the pressure limit of a toroidal plasma equilibrium in a three-dimensional geometry, an azimuthally symmetric toroidal plasma was considered. In a tokamak-like plasma, the net toroidal current is necessary for a finite ..beta.. plasma equilibrium. If external conductors are used to provide the rotational transform, iota, the plasma pressure is limited to ..beta.. = (iota/2..pi..)/sup 2//2A, where A is the aspect ratio.

  17. A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods

    PubMed Central

    Li, Xiaofan; Nie, Qing

    2015-01-01

    Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated. PMID:26487788

  18. Revisiting Turbulence Model Validation for High-Mach Number Axisymmetric Compression Corner Flows

    NASA Technical Reports Server (NTRS)

    Georgiadis, Nicholas J.; Rumsey, Christopher L.; Huang, George P.

    2015-01-01

    Two axisymmetric shock-wave/boundary-layer interaction (SWBLI) cases are used to benchmark one- and two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. This validation exercise was executed in the philosophy of the NASA Turbulence Modeling Resource and the AIAA Turbulence Model Benchmarking Working Group. Both SWBLI cases are from the experiments of Kussoy and Horstman for axisymmetric compression corner geometries with SWBLI inducing flares of 20 and 30 degrees, respectively. The freestream Mach number was approximately 7. The RANS closures examined are the Spalart-Allmaras one-equation model and the Menter family of kappa - omega two equation models including the Baseline and Shear Stress Transport formulations. The Wind-US and CFL3D RANS solvers are employed to simulate the SWBLI cases. Comparisons of RANS solutions to experimental data are made for a boundary layer survey plane just upstream of the SWBLI region. In the SWBLI region, comparisons of surface pressure and heat transfer are made. The effects of inflow modeling strategy, grid resolution, grid orthogonality, turbulent Prandtl number, and code-to-code variations are also addressed.

  19. Stability of the laminar wake behind spinning axisymmetric bluff bodies: sensitivity and control

    NASA Astrophysics Data System (ADS)

    Jimenez-Gonzalez, Jose Ignacio; Martinez-Bazan, Carlos; Coenen, Wilfried; Manglano, Carlos; Sevilla, Alejandro

    2014-11-01

    We carry out direct and adjoint global stability analyses of the laminar wake behind several spinning axisymmetric bluff bodies, i.e. sphere, hemisphere, bullet-shaped bodies of ellipsoidal nose and spherical nose respectively; for moderate Reynolds numbers (Re <= 450) and values of the spin parameter (Ω <= 1), defined as the ratio between the azimuthal velocity at the outer body surface and the free-stream velocity. Both the axisymmetric base flow computations and the assembling of the eigenvalue problems are tackled by means of the finite element solver FreeFEM + + , computing finally the eigenmodes with an Arnoldi algorithm in Matlab. We show that spin acts as a stabilization mechanism for the wake behind bodies with a cylindrical trailing part, while it destabilizes the wake of the other geometries. The computation of the adjoint modes and the identification of the wavemaker allow us to discuss the nature of the different unstable modes found and understand the differences in the stabilizing or destabilizing effect of rotation due to the base flow modifications. The controllability of the unstable regimes by means of base bleed is also addressed. Supported by the Spanish MINECO, Junta de Andalucía and EU Funds under Projects DPI2011-28356-C03-03 and P11-TEP7495.

  20. Surface complexation and precipitate geometry for aqueous Zn(II) sorption on ferrihydrite I: X-ray absorption extended fine structure spectroscopy analysis

    USGS Publications Warehouse

    Waychunas, G.A.; Fuller, C.C.; Davis, J.A.

    2002-01-01

    "Two-line" ferrihydrite samples precipitated and then exposed to a range of aqueous Zn solutions (10-5 to 10-3 M), and also coprecipitated in similar Zn solutions (pH 6.5), have been examined by Zn and Fe K-edge X-ray absorption spectroscopy. Typical Zn complexes on the surface have Zn-O distances of 1.97(0.2) A?? and coordination numbers of about 4.0(0.5), consistent with tetrahedral oxygen coordination. This contrasts with Zn-O distances of 2.11(.02) A?? and coordination numbers of 6 to 7 in the aqueous Zn solutions used in sample preparation. X-ray absorption extended fine structure spectroscopy (EXAFS) fits to the second shell of cation neighbors indicate as many as 4 Zn-Fe neighbors at 3.44(.04) A?? in coprecipitated samples, and about two Zn-Fe neighbors at the same distance in adsorption samples. In both sets of samples, the fitted coordination number of second shell cations decreases as sorption density increases, indicating changes in the number and type of available complexing sites or the onset of competitive precipitation processes. Comparison of our results with the possible geometries for surface complexes and precipitates suggests that the Zn sorption complexes are inner sphere and at lowest adsorption densities are bidentate, sharing apical oxygens with adjacent edge-sharing Fe(O,OH)6 octahedra. Coprecipitation samples have complexes with similar geometry, but these are polydentate, sharing apices with more than two adjacent edge-sharing Fe(O,OH)6 polyhedra. The results are inconsistent with Zn entering the ferrihydrite structure (i.e., solid solution formation) or formation of other Zn-Fe precipitates. The fitted Zn-Fe coordination numbers drop with increasing Zn density with a minimum of about 0.8(.2) at Zn/(Zn + Fe) of 0.08 or more. This change appears to be attributable to the onset of precipitation of zinc hydroxide polymers with mainly tetrahedral Zn coordination. At the highest loadings studied, the nature of the complexes changes further

  1. REVIEW ARTICLE: Control of non-axisymmetric toroidal plasmas

    NASA Astrophysics Data System (ADS)

    Boozer, Allen H.

    2010-10-01

    The control of non-axisymmetric toroidal plasmas, stellarators, has a different character than the control of tokamaks for two reasons. Non-axisymmetric magnetic fields (1) can provide an arbitrarily large fraction of the poloidal magnetic field and (2) can strongly center the plasma in the chamber making it impossible to lose position control. The focus of stellarator design is on plasmas that are stable without feedback, need little or no change in the external magnetic field as the plasma evolves, and require no external power to maintain the desired magnetic configuration. The physics of non-axisymmetric fields is the same whether in a tokamak or a stellarator and whether introduced intentionally or accidentally. Fundamental physics indicates that plasma shape, which is controlled by the distribution of the external magnetic field that is normal to the plasma surface, is the primary control for fusion plasmas. The importance of non-axisymmetric control is set by the importance of toroidal plasma physics. Informed decisions on the development strategy of tokamaks, as well as magnetic fusion in general, require an understanding of the capabilities and difficulties of plasma control at various levels of non-axisymmetric shaping.

  2. Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

    SciTech Connect

    Post, R F; Fowler, T K; Bulmer, R; Byers, J; Hua, D; Tung, L

    2004-07-15

    The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K

  3. Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

    SciTech Connect

    Post, R.F.; Fowler, T.K.; Bulmer, R.; Byers, J.; Hua, D.; Tung, L.

    2005-01-15

    The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma.At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process,and a new code SYMTRAN (by Hua and Fowler)that solves the coupled radial and axial particle and energy transport in a K-S T-M. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values.The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma.Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging.Our studies have confirmed the viability of the K-S T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution.In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M.

  4. Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.; Hall, Philip

    1990-01-01

    A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.

  5. Wind Tunnel Test Results for Gas Flows Inside Axisymmetric Cavities on Cylindric Bodies with Nose Cones

    NASA Technical Reports Server (NTRS)

    Shvets, A. L.; Gilinsky, M.; Blankson, I. M.

    2004-01-01

    Experimental test results of air flow inside and at the cylindrical cavity located on axisymmetric body are presented. These tests were conducted in the wind tunnel A-7 of Institute of Mechanics at Moscow State University. Pressure distribution along the cavities and optical measurements were obtained. Dependence of these characteristics of length of a cavity in the range: L/D = 0.5 - 14 and free stream Mach in the range: M(sub infinity) = 0.6 - 3.0 was determined. Flow structure inside the cavity, cause of flow regime change, separation zones geometry and others were studied. In particular, the flow modes of with open and closed separation zones are determined.

  6. On the vibration of axisymmetric shells

    NASA Astrophysics Data System (ADS)

    Heppler, G. R.; Wahl, L.

    1989-05-01

    The application of nonconventional basis functions to the linear vibration problem is explored. By employing shell coordinates the elements allow the exact geometrical modelling of shells of revolution with arbitrary meridians and the elements are able to reproduce strain free states under an arbitrary rigid body motion due to the use of these special basis functions. A generalization of the Reissner Mindlin plate theories is used because they have a broader range of applicability than the usual thin/shallow shell theories and also the trial functions need only be of class C(sup 0). The geometry treated is a hyperbola of revolution, in two configurations.

  7. Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.

    PubMed

    Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R

    2013-04-01

    A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented. PMID:23556573

  8. Potential flow past axisymmetric bodies at angle of attack

    NASA Technical Reports Server (NTRS)

    Kuhlman, J. M.; Shu, J.-Y.

    1984-01-01

    The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.

  9. Stationary axisymmetric fields in a teleparallel theory of gravitation

    NASA Astrophysics Data System (ADS)

    Saez, D.

    1984-12-01

    The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.

  10. Study of axisymmetric flow problems by Hele-Shaw models

    NASA Astrophysics Data System (ADS)

    Rao, P. V.; Sachan, J. S.

    1980-05-01

    Hele-Shaw models have been applied for solving two-dimensional, irrotational flow problems such as flow past bodies or radial seepage flow. The gap between the two plates is varied as a cubic parabola in the radial direction. Results are presented for seven axisymmetric models, including a cylindrical body with 60-deg conical head forms, an axisymmetric sluice entrance with a compound elliptical transition and radial flow to a well with a free surface. Pressure distributions were computed and compared with water-tunnel data, wind-tunnel data, finite-differential solutions and exact solutions.

  11. Impingement of supersonic jets on an axisymmetric deflector

    NASA Astrophysics Data System (ADS)

    Prasad, J. K.; Mehta, R. C.; Sreekanth, A. K.

    1994-07-01

    The phenomenon of supersonic jets and their interaction with solid surfaces is found in many engineering applications such as impingement of exhaust from launch vehicles during the liftoff phase, during stage separation of multistage rockets, and VTOL/STOL operation of aircraft, etc. In this paper, experimental and numerical studies are carried out to investigate impingement flowfield produced on a typical axisymmetric jet deflector. The experiments consisted of schlieren flow visualization and measurements of pressure. The present study will be useful for the design of a typical axisymmetric jet deflector during the liftoff phase of a rocket.

  12. Geometry in Medias Res

    ERIC Educational Resources Information Center

    Cukier, Mimi; Asdourian, Tony; Thakker, Anand

    2012-01-01

    Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

  13. Dynamic Geometry on WWW.

    ERIC Educational Resources Information Center

    Kuntz, Gilles

    The first section of this paper on World Wide Web applications related to dynamic geometry addresses dynamic geometry and teaching, including the relationship between dynamic geometry and direct manipulation, key features of dynamic geometry environments, the importance of direct engagement of the learner using construction software for…

  14. Effects of forebody geometry on subsonic boundary-layer stability

    NASA Technical Reports Server (NTRS)

    Dodbele, Simha S.

    1990-01-01

    As part of an effort to develop computational techniques for design of natural laminar flow fuselages, a computational study was made of the effect of forebody geometry on laminar boundary layer stability on axisymmetric body shapes. The effects of nose radius on the stability of the incompressible laminar boundary layer was computationally investigated using linear stability theory for body length Reynolds numbers representative of small and medium-sized airplanes. The steepness of the pressure gradient and the value of the minimum pressure (both functions of fineness ratio) govern the stability of laminar flow possible on an axisymmetric body at a given Reynolds number. It was found that to keep the laminar boundary layer stable for extended lengths, it is important to have a small nose radius. However, nose shapes with extremely small nose radii produce large pressure peaks at off-design angles of attack and can produce vortices which would adversely affect transition.

  15. Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks

    NASA Astrophysics Data System (ADS)

    Hanson, J. D.; Anderson, D. T.; Cianciosa, M.; Franz, P.; Harris, J. H.; Hartwell, G. H.; Hirshman, S. P.; Knowlton, S. F.; Lao, L. L.; Lazarus, E. A.; Marrelli, L.; Maurer, D. A.; Schmitt, J. C.; Sontag, A. C.; Stevenson, B. A.; Terranova, D.

    2013-08-01

    Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad-Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.

  16. MHD-stable plasma confinement in an axisymmetric mirror system

    SciTech Connect

    Stupakov, G.V.

    1988-02-01

    If the magnetic field of a nonparaxial mirror system is chosen appropriately, it is possible to maintain a sharp plasma boundary in an open axisymmetric confinement system in a manner which is stable against flute modes (both global and small-scale). Stability prevails in the ideal MHD approximation without finite-ion-Larmor radius effects.

  17. Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry

    SciTech Connect

    Long-Poe Ku and Allen H. Boozer

    2009-06-05

    If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.

  18. Stability of a compound sessile drop at the axisymmetric configuration.

    PubMed

    Zhang, Ying; Chatain, Dominique; Anna, Shelley L; Garoff, Stephen

    2016-01-15

    The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number. PMID:26433481

  19. Consistent lattice Boltzmann methods for incompressible axisymmetric flows.

    PubMed

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

    2016-08-01

    In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407

  20. Non-Linear Lessons from Axisymmetric Vortex Rings

    NASA Technical Reports Server (NTRS)

    Shariff, Karim; Mansour, Nagi (Technical Monitor)

    2001-01-01

    For presentation at Northwestern University, May 14-28, 2001, the talk will present two types of phenomena, both recognizable to students of nonlinearity, that are exhibited by axisymmetric vortex rings in numerical and laboratory experiments. (1) The first type of phenomenon is reminiscent of inelastic solitons.

  1. Consistent lattice Boltzmann methods for incompressible axisymmetric flows

    NASA Astrophysics Data System (ADS)

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

    2016-08-01

    In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

  2. Distortion of homogeneous turbulence by axisymmetric strain and dilatation

    NASA Technical Reports Server (NTRS)

    Lee, Moon Joo

    1989-01-01

    Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: the axisymmetric contraction (AC, nozzle-type flow), and the axisymmetric expansion (AE, diffuser-type flow). The paper explores the differences in effects of the two axisymmetric strain modes on the anisotropy of correlations and structures of turbulence; examines the effect of dilatation on the distortion of turbulence; and provides a theoretical background for turbulence model development. It is found that velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; contraction produces much higher anisotropy in velocity and vorticity than expansion; root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. A simple model that reflects the dependence of turbulence evolution on structural parameters such as the Reynolds-stress anisotropy and total strain is proposed, and is shown to outperform all other models for all cases examined, regardless of the mean strain rate.

  3. Non-axisymmetric instabilities in discs with imposed zonal flows

    NASA Astrophysics Data System (ADS)

    Vanon, R.; Ogilvie, G. I.

    2016-09-01

    We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is ≳ 8H, where H is the disc's scale height, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.

  4. Generation and Properties of Large-Scale Non-axisymmetric Magnetic Fields by Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Pipin, Valery; Kosovichev, Alexander

    2015-08-01

    Large-scale non-axisymmetric magnetic fields generated by the solar dynamo, and presumably responsible for the phenomenon of "active longitudes", play an important role in the distribution of solar activity and flares. By calculating 3D mean-field dynamo models, we show that nonlinear coupling between axisymmetric and non-axisymmetric modes, e.g. due to the magnetic feedback on the alpha-effect (see, e.g., [1]), can maintain a large-scale non-axisymmetric dynamo process. Non-axisymmetric random fluctuations of dynamo parameters can be another source for the non-axisymmetric magnetic fields on the Sun. Such fluctuations can provide a mechanism of the magnetic energy transfer from the global field to the non-axisymmetric modes. It is shown that the rotational periods of the non-axisymmetric field correspond to the dynamo process operating in the subsurface shear layer which is located in the range of depths 0.85-0.95R. We find that the magnetic helicity conservation quenches generation of the non-axisymmetric dynamo modes as well as it does for the axisymmetric dynamo. It is concluded that the 3D mean-field non-axisymmetric dynamo models can potentially explain the observed distribution of the solar magnetic activity.1. Moss, D.,Non-axisymmetric solar magnetic fields, 1999, MNRAS, 306, 300On 3/18/2015 2:29 PM, Valery Pipin wrote:

  5. Learning Geometry through Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Forsythe, Sue

    2007-01-01

    In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…

  6. Computations of Internal and External Axisymmetric Nozzle Aerodynamics at Transonic Speeds

    NASA Technical Reports Server (NTRS)

    Dalbello, Teryn; Georgiadis, Nicholas; Yoder, Dennis; Keith, Theo

    2003-01-01

    Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles have been completed in support of NASA's Next Generation Launch Technology Program to investigate the effects of high-speed nozzle geometries on the nozzle internal flow and the surrounding boattail regions. These computations span the very difficult transonic flight regime, with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined in Wind, including an Explicit Algebraic Stress model (EASM). Computations on two nozzle geometries have been completed at freestream Mach numbers ranging from 0.6 to 0.9, driven by nozzle pressure ratios (NPR) ranging from 2.9 to 5. Results obtained on converging-only geometry indicate reasonable agreement to experimental data, with the EASM and Shear Stress Transport (SST) turbulence models providing the best agreement. Calculations completed on a converging-diverging geometry involving large-scale internal flow separation did not converge to a true steady-state solution when run with variable timestepping (steady-state). Calculations obtained using constant timestepping (time-accurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was found to be the result of difficulties in using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show fairly good agreement with experimental data. The SST turbulence model demonstrates the best over-all agreement with experimental data.

  7. An elementary discussion of propellant flame geometry

    SciTech Connect

    Buckmaster, J.; Jackson, T.L.; Yao, J.

    1999-05-01

    The authors examine the geometry of diffusion flames generated by the burning of a heterogeneous solid propellant, using a simple model designed to provide qualitative insights. In the fast chemistry limit a strategy is used which has its roots in Burke and Schumann`s 1928 study of diffusion flames, albeit with different boundary conditions. This shows that the stoichiometric level surface (SLS) intersects the propellant surface at a point displaced from the fuel/oxidizer interface, and the variations of this displacement with Peclet number are discussed. The authors show that for model sandwich propellants, or their axisymmetric counterpart, the geometry of the SLS when the core is oxidizer is quite different from the geometry of the SLS when the core is fuel. Also, it is much easier to quench the flame on an oxidizer core, by reducing the Peclet number, than it is to quench the flame on a fuel core. When finite chemistry effects are accounted for, the flame only occupies a portion of the SLS, and there is a leading edge structure in which premixing plays a role. Enhancement of the burning rate due to premixing is identified, but a well-defined tribrachial structure is not observed. The authors show how a sharp reduction in pressure can lead to a detachment of the flame from the SLS, with subsequent quenching as it is swept downstream.

  8. An axisymmetric boundary element formulation of sound wave propagation in fluids including viscous and thermal losses.

    PubMed

    Cutanda-Henríquez, Vicente; Juhl, Peter Møller

    2013-11-01

    The formulation presented in this paper is based on the boundary element method (BEM) and implements Kirchhoff's decomposition into viscous, thermal, and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses are solved using extended boundary conditions that assume (i) negligible temperature fluctuations at the boundary and (ii) normal and tangential matching of the boundary's particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers as is the case with the existing finite element method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions. PMID:24180751

  9. Effect of swirl decay on vortex breakdown in a confined steady axisymmetric flow

    NASA Astrophysics Data System (ADS)

    Shtern, Vladimir N.; del Mar Torregrosa, María; Herrada, Miguel A.

    2012-04-01

    This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)-(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears.

  10. Spiral streaklines in pre-vortex breakdown regions of axisymmetric swirling flows

    NASA Astrophysics Data System (ADS)

    Hourigan, K.; Graham, L. J. W.; Thompson, M. C.

    1995-12-01

    In steady swirling flows in closed cylinders, it has been common to observe the transition to spirals of otherwise straight dye streaklines. This occurs in the regions where bubble type breakdown occurs but at a slightly lower Reynolds number. These regions are of particular interest for those seeking to explain the origins of vortex breakdown. The hitherto unexplained occurrence of the spiral streaklines, postulated previously to be due to non-axisymmetry of the flow, is found to be due to small offsets of the dye injection from the central axis. The important implications of this finding are that (i) non-axisymmetry is not a necessary route to bubble-type vortex breakdown, and (ii) that flows displaying spiral streaklines may be still sufficiently axisymmetrical for comparison with numerical and theoretical treatments of the breakdown phenomenon.

  11. Experimental Study of an Axisymmetric Dual Throat Fluidic Thrust Vectoring Nozzle for Supersonic Aircraft Application

    NASA Technical Reports Server (NTRS)

    Flamm, Jeffrey D.; Deere, Karen A.; Mason, Mary L.; Berrier, Bobby L.; Johnson, Stuart K.

    2007-01-01

    An axisymmetric version of the Dual Throat Nozzle concept with a variable expansion ratio has been studied to determine the impacts on thrust vectoring and nozzle performance. The nozzle design, applicable to a supersonic aircraft, was guided using the unsteady Reynolds-averaged Navier-Stokes computational fluid dynamics code, PAB3D. The axisymmetric Dual Throat Nozzle concept was tested statically in the Jet Exit Test Facility at the NASA Langley Research Center. The nozzle geometric design variables included circumferential span of injection, cavity length, cavity convergence angle, and nozzle expansion ratio for conditions corresponding to take-off and landing, mid climb and cruise. Internal nozzle performance and thrust vectoring performance was determined for nozzle pressure ratios up to 10 with secondary injection rates up to 10 percent of the primary flow rate. The 60 degree span of injection generally performed better than the 90 degree span of injection using an equivalent injection area and number of holes, in agreement with computational results. For injection rates less than 7 percent, thrust vector angle for the 60 degree span of injection was 1.5 to 2 degrees higher than the 90 degree span of injection. Decreasing cavity length improved thrust ratio and discharge coefficient, but decreased thrust vector angle and thrust vectoring efficiency. Increasing cavity convergence angle from 20 to 30 degrees increased thrust vector angle by 1 degree over the range of injection rates tested, but adversely affected system thrust ratio and discharge coefficient. The dual throat nozzle concept generated the best thrust vectoring performance with an expansion ratio of 1.0 (a cavity in between two equal minimum areas). The variable expansion ratio geometry did not provide the expected improvements in discharge coefficient and system thrust ratio throughout the flight envelope of typical a supersonic aircraft. At mid-climb and cruise conditions, the variable geometry

  12. Distributed forcing of the flow past a blunt-based axisymmetric bluff body

    NASA Astrophysics Data System (ADS)

    Jardin, Thierry; Bury, Yannick; DAEP Team

    2012-11-01

    The topology of bluff body wakes may be highly sensitive to forcing at frequencies close to intrinsic flow instabilities. In a similar way, a steady but spatially varying forcing at wavelengths close to specific flow instabilities can lead to analogous outcomes. Such forcing is commonly referred to as distributed forcing. However, although distributed forcing has proven to be a relevant control strategy for three-dimensional flows past nominally two-dimensional geometries (e.g. extruded circular cylinder at Re > 180), its impact on the flow past nominally three-dimensional geometries is still unknown. Here we assess the receptivity of the flow past a blunt-based axisymmetric bluff body to an azimuthally distributed forcing applied at the periphery of the bluff-body base. We show that the impact of RSPa, RSPb and RSPc instabilities on the drag fluctuations experienced by the bluff body can be suppressed, depending on the forcing wavelengths. The authors acknowledge the French Ministry of Defence and DGA for funding this work.

  13. Collection-efficient, axisymmetric vacuum sublimation module for the purification of solid materials

    NASA Astrophysics Data System (ADS)

    May, Michael; Paul, Elizabeth; Katovic, Vladimir

    2015-11-01

    A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material.

  14. The Role of Axisymmetric Reconnection Events in JET Discharges with Extreme Shear Reversal

    SciTech Connect

    B.C. Stratton; J.A. Breslau; R.V. Budny; S.C. Jardin; W. Park; H.R. Strauss; L.E. Zakharov; B. Alper; V. Drozdov; N.C. Hawkes; S. Reyes-Cortes; and Contributors to the EFDA-JET Work Programme

    2001-12-03

    Injection of Lower Hybrid Heating and Current Drive into the current ramp-up phase of Joint European Torus (JET) discharges can produce extremely reversed q-profiles characterized by a core region of very small or zero current density (within Motional Stark Effect diagnostic measurement errors) and q(subscript min) > 1. T(subscript e)-profiles show sawtooth-like collapses and the presence of an internal transport barrier. Accurate equilibrium reconstructions of these discharges are obtained using the ESC code, which was recently extended to allow equilibrium reconstructions in which a free boundary solver determines the plasma boundary and a fixed boundary solver provides the magnetic geometry and current density profile. The core current density does not appear to go negative, although current diffusion calculations indicate that sufficient non-inductive current drive to cause this is present. This is explained by nonlinear resistive MHD simulations in toroidal geometry which predict that these discharges undergo n=0 reconnection events (axisymmetric sawteeth) that redistribute the current to hold the core current density near zero.

  15. Combinatorial Geometry Printer Plotting.

    Energy Science and Technology Software Center (ESTSC)

    1987-01-05

    Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.

  16. Seismic Wave Propagation in Fully Anisotropic Axisymmetric Media: Applications and Practical Considerations

    NASA Astrophysics Data System (ADS)

    van Driel, Martin; Nissen-Meyer, Tarje; Stähler, Simon; Waszek, Lauren; Hempel, Stefanie; Auer, Ludwig; Deuss, Arwen

    2014-05-01

    We present a numerical method to compute high-frequency 3D elastic waves in fully anisotropic axisymmetric media. The method is based on a decomposition of the wavefield into a series of uncoupled 2D equations, for which the dependence of the wavefield on the azimuth can be solved analytically. The remaining 2D problems are then solved using a spectral element method (AxiSEM). AxiSEM was recently published open-source (Nissen-Meyer et al. 2014) as a production ready code capable to compute global seismic wave propagation up to frequencies of ~2Hz. It accurately models visco-elastic dissipation and anisotropy (van Driel et al., submitted to GJI) and runs efficiently on HPC resources using up to 10K cores. At very short period, the Fresnel Zone of body waves is narrow and sensitivity is focused around the geometrical ray. In cases where the azimuthal variations of structural heterogeneity exhibit long spatial wavelengths, so called 2.5D simulations (3D wavefields in 2D models) provide a good approximation. In AxiSEM, twodimensional variations in the source-receiver plane are effectively modelled as ringlike structures extending in the out-of-plane direction. In contrast to ray-theory, which is widely used in high-frequency applications, AxiSEM provides complete waveforms, thus giving access to frequency dependency, amplitude variations, and peculiar wave effects such as diffraction and caustics. Here we focus on the practical implications of the inherent axisymmetric geometry and show how the 2.5D-features of our method method can be used to model realistic anisotropic structures, by applying it to problems such as the D" region and the inner core.

  17. Neoclassical transport coefficients for general axisymmetric equilibria in the banana regime

    NASA Astrophysics Data System (ADS)

    Angioni, C.; Sauter, O.

    2000-04-01

    Using the standard approach of neoclassical theory, a set of relatively simple kinetic equations has been obtained, suited for an implementation in a numerical code to compute a related set of distribution functions. The transport coefficients are then expressed by simple integrals of these functions and they can be easily computed numerically. The code CQL3D [R. W. Harvey and M. G. McCoy, in Proceedings of IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas, Montreal, 1992 (International Atomic Energy Agency, Vienna, 1993), pp. 489-526], which uses the full collision operator and considers the realistic axisymmetric configuration of the magnetic surfaces, has been modified to solve the bounce-averaged version of these equations. The coefficients have then been computed for a wide variety of equilibrium parameters, high-lighting interesting features of the influence of geometry at small aspect ratio. Differences with the most recent formulas for the ion neoclassical heat conductivity are pointed out. A set of formulas, which fit the code results, is obtained to easily evaluate all the neoclassical transport coefficients in the banana regime, at all aspect ratios, in general axisymmetric equilibria. This work extends to all the other transport coefficients, at least in the banana regime, the work of Sauter et al. [O. Sauter, C. Angioni, and Y. R. Lin-Liu, Phys. Plasmas 6, 2834 (1999)] which evaluates the neoclassical conductivity and all the bootstrap current coefficients. Formulas for arbitrary collisionality regime are proposed, obtained combining our results for the banana regime with the results of Hinton and Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)], adapted for small aspect ratio.

  18. General 2 charge geometries

    NASA Astrophysics Data System (ADS)

    Taylor, Marika

    2006-03-01

    Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.

  19. Geometry and Erdkinder.

    ERIC Educational Resources Information Center

    McDonald, Nathaniel J.

    2001-01-01

    Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…

  20. Bis(thiosemicarbazonato) chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II)

    NASA Astrophysics Data System (ADS)

    Chandra, Sulekh; Singh, R.

    1985-01-01

    Bis chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II) with the enolic form of diethyl ketone and methyl n-propyl thiosemicarbazones were synthesized and characterized by elemental analyses, magnetic moments, i.r. and electronic and electron spin resonance spectral studies. All the complexes were found to have the composition ML 2 [where M = Co(II), Ni(II), Cu(II), Pd(ii) and Pt(II) and L = thiosemicarbazones of diethyl ketone and methyl n-propyl ketone]. Co(II) and Cu(II) complexes are paramagnetic and may have polymeric six-coordinate octahedral and square planar geometries, respectively. The Ni(II), Pd(II) and Pt(II) complexes are diamagnetic and may have square planar geometries. Pyridine adducts (ML 2·2Py) of Ni(II) and Cu(II) complexes were also prepared and characterized.

  1. Non-axisymmetric instability of core-annular flow

    NASA Astrophysics Data System (ADS)

    Hu, Howard H.; Patankar, Neelesh

    1995-05-01

    Stability of core-annular flow of water and oil in a vertical circular pipe is studied with respect to non-axisymmetric disturbances. Results show that when the oil core is thin, the flow is most unstable to the asymmetric sinuous mode of disturbance, and the core moves in the form of corkscrew waves as observed in experiments. The asymmetric mode of disturbance is the most dangerous mode for quite a wide range of material and flow parameters. This asymmetric mode persists in vertical pipes with upward and downward flows and in horizontal pipes. The analysis also applies to the instability of freely rising axisymmetric cigarette smoke or a thermal plume. The study predicts a unique wavelength for the asymmetric meandering waves.

  2. Application of the PTT model to axisymmetric free surface flows

    NASA Astrophysics Data System (ADS)

    Merejolli, R.; Paulo, G. S.; Tomé, M. F.

    2013-10-01

    This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters ɛ and ξ are investigated.

  3. Design optimization of axisymmetric bodies in nonuniform transonic flow

    NASA Technical Reports Server (NTRS)

    Lan, C. Edward

    1989-01-01

    An inviscid transonic code capable of designing an axisymmetric body in a uniform or nonuniform flow was developed. The design was achieved by direct optimiation by coupling an analysis code with an optimizer. Design examples were provided for axisymmetric bodies with fineness ratios of 8.33 and 5 at different Mach numbers. It was shown that by reducing the nose radius and increasing the afterbody thickness of initial shapes obtained from symmetric NACA four-digit airfoil contours, wave drag could be reduced by 29 percent for a body of fineness ratio 8.33 in a nonuniform transonic flow of M = 0.98 to 0.995. The reduction was 41 percent for a body of fineness ratio 5 in a uniform transonic flow of M = 0.925 and 65 percent for the same body but in a nonuniform transonic flow of M = 0.90 to 0.95.

  4. Toroidal angular momentum transport with non-axisymmetric magnetic fields

    NASA Astrophysics Data System (ADS)

    Seol, J.; Park, B. H.

    2016-05-01

    In this study, we calculate the radial transport of the toroidal angular momentum in the presence of non-axisymmetric magnetic fields. It is shown that the radial transport of the toroidal angular momentum, R 2 ∇ ζ . V , is proportional to the first order of gyro-radius. This implies that the neoclassical toroidal viscosity caused by asymmetric magnetic fields can change the toroidal rotation significantly.

  5. Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes

    NASA Astrophysics Data System (ADS)

    Giagkiozis, I.; Goossens, M.; Verth, G.; Fedun, V.; Van Doorsselaere, T.

    2016-06-01

    It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.

  6. Axisymmetric MHD Instabilities in Solar/Stellar Tachoclines

    NASA Astrophysics Data System (ADS)

    Dikpati, Mausumi; Gilman, Peter A.; Cally, Paul S.; Miesch, Mark S.

    2009-02-01

    Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.

  7. Small Engine Technology (SET) - Task 14 Axisymmetric Engine Simulation Environment

    NASA Technical Reports Server (NTRS)

    Miller, Max J.

    1999-01-01

    As part of the NPSS (Numerical Propulsion Simulation System) project, NASA Lewis has a goal of developing an U.S. industry standard for an axisymmetric engine simulation environment. In this program, AlliedSignal Engines (AE) contributed to this goal by evaluating the ENG20 software and developing support tools. ENG20 is a NASA developed axisymmetric engine simulation tool. The project was divided into six subtasks which are summarized below: Evaluate the capabilities of the ENG20 code using an existing test case to see how this procedure can capture the component interactions for a full engine. Link AE's compressor and turbine axisymmetric streamline curvature codes (UD0300M and TAPS) with ENG20, which will provide the necessary boundary conditions for an ENG20 engine simulation. Evaluate GE's Global Data System (GDS), attempt to use GDS to do the linking of codes described in Subtask 2 above. Use a turbofan engine test case to evaluate various aspects of the system, including the linkage of UD0300M and TAPS with ENG20 and the GE data storage system. Also, compare the solution results with cycle deck results, axisymmetric solutions (UD0300M and TAPS), and test data to determine the accuracy of the solution. Evaluate the order of accuracy and the convergence time for the solution. Provide a monthly status report and a final formal report documenting AE's evaluation of ENG20. Provide the developed interfaces that link UD0300M and TAPS with ENG20, to NASA. The interface that links UD0300M with ENG20 will be compatible with the industr,, version of UD0300M.

  8. Axisymmetric Implementation for 3D-Based DSMC Codes

    NASA Technical Reports Server (NTRS)

    Stewart, Benedicte; Lumpkin, F. E.; LeBeau, G. J.

    2011-01-01

    The primary objective in developing NASA s DSMC Analysis Code (DAC) was to provide a high fidelity modeling tool for 3D rarefied flows such as vacuum plume impingement and hypersonic re-entry flows [1]. The initial implementation has been expanded over time to offer other capabilities including a novel axisymmetric implementation. Because of the inherently 3D nature of DAC, this axisymmetric implementation uses a 3D Cartesian domain and 3D surfaces. Molecules are moved in all three dimensions but their movements are limited by physical walls to a small wedge centered on the plane of symmetry (Figure 1). Unfortunately, far from the axis of symmetry, the cell size in the direction perpendicular to the plane of symmetry (the Z-direction) may become large compared to the flow mean free path. This frequently results in inaccuracies in these regions of the domain. A new axisymmetric implementation is presented which aims to solve this issue by using Bird s approach for the molecular movement while preserving the 3D nature of the DAC software [2]. First, the computational domain is similar to that previously used such that a wedge must still be used to define the inflow surface and solid walls within the domain. As before molecules are created inside the inflow wedge triangles but they are now rotated back to the symmetry plane. During the move step, molecules are moved in 3D but instead of interacting with the wedge walls, the molecules are rotated back to the plane of symmetry at the end of the move step. This new implementation was tested for multiple flows over axisymmetric shapes, including a sphere, a cone, a double cone and a hollow cylinder. Comparisons to previous DSMC solutions and experiments, when available, are made.

  9. Use of a twisted 3D Cauchy condition surface to reconstruct the last closed magnetic surface in a non-axisymmetric fusion plasma

    NASA Astrophysics Data System (ADS)

    Itagaki, Masafumi; Okubo, Gaku; Akazawa, Masayuki; Matsumoto, Yutaka; Watanabe, Kiyomasa; Seki, Ryosuke; Suzuki, Yasuhiro

    2012-12-01

    The three-dimensional (3D) Cauchy condition surface (CCS) method code, ‘CCS3D’, is now under development to reconstruct the 3D magnetic field profile outside a non-axisymmetric fusion plasma using only magnetic sensor signals. A new ‘twisted CCS’ is introduced, whose elliptic cross-section rotates with the variation in plasma geometry in the toroidal direction of a helical-type device. Independent of the toroidal angle, this CCS can be placed at a certain distance from the last closed magnetic surface (LCMS). With this new CCS, it is found through test calculations for the Large Helical Device that the numerical accuracy in the reconstructed field is improved. Furthermore, the magnetic field line tracing indicates the LCMS more precisely than with the use of the axisymmetric CCS. A new idea to determine the LCMS numerically is also proposed.

  10. The AGCE related studies of baroclinic flows in spherical geometry

    NASA Technical Reports Server (NTRS)

    Hyun, J. M.

    1983-01-01

    Steady state, axisymmetric motions of a Boussineaq fluid continued in rotating spherical anmulus are considered. The motions are driven by latitudinally varying temperature gradient at the shells. Linearized formulations for a narrow gap are derived and the flow field is divided into the Ekman layers and the geostrophic interior. The Ekman layer flows are consistent with the known results for cylindrical geometries. Within the framework of rather restrictive assumptions, the interior flows are solved by a series of associated Legendre polynomials. The solutions show qualitative features valid at midlatitudes.

  11. DEP thermal convection in annular geometry under microgravity conditions

    NASA Astrophysics Data System (ADS)

    Yoshikawa, Harunori; Crumeyrolle, Olivier; Mutabazi, Innocent

    2012-11-01

    Thermal convection driven by the dielectrophoretic force is investigated in annular geometry in microgravity environments. A radial heating and a radial alternating electric field are imposed on a dielectric fluid layer filling the gap of two concentric infinite-length cylinders. The resulting dielectric force field is regarded as spatially varying radial gravity that can develop thermal convection. The linear stability problem of a purely conductive basic state is solved by a spectral-collocation method for both axisymmetric and non-axisymmetric disturbances. A stationary non-axisymmetric mode becomes first unstable at a critical Rayleigh number to develop convection. The stability boundary shows asymmetry with respect to heating direction. For an outward heating the critical value approaches that of the Rayleigh-Bénard problem (1708) as the gap size decreases, while it converges to larger values in the narrow gap limit. For an inward heating the instability occurs only when the gap is narrower than a certain value. The critical number diverges with increasing the gap size. Instability mechanism is examined from energetic viewpoints. The feedback of electric field to temperature disturbances is found to stabilize the conductive state for narrow gaps. This work has been partly supported by the CNES, the CNRS and the FEDER.

  12. Holographic measurement of wave propagation in axi-symmetric shells

    NASA Technical Reports Server (NTRS)

    Evensen, D. A.; Aprahamian, R.; Jacoby, J. L.

    1972-01-01

    The report deals with the use of pulsed, double-exposure holographic interferometry to record the propagation of transverse waves in thin-walled axi-symmetric shells. The report is subdivided into sections dealing with: (1) wave propagation in circular cylindrical shells, (2) wave propagation past cut-outs and stiffeners, and (3) wave propagation in conical shells. Several interferograms are presented herein which show the waves reflecting from the shell boundaries, from cut-outs, and from stiffening rings. The initial response of the shell was nearly axi-symmetric in all cases, but nonsymmetric modes soon appeared in the radial response. This result suggests that the axi-symmetric response of the shell may be dynamically unstable, and thus may preferentially excite certain circumferential harmonics through parametric excitation. Attempts were made throughout to correlate the experimental data with analysis. For the most part, good agreement between theory and experiment was obtained. Occasional differences were attributed primarily to simplifying assumptions used in the analysis. From the standpoint of engineering applications, it is clear that pulsed laser holography can be used to obtain quantitative engineering data. Areas of dynamic stress concentration, stress concentration factors, local anomalies, etc., can be readily determined by holography.

  13. Options for axisymmetric operation of MFTF-B

    SciTech Connect

    Fenstermacher, M.E.; Devoto, R.S.; Thomassen, K.I.

    1986-03-30

    The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 10/sup 13/ cm/sup -3/, have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved.

  14. Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

    SciTech Connect

    Warne, Larry K.; Jorgenson, Roy E.

    2014-10-01

    This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank

  15. Energy and energy flux in axisymmetric slow and fast waves

    NASA Astrophysics Data System (ADS)

    Moreels, M. G.; Van Doorsselaere, T.; Grant, S. D. T.; Jess, D. B.; Goossens, M.

    2015-06-01

    Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions. Appendix A is available in electronic form at http://www.aanda.org

  16. Axisymmetric Simulations of the ITER Vertical Stability Coil

    SciTech Connect

    Titus, Peter H.

    2013-07-09

    The ITER in-vessel coil system includes Vertical Stability (VS) coils and Edge Localized Mode (ELM) coils. There are two large VS ring coils, one upper and one lower. Each has four turns which are independently connected. The VS coils are needed for successful operation of ITER for most all of its operating modes. The VS coils must be highly reliable and fault tolerant. The operating environment includes normal and disruption Lorentz forces. To parametrically address all these design conditions in a tractable analysis requires a simplified model. The VS coils are predominately axisymmetric, and this suggests that an axisymmetric model can be meaningfully used to address the variations in mechanical design, loading, material properties, and time dependency. The axisymmetric finite element analysis described in this paper includes simulations of the bolted frictional connections used for the mounting details. Radiation and elastic-plastic response are modeled particularly for the extreme faulted conditions. Thermal connectivity is varied to study the effects of partial thermal connection of the actively cooled conductor to the remaining structure.

  17. Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

    SciTech Connect

    Goswami, A.; Sing Babu, P.; Pandit, V. S.

    2012-12-15

    This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

  18. Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

    NASA Astrophysics Data System (ADS)

    Goswami, A.; Sing Babu, P.; Pandit, V. S.

    2012-12-01

    This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

  19. The Axisymmetric Tandem Mirror: A Magnetic Mirror Concept Game Changer Magnet Mirror Status Study Group

    SciTech Connect

    Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T

    2008-10-24

    Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT

  20. TSAAS: finite-element thermal and stress analysis of plane and axisymmetric solids with orthotropic temperature-dependent material properties

    SciTech Connect

    Browning, R.V.; Anderson, C.A.

    1982-02-01

    The finite element method is used to determine the temperatures, displacements, stresses, and strains in axisymmetric solids with orthotropic, temperature-dependent material properties under axisymmetric thermal and mechanical loads. The mechanical loads can be surface pressures, surface shears, and nodal point forces as well as an axial or centripetal acceleration. The continuous solid is replaced by a system of ring elements with triangular or quadrilateral cross sections. Accordingly, the method is valid for solids that are composed of many different materials and that have complex geometry. Nonlinear mechanical behavior as typified by plastic, locking, or creeping materials can be approximated. Two dimensional mesh generation, plotting, and editing features allow the computer program to be readily used. In addition to a stress analysis program that is based on a modified version of the SAAS code, TSAAS can carry out a transient thermal analysis with the finite element mesh used in stress analysis. An implicit time differencing scheme allows the use of arbitrary time steps with consequent fast running times. At specified times, the program will return to SAAS for thermal stress analysis. Nonlinear thermal properties and Arrhenius reaction kinetics are also incorporated into TSAAS. Several versions of TSAAS are in use at Los Alamos, running on CDC-7600, CRAY-1 and VAX 11/780 computers. This report describes the nominal TSAAS; other versions may have some unique features.

  1. Light propagation in the field of a moving axisymmetric body: Theory and applications to the Juno mission

    NASA Astrophysics Data System (ADS)

    Hees, A.; Bertone, S.; Le Poncin-Lafitte, C.

    2014-10-01

    Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the time transfer function formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the time transfer functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the time transfer function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral that is easily computable numerically. We also provide the derivatives of the time transfer function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the Juno mission in the Jovian system.

  2. Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

    NASA Technical Reports Server (NTRS)

    Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

    1973-01-01

    A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

  3. Two-coordinate, quasi-two-coordinate, and distorted three coordinate, T-shaped chromium(II) amido complexes: unusual effects of coordination geometry on the lowering of ground state magnetic moments.

    PubMed

    Boynton, Jessica N; Merrill, W Alexander; Reiff, William M; Fettinger, James C; Power, Philip P

    2012-03-01

    The synthesis and characterization of the mononuclear chromium(II) terphenyl substituted primary amido-complexes Cr{N(H)Ar(Pr(i)(6))}(2) (Ar(Pr(i)(6)) = C(6)H(3)-2,6-(C(6)H(2)-2,4,6-(i)Pr(3))(2) (1), Cr{N(H)Ar(Pr(i)(4))}(2) (Ar(Pr(i)(4)) = C(6)H(3)-2,6-(C(6)H(3)-2,6-(i)Pr(2))(2) (2), Cr{N(H)Ar(Me(6))}(2) (Ar(Me(6)) = C(6)H(3)-2,6-(C(6)H(2)-2,4,6-Me(3))(2) (4), and the Lewis base adduct Cr{N(H)Ar(Me(6))}(2)(THF) (3) are described. Reaction of the terphenyl primary amido lithium derivatives Li{N(H)Ar(Pr(i)(6))} and Li{N(H)Ar(Pr(i)(4))} with CrCl(2)(THF)(2) in a 2:1 ratio afforded complexes 1 and 2, which are extremely rare examples of two coordinate chromium and the first stable chromium amides to have linear coordinated high-spin Cr(2+). The reaction of the less crowded terphenyl primary amido lithium salt Li{N(H)Ar(Me(6))} with CrCl(2)(THF)(2) gave the tetrahydrofuran (THF) complex 3, which has a distorted T-shaped metal coordination. Desolvation of 3 at about 70 °C gave 4 which has a formally two-coordinate chromous ion with a very strongly bent core geometry (N-Cr-N= 121.49(13)°) with secondary Cr--C(aryl ring) interactions of 2.338(4) Å to the ligand. Magnetometry studies showed that the two linear chromium species 1 and 2 have ambient temperature magnetic moments of about 4.20 μ(B) and 4.33 μ(B) which are lower than the spin-only value of 4.90 μ(B) typically observed for six coordinate Cr(2+). The bent complex 4 has a similar room temperature magnetic moment of about 4.36 μ(B). These studies suggest that the two-coordinate chromium complexes have significant spin-orbit coupling effects which lead to moments lower than the spin only value of 4.90 μ(B) because λ (the spin orbit coupling parameter) is positive. The three-coordinated complex 3 had a magnetic moment of 3.79 μ(B). PMID:22356657

  4. Particle trajectory computer program for icing analysis of axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.

    1982-01-01

    General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.

  5. Constants of motion in stationary axisymmetric gravitational fields

    NASA Astrophysics Data System (ADS)

    Markakis, C.

    2014-07-01

    The motion of test particles in stationary axisymmetric gravitational fields is generally non-integrable unless a non-trivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant in Kerr-de Sitter space-time is the only example known to date. Proposed astrophysical tests of the black hole no-hair theorem have often involved integrable gravitational fields more general than the Kerr family, but the existence of such fields has been a matter of debate. To elucidate this problem, we treat its Newtonian analogue by systematically searching for non-trivial constants of motion polynomial in the momenta and obtain two theorems. First, solving a set of quadratic integrability conditions, we establish the existence and uniqueness of the family of stationary axisymmetric potentials admitting a quadratic constant. As in Kerr-de Sitter space-time, the mass moments of this class satisfy a `no-hair' recursion relation M2l +2 = a2M2l, and the constant is Noether related to a second-order Killing-Stäckel tensor. Second, solving a new set of quartic integrability conditions, we establish non-existence of quartic constants. Remarkably, a subset of these conditions is satisfied when the mass moments obey a generalized `no-hair' recursion relation M2l +4 = (a2 + b2)M2l +2 - a2b2M2l. The full set of quartic integrability conditions, however, cannot be satisfied non-trivially by any stationary axisymmetric vacuum potential.

  6. The Beauty of Geometry

    ERIC Educational Resources Information Center

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  7. Geometry of multihadron production

    SciTech Connect

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

  8. Want to Play Geometry?

    ERIC Educational Resources Information Center

    Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem

    2009-01-01

    Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…

  9. Euclidean Geometry via Programming.

    ERIC Educational Resources Information Center

    Filimonov, Rossen; Kreith, Kurt

    1992-01-01

    Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…

  10. Geometry + Technology = Proof

    ERIC Educational Resources Information Center

    Lyublinskaya, Irina; Funsch, Dan

    2012-01-01

    Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

  11. An axisymmetric PFEM formulation for bottle forming simulation

    NASA Astrophysics Data System (ADS)

    Ryzhakov, Pavel B.

    2016-05-01

    A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

  12. Marginally stable circular orbits in stationary axisymmetric spacetimes

    NASA Astrophysics Data System (ADS)

    Beheshti, Shabnam; Gasperín, Edgar

    2016-07-01

    We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.

  13. Axisymmetric Turbulent Wakes with New Nonequilibrium Similarity Scalings

    NASA Astrophysics Data System (ADS)

    Nedić, J.; Vassilicos, J. C.; Ganapathisubramani, B.

    2013-10-01

    The recently discovered nonequilibrium turbulence dissipation law implies the existence of axisymmetric turbulent wake regions where the mean flow velocity deficit decays as the inverse of the distance from the wake-generating body and the wake width grows as the square root of that distance. This behavior is different from any documented boundary-free turbulent shear flow to date. Its existence is confirmed in wind tunnel experiments of wakes generated by plates with irregular edges placed normal to an incoming free stream. The wake characteristics of irregular bodies such as buildings, bridges, mountains, trees, coral reefs, and wind turbines are critical in many areas of environmental engineering and fluid mechanics.

  14. The inviscid stability of supersonic flow past axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.

    1990-01-01

    The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).

  15. Preserving spherical symmetry in axisymmetric coordinates for diffusion problems

    SciTech Connect

    Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.

    2013-07-01

    Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)

  16. Computed and measured turbulence in axisymmetric reciprocating engines

    NASA Technical Reports Server (NTRS)

    Grasso, F.; Bracco, F. V.

    1983-01-01

    The turbulent flowfield of a spark-ignition engine affects strongly the combustion characteristics of the engine. The flowfield depends on the design of the combustion chamber and the intake system. The present investigation is concerned with the effect of chamber design, and engine operating conditions on top dead center turbulence prior to ignition. It is shown that many of the trends which were identified in earlier studies can be obtained from a single model. The employed model takes into account a two-dimensional axisymmetric flowfield. Attention is given to governing equations, boundary and initial conditions, a comparison of the computed results with measurements, and the effect of swirl and squish.

  17. Fusion-product transport in axisymmetric tokamaks: losses and thermalization

    SciTech Connect

    Hively, L.M.

    1980-01-01

    High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-..beta.., non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated.

  18. Axisymmetric vibrations of laminated composite conical shells with varying thickness

    SciTech Connect

    Shikanai, G.; Suzuki, K.; Kojima, M.

    1995-11-01

    An exact solution procedure is presented for solving axisymmetric free vibrations of laminated composite conical shells with varying thickness. Based on the classical lamination theory neglecting shear deformation and rotary inertia, equations of motion and boundary conditions are obtained from the stationary conditions of the Lagrangian. The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply conical shells. Numerical studies are made for conical shells having both ends clamped to show the effects of the number of laminae, stacking sequences and other parameters upon the frequencies.

  19. Vortex motion in axisymmetric piston-cylinder configurations

    NASA Technical Reports Server (NTRS)

    Shih, T. I. P.; Smith, G. E.; Springer, G. S.

    1982-01-01

    By using the Beam and Warming implicit-factored method of solution of the Navier-Stokes equations, velocities were calculated inside axisymmetric piston cylinder configurations during the intake and compression strokes. Results are presented in graphical form which show the formation, growth and breakup of those vortices which form during the intake stroke by the jet issuing from the valve. It is shown that at bore-to-stroke ratio of less than unity, the vortices may breakup during the intake stroke. It is also shown that vortices which do not breakup during the intake stroke coalesce during the compression stroke.

  20. Axisymmetric inviscid swirling flows produced by bellmouth and centerbody

    NASA Technical Reports Server (NTRS)

    Nakamura, Y.; Yasuhara, M.; Hama, T.

    1982-01-01

    The effect of large deformation in the flow between the bellmouth and centerbody is considered analytically for application to studies of vortex breakdown in a pipe. Basic equations are defined for axisymmetric inviscid swirling flows at the inflow and outflow sections. Axial and circumferential velocity component profiles are presented, and comparisons are made with trials involving vane angles of 42 deg and Re of 2300. Axial components of the prediction matched well in the inner half of the pipe radius and not well with the outer, while circumferential predictions were good only at the axis. A lack of viscosity was concluded to result in the inaccuracies near the wall.

  1. Axisymmetric inviscid swirling flows produced by bellmouth and centerbody

    NASA Astrophysics Data System (ADS)

    Nakamura, Y.; Yasuhara, M.; Hama, T.

    1982-04-01

    The effect of large deformation in the flow between the bellmouth and centerbody is considered analytically for application to studies of vortex breakdown in a pipe. Basic equations are defined for axisymmetric inviscid swirling flows at the inflow and outflow sections. Axial and circumferential velocity component profiles are presented, and comparisons are made with trials involving vane angles of 42 deg and Re of 2300. Axial components of the prediction matched well in the inner half of the pipe radius and not well with the outer, while circumferential predictions were good only at the axis. A lack of viscosity was concluded to result in the inaccuracies near the wall.

  2. Ballooning stability of axisymmetric plasmas with sheared equilibrium flows

    NASA Technical Reports Server (NTRS)

    Bhattacharjee, A.; Iacono, R.; Milovich, J. L.; Paranicas, C.

    1989-01-01

    A WKB theory is formulated for large-n ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning respresentation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/n), where n is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.

  3. Numerical boundary condition procedure for the transonic axisymmetric inverse problem

    NASA Technical Reports Server (NTRS)

    Shankar, V.

    1981-01-01

    Two types of boundary condition procedures for the axisymmetric inverse problem are described. One is a Neumann type boundary condition (analogous to the analysis problem) and the other is a Dirichlet type boundary conditon, both requiring special treatments to make the inverse scheme numerically stable. The dummy point concept is utilized in implementing both. Results indicate the Dirichlet type inverse boundary condition is more robust and conceptually simpler to implement than the Neumann type procedure. A few results demonstrating the powerful capability of the newly developed inverse method that can handle both shocked as well as shockless body design are included.

  4. Constant Density Approximations for the Flow Behind Axisymmetric Shock Waves

    NASA Technical Reports Server (NTRS)

    Munson, Albert G.

    1961-01-01

    The incompressible rotational flow equations are used to obtain solutions for the flow behind axisymmetric shock waves with conic longitudinal sections. The nonlinear part of the term due to rotation is retained in the analysis. Numerical results for standoff distance and stagnation point velocity gradient are presented for the case in which the shock wave is a paraboloid, a sphere, or an oblate or prolate ellipsoid. A similarity parameter is proposed which correlates approximately the flow behind geometrically similar shock waves at different free-stream conditions.

  5. Macroscopic analysis of axisymmetric functionally gradient material under thermal loading

    SciTech Connect

    Kwon, P.; Dharan, C.K.H.; Ferrari, M. )

    1994-06-01

    The axisymmetric functionally gradient materials (FGMs) subject to nonuniform temperature variations were studied with the combined use of homogenization and inhomogeneous eigenstrained media analysis. The material properties and the temperature variations were assumed to depend on the radial coordinate only. The inhomogeneous material properties of the FGM cylinder can be obtained by modulating the concentration level of spherical alumina particles in an aluminum matrix. The resulting stresses due to the temperature variation are presented for numerous distribution functions of alumina particles. It is shown that the particle distribution extensively influences the intensity and profile of the thermal stresses.

  6. Quasi-static axisymmetric eversion hemispherical domes made of elastomers

    NASA Astrophysics Data System (ADS)

    Kabrits, Sergey A.; Kolpak, Eugeny P.

    2016-06-01

    The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.

  7. Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet

    NASA Technical Reports Server (NTRS)

    Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.

    2000-01-01

    This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.

  8. Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

    NASA Astrophysics Data System (ADS)

    Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.; Christodoulakis, T.

    2016-05-01

    In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.

  9. Non-axisymmetric flows on hot Jupiters with oblique magnetic fields

    SciTech Connect

    Batygin, Konstantin; Stanley, Sabine

    2014-10-10

    Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the perturbed circulation and show that the fractional distortion of zonal jets scales as the product of the field obliquity and the Elsässer number. The results obtained herein suggest that on planets with oblique magnetic fields, advective shifts of dayside hotspots may have substantial latitudinal components. This prediction may be tested observationally using the eclipse mapping technique.

  10. Flight Test Results of an Axisymmetric Channeled Center Body Supersonic Inlet at Off-Design Conditions

    NASA Technical Reports Server (NTRS)

    St. John, Clinton W.; Frederick, Michael Alan

    2013-01-01

    Flight-testing of a channeled center-body axisymmetric supersonic inlet design concept was conducted at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center in collaboration with the NASA Glenn Research Center (Cleveland, Ohio) and TechLand Research, Inc. (North Olmsted, Ohio). This testing utilized the Propulsion Flight Test Fixture, flown on the NASA F-15B research test bed airplane (NASA tail number 836) at local experiment Mach numbers up to 1.50. The translating channeled center-body inlet was designed by TechLand Research, Inc. (U.S. Patent No. 6,276,632 B1) to allow for a novel method of off-design flow matching, with original test planning conducted under a NASA Small Business Innovative Research study. Data were collected in flight at various off-design Mach numbers for fixed-geometry representations of both the channeled center-body design and an equivalent area smooth center-body design for direct comparison of total pressure recovery and limited distortion measurements.

  11. Non-axisymmetric Flows on Hot Jupiters with Oblique Magnetic Fields

    NASA Astrophysics Data System (ADS)

    Batygin, Konstantin; Stanley, Sabine

    2014-10-01

    Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the perturbed circulation and show that the fractional distortion of zonal jets scales as the product of the field obliquity and the Elsässer number. The results obtained herein suggest that on planets with oblique magnetic fields, advective shifts of dayside hotspots may have substantial latitudinal components. This prediction may be tested observationally using the eclipse mapping technique.

  12. Spreading of non-planar non-axisymmetric gravity and turbidity currents

    NASA Astrophysics Data System (ADS)

    Zgheib, Nadim; Bonometti, Thomas; Balachandar, S.

    2014-11-01

    The dynamics of non-axisymmetric turbidity currents is considered here. The study comprises a series of experiments for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of diameter 280 geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther and deposits more particles along the initial minor axis of the rectangular cross section. Interestingly, this departure from axisymmetry cannot be predicted by current theoretical methods such as the Box Model. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio, local curvature and mixture density. NSF-PIRE OISE-0968313.

  13. TRANSIENT RESPONSE OF ABLATING AXISYMMETRIC BODIES INCLUDING THE EFFECTS OF SHAPE CHANGE

    NASA Technical Reports Server (NTRS)

    Howser, L. M.

    1994-01-01

    A computer program has been developed to analyze the transient response of an ablating axisymmetric body, including the effect of shape change. The governing differential equation, the boundary conditions for the analysis on which the computer program is based, and the method of solution of the resulting finite-difference equations are discussed in the documentation. Some of the features of the analysis and the associated program are (1) the ablation material is considered to be orthotropic with temperature-dependent thermal properties; (2) the thermal response of the entire body is considered simultaneously; (3) the heat transfer and pressure distribution over the body are adjusted to the new geometry as ablation occurs; (4) the governing equations and several boundary-condition options are formulated in terms of generalized orthogonal coordinates for fixed points in a moving coordinate system; (5) the finite-difference equations are solved implicitly; and (6) other instantaneous body shapes can be displayed with a user-supplied plotting routine. The physical problem to be modeled with the analysis is described by FORTRAN input variables. For example, the external body geometry is described in the W, Z coordinates; material density is given; and the stagnation cold-wall heating rate is given in a time-dependent array. Other input variables are required which control the solution, specify boundary conditions, and determine output from the program. The equations have been programmed so that either the International System of Units or the U. S. Customary Units may be used. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 Series computer. This program was developed in 1972.

  14. Collection-efficient, axisymmetric vacuum sublimation module for the purification of solid materials.

    PubMed

    May, Michael; Paul, Elizabeth; Katovic, Vladimir

    2015-11-01

    A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material. PMID:26628150

  15. Stokes flow in ellipsoidal geometry

    NASA Astrophysics Data System (ADS)

    Vafeas, Panayiotis; Dassios, George

    2006-09-01

    Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich-Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading

  16. Axisymmetric and non-axisymmetric exhaust jet induced effects on a V/STOL vehicle design. Part 3: Experimental technique

    NASA Technical Reports Server (NTRS)

    Schnell, W. C.

    1982-01-01

    The jet induced effects of several exhaust nozzle configurations (axisymmetric, and vectoring/modulating varients) on the aeropropulsive performance of a twin engine V/STOL fighter design was determined. A 1/8 scale model was tested in an 11 ft transonic tunnel at static conditions and over a range of Mach Numbers from 0.4 to 1.4. The experimental aspects of the static and wind-on programs are discussed. Jet effects test techniques in general, fow through balance calibrations and tare force corrections, ASME nozzle thrust and mass flow calibrations, test problems and solutions are emphasized.

  17. Seismic wave propagation in fully anisotropic axisymmetric media

    NASA Astrophysics Data System (ADS)

    van Driel, Martin; Nissen-Meyer, Tarje

    2014-11-01

    We present a numerical method to compute 3-D elastic waves in fully anisotropic axisymmetric media. This method is based on a decomposition of the wave equation into a series of uncoupled 2-D equations for which the dependence of the wavefield on the azimuth can be solved analytically. Four independent equations up to quadrupole order appear as solutions for moment-tensor sources located on the symmetry axis while single forces can be accommodated by two separate solutions up to dipole order. This decomposition gives rise to an efficient solution of the 3-D wave equation in a 2-D axisymmetric medium. First, we prove the validity of the decomposition of the wavefield in the presence of general anisotropy. Then we use it to derive the reduced 2-D equations of motions and discretize them using the spectral element method. Finally, we benchmark the numerical implementation for global wave propagation at 1 Hz and consider inner core anisotropy as an application for high-frequency wave propagation in anisotropic media at frequencies up to 2 Hz.

  18. Fast solver for systems of axisymmetric ring vortices

    NASA Astrophysics Data System (ADS)

    Strickland, James H.; Amos, Donald E.

    1992-03-01

    A method that is capable of efficient calculation of the axisymmetric flowfield produced by a large system of ring vortices is presented in this paper. The system of ring vortices can, in turn, be used to model body surfaces and wakes in incompressible unsteady axisymmetric flowfields. This method takes advantage of source-point and field-point series expansion, which enables one to make calculations for interactions between groups of vortices that are in well-separated spatial domains rather than having to consider interactions between every pair of vortices. A FORTRAN computer code, RSOLV, has been written to execute the fast solution technique. For 100 vortices in the field, there is virtually no CPU time savings with the fast solver. For 10,000 vortices in the flow, the fast solver obtains solutions in about 1-3 percent of the time required for the direct solution technique. Formulas for the self-induced velocity of discretized regions of the flowfield have been developed. Use of these formulas allows correct convection of discretized patches of vorticity in the flowfiled.

  19. Finite axisymmetric charged dust disks in conformastatic spacetimes

    SciTech Connect

    Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Ospina, Paolo A.

    2008-09-15

    An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonzalez and Reina [G. A. Gonzalez and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.

  20. Generalized energy principle for flute perturbations in axisymmetric mirror machines

    SciTech Connect

    Lansky, I.M.; Ryutov, D.D.

    1993-01-20

    Axial symmetry is a very desirable property of the mirror devices both for fusion and neutron source applications. The main obstacle to be circumvented in the development of such systems, is the flute instability of axisymmetric mirrors. In recent years there appeared a number of proposals, devoted to the stabilization of the flute perturbations in the framework of axisymmetric magnetic configurations, which are based on the combining of the MHD unstable central cell with various types of end-cell stabilizers. In the present paper we concentrate ourselves just on this scheme, including long solenoid with a uniform field, conjugated with the end stabilizing anchor, intended to provide MHD stability of the system as a whole. The attractive feature of such a configuration is that it allows to exploit finite larmor radius (FLR) effects for the stabilization of the flute perturbations. As is well known, FLR effects, being strong, stabilize all flute modes, except the one with azimuthal number m = 1, corresponding to the ``rigid`` displacement of the plasma column (the ``global`` mode). Consequently, in the conditions when FLR effects dominate, the anchor has to stabilize the ``global` mode only. Bearing in mind a favorable influence of FLR effects we, however, don`t restrict our paper by discussion of only ``global`` mode stability and consider a general case of an arbitrary azimuthal mode.

  1. Modeling of non-axisymmetric magnetic perturbations in tokamaks

    NASA Astrophysics Data System (ADS)

    Sun, Y.; Liang, Y.; Qian, J.; Shen, B.; Wan, B.

    2015-04-01

    A numerical model to evaluate the effects of the non-axisymmetric magnetic perturbations on magnetic topology and magnetic field ripple in tokamaks is presented in this paper. It is illustrated by using an example magnetic field perturbation induced by a coil system on the EAST tokamak. The influence of the choice of the coordinates on the spectrum is presented. The amplitude of resonant components of the spectrum are found to be independent of the coordinates system, while that of the non-resonant components are not. A better way to describe the edge topology by using the Chirikov parameter profile is proposed and checked by the numerical Poincaré plot results. The contribution of the magnetic perturbation on local toroidal field ripple can be significant. One approximate method to model the helical ripple on the perturbed flux surface induced by a given non-axisymmetric magnetic field perturbation is presented. All of the spectrum analysis is applicable in case the plasma response is taken into account in the input of perturbed magnetic field.

  2. THE ADVECTION OF SUPERGRANULES BY THE SUN'S AXISYMMETRIC FLOWS

    SciTech Connect

    Hathaway, David H.; Williams, Peter E.; Rosa, Kevin Dela; Cuntz, Manfred E-mail: peter.williams@nasa.go

    2010-12-10

    We show that the motions of supergranules are consistent with a model in which they are simply advected by the axisymmetric flows in the Sun's surface shear layer. We produce a 10 day series of simulated Doppler images at a 15 minute cadence that reproduces most spatial and temporal characteristics seen in the SOHO/MDI Doppler data. Our simulated data have a spectrum of cellular flows with just two components-a granule component that peaks at spherical wavenumbers of about 4000 and a supergranule component that peaks at wavenumbers of about 110. We include the advection of these cellular components by the axisymmetric flows-differential rotation and meridional flow-whose variations with latitude and depth (wavenumber) are consistent with observations. We mimic the evolution of the cellular pattern by introducing random variations to the phases of the spectral components at rates that reproduce the levels of cross-correlation as functions of time and latitude. Our simulated data do not include any wave-like characteristics for the supergranules yet can reproduce the rotation characteristics previously attributed to wave-like behavior. We find rotation rates which appear faster than the actual rotation rates and attribute this to projection effects. We find that the measured meridional flow does accurately represent the actual flow and that the observations indicate poleward flow to 65{sup 0}-70{sup 0} latitude with equatorward countercells in the polar regions.

  3. Resolving the uncertainties of non-axisymmetric fields in tokamaks

    NASA Astrophysics Data System (ADS)

    in, Yongkyoon; Seol, J.; Ko, W. H.; Lee, S. G.; Yoon, S. W.; Lee, H. H.; Jeon, Y. M.; Kim, J.; Bak, J. G.; Park, H.; Park, J. K.; Yun, G. S.; 3D Physics Task Force Team

    2015-11-01

    Recent study suggests that KSTAR could be a benefactor of the extremely low level of intrinsic error field in n =1 resonant magnetic perturbation (RMP) driven edge localized modes (ELM) control. Specifically, when the n = 1 RMP currents increases in order to suppress/mitigate ELMs, a kink-resonant mode-locking is not usually invoked in KSTAR, unlike in other devices. Besides we have discovered that the mid-plane RMP appeared much more effective than the off-midplane RMPs in affecting the ELMs with strong density pump-outs and enhanced ELM frequency. Presently, the enhanced understanding of non-axisymmetric field in tokamaks has been in great need, in particular, for the ITER RMP requirements. As the prevailing design of in-vessel RMP coils in ITER is similar to that in KSTAR, we are keen to resolve the uncertainties of the non-axisymmetric fields on transport and stability, and their limits, contributing directly to ITER and beyond.

  4. Axisymmetric Flow Properties for Magnetic Elements of Differing Strength

    NASA Technical Reports Server (NTRS)

    Rightmire-Upton, Lisa; Hathaway, David H.

    2012-01-01

    Aspects of the structure and dynamics of the flows in the Sun's surface shear layer remain uncertain and yet are critically important for understanding the observed magnetic behavior. In our previous studies of the axisymmetric transport of magnetic elements we found systematic changes in both the differential rotation and the meridional flow over the course of Solar Cycle 23. Here we examine how those flows depend upon the strength (and presumably anchoring depth) of the magnetic elements. Line of sight magnetograms obtained by the HMI instrument aboard SDO over the course of Carrington Rotation 2097 were mapped to heliographic coordinates and averaged over 12 minutes to remove the 5-min oscillations. Data masks were constructed based on the field strength of each mapped pixel to isolate magnetic elements of differing field strength. We used Local Correlation Tracking of the unmasked data (separated in time by 1- to 8-hours) to determine the longitudinal and latitudinal motions of the magnetic elements. We then calculated average flow velocities as functions of latitude and longitude from the central meridian for approx 600 image pairs over the 27-day rotation. Variations with longitude indicate and characterize systematic errors in the flow measurements associated with changes in the signal from disk center to limb. Removing these systematic errors reveals changes in the axisymmetric flow properties that reflect changes in flow properties with depth in the surface shear layer.

  5. Axisymmetric Boundary Element Method for vesicles in a capillary

    NASA Astrophysics Data System (ADS)

    Trozzo, R.; Boedec, G.; Leonetti, M.; Jaeger, M.

    2015-05-01

    The problem of a vesicle transported by a fluid flow can present a large range of length scales. One example is the case of a vesicle producing a tether, and eventually pearls, in an elongational flow. Another case occurs when a lubrication film is formed, such as during the short range interaction between two vesicles. Such problems are still challenging for 3D simulations. On the other hand, a good understanding could be obtained by first considering the axisymmetric regime when such a regime exists. An axisymmetric model could then be used, without the criticisms that can be made of a 2D approach. We propose such a model, primarily interested in flows through narrow cylindrical capillaries. Two options are compared, with and without explicit representation of the capillary boundaries by a mesh. The numerical effort is characterized as a function of the vesicle's initial shape, the flow magnitude and the confinement. The model is able to treat typical configurations of red blood cells flowing through very narrow pores with extremely thin lubrication films.

  6. Two-integral distribution functions for axisymmetric galaxies

    NASA Technical Reports Server (NTRS)

    Hunter, C.; Qian, Edward

    1993-01-01

    The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.

  7. Acoustic intensity calculations for axisymmetrically modeled fluid regions

    NASA Technical Reports Server (NTRS)

    Hambric, Stephen A.; Everstine, Gordon C.

    1992-01-01

    An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones.

  8. Aerodynamic Flow Control of a Moving Axisymmetric Platform

    NASA Astrophysics Data System (ADS)

    Lambert, Thomas J.; Vukasinovic, Bojan; Glezer, Ari

    2013-11-01

    Active fluidic control of induced aerodynamic forces and moments on a moving axisymmetric platform is investigated in wind tunnel experiments. Actuation is effected by controlled interactions between an azimuthal array of integrated synthetic jets with the cross flow to induce localized flow attachment domains over the aft end of the model and thereby alter the global aerodynamic forces and moments. The axisymmetric platform is wire-mounted on a 6 DOF traverse such that each of the eight mounting wires is connected to a servo motor with an in-line load cell for monitoring the wire tension. The desired platform motion is controlled in closed-loop by a laboratory computer. The effects of continuous and transitory actuation on the induced aerodynamic forces of the moving platform are investigated in detail using high-speed PIV. The time-dependent changes in the forces are explored for model maneuvering and stabilization. It is found that the actuation induces forces and moments that are on the order of the forces and moments of the baseline flow. These measurements agree with preliminary results on the stabilization of a model moving in a single DOF demonstrating the effectiveness of the actuation for trajectory stabilization. Supported by the ARO.

  9. Non-axisymmetrical freeform design for short LED street lamp

    NASA Astrophysics Data System (ADS)

    Jen, Ching-Hsuan; Chen, Yi-Yung; Whang, Allen Jong-Woei; Lu, Ming-Jun

    2011-10-01

    Based on energy savings trend, LED has been developing as the main force of the future lighting, especially the road lighting. For controlling the intensity distribution of LED, the concept of freeform design has been proposed in many articles with transmission or reflection components but mainly focus on axial symmetrical types or dual axial symmetrical types. We, in this paper, design a non-axisymmetrical freeform system applying in a short LED street lamp whose dimension is 10cm (W) x 10cm (L) x 7cm (H) that has an advantage, easy maintaining. For coordinate transformation and simplifying the non- axisymmetrical system, we create two virtual surfaces and design the slope of each discrete point on the freeform surface to control the light path between the two virtual surfaces and avoid the total internal reflection. The short street lamp has four LEDs to light 3m square and each LED light a triangle area. According to the simulation results, the uniformity of illumination is 1:3 and the optical efficiency is more than 80% that meet the legal requirements of street lamp. In short, to reduce manufacturing and maintenance costs, the proposed design is appropriate to use in the actual lighting on the road and to replace the traditional street lamps.

  10. Finite axisymmetric charged dust disks in conformastatic spacetimes

    NASA Astrophysics Data System (ADS)

    González, Guillermo A.; Gutiérrez-Piñeres, Antonio C.; Ospina, Paolo A.

    2008-09-01

    An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by González and Reina [G. A. González and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).MNRAA40035-871110.1111/j.1365-2966.2006.10819.x], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.

  11. Nozzle design study for a quasi-axisymmetric scramjet-powered vehicle at Mach 7.9 flight conditions

    NASA Astrophysics Data System (ADS)

    Tanimizu, Katsuyoshi; Mee, David J.; Stalker, Raymond J.; Jacobs, Peter A.

    2013-09-01

    A nozzle shape optimization study for a quasi-axisymmetric scramjet has been performed for a Mach 7.9 operating condition with hydrogen fuel, aiming at the application of a hypersonic airbreathing vehicle. In this study, the nozzle geometry which is parameterized by a set of design variables, is optimized for the single objective of maximum net thrust using an in-house CFD solver for inviscid flowfields with a simple force prediction methodology. The combustion is modelled using a simple chemical reaction code. The effects of the nozzle design on the overall vehicle performance are discussed. For the present geometry, net thrust is achieved for the optimized vehicle design. The results of the nozzle-optimization study show that performance is limited by the nozzle area ratio that can be incorporated into the vehicle without leading to too large a base diameter of the vehicle and increasing the external drag of the vehicle. This study indicates that it is very difficult to achieve positive thrust at Mach 7.9 using the basic geometry investigated.

  12. Mantle viscosity stratification and flow geometry - Implications for surface motions on earth and Venus

    NASA Technical Reports Server (NTRS)

    Kiefer, Walter S.

    1993-01-01

    For a fixed heat flow, the surface flow velocity of a convecting layer is not strongly sensitive to the variation of viscosity as a function of depth. Thus, the inferred absence of a low viscosity asthenosphere on Venus can not account for the limited surface motions there. The surface velocity is dependent on the convective geometry. Cartesian geometry convection can produce large surface velocities if the high viscosity surface layer is broken in places by weak zones. On the other hand, a high viscosity surface layer may inhibit the development of large surface velocities in axisymmetric convection.

  13. Mantle viscosity stratification and flow geometry - Implications for surface motions on earth and Venus

    NASA Astrophysics Data System (ADS)

    Kiefer, W. S.

    1993-02-01

    For a fixed heat flow, the surface flow velocity of a convecting layer is not strongly sensitive to the variation of viscosity as a function of depth. Thus, the inferred absence of a low viscosity asthenosphere on Venus can not account for the limited surface motions there. The surface velocity is dependent on the convective geometry. Cartesian geometry convection can produce large surface velocities if the high viscosity surface layer is broken in places by weak zones. On the other hand, a high viscosity surface layer may inhibit the development of large surface velocities in axisymmetric convection.

  14. Effects of Large-scale Non-axisymmetric Perturbations in the Mean-field Solar Dynamo.

    NASA Astrophysics Data System (ADS)

    Pipin, V. V.; Kosovichev, A. G.

    2015-11-01

    We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R⊙ has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number Rm. In the range of Rm = 104-106 the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.

  15. Gingerbread-House Geometry.

    ERIC Educational Resources Information Center

    Emenaker, Charles E.

    1999-01-01

    Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

  16. What Is Geometry?

    ERIC Educational Resources Information Center

    Chern, Shiing-Shen

    1990-01-01

    Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)

  17. Noncommutative Geometry and Physics

    NASA Astrophysics Data System (ADS)

    Connes, Alain

    2006-11-01

    In this very short essay we shall describe a "spectral" point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a "sum over geometries" on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of "observables" in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.

  18. Proof in Transformation Geometry

    ERIC Educational Resources Information Center

    Bell, A. W.

    1971-01-01

    The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

  19. Wave Propagation in Axi-Symmetrical Magmatic Conduits Due to an Internal Source

    NASA Astrophysics Data System (ADS)

    De Negri, R. S.; Sanchez-Sesma, F. J.; Arciniega-Ceballos, A.

    2014-12-01

    The classical Trefftz's method is implemented to simulate wave propagation in and around axi-symmetrical magmatic conduits. In this fluid-solid system the fluid (magma) is confined by an elastic unbounded medium that represents the surrounding rock. Our aim is to associate wave behavior with mechanical and geometrical conduit characteristics. The source is assumed to be at a point along the conduit centered axis medium are constructed in both cases as linear combinations of particular solutions.Within the fluid such solutions are spherical standing waves that are smooth at the origins. In the elastic solid region the field is constructed with monopoles and dipoles for the P waves and spheroidal dipoles for SV waves. The particular solutions satisfy the elastodynamic equations that govern the wave motion at those media and are associated to origins (selected points) distributed along the conduit axis. For the surrounding rock the solutions are sources that satisfy Sommerfeld's radiation condition. These sets of solutions are assumed to be complete. This conjecture is exact in 2D acoustic problems. The conduit can be closed or open at the ends and the surrounding elastic domain is unbounded. In order to find the coefficients of Trefftz's wave expansions, boundary conditions at the fluid-solid interface (null shear and continuity of pressures and normal velocities) are satisfied in the least squares sense. The solution is obtained in the frequency domain and the source time function can be introduced using Fourier analysis.Regardless the low order of the formulation our results display a rich variety of behaviors. For a uniform infinite cylinder we reproduced the exact analytical solution. In addition, this approach allows identifying some important effects of the conduit geometry, including changes of sections. Lateral and longitudinal resonances of irregular axi-symmetric conduits are well resolved. The stiffness of the solid domain with respect to the fluid

  20. Common Geometry Module

    Energy Science and Technology Software Center (ESTSC)

    2005-01-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less

  1. CMS Geometry Through 2020

    NASA Astrophysics Data System (ADS)

    Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.

    2014-06-01

    CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

  2. Fluctuations of spherical waves in a turbulent atmosphere: effect of the axisymmetric approximation in computational methods.

    PubMed

    Salomons, E M

    2000-10-01

    The validity of the axisymmetric parabolic-equation (PE) method for line-of-sight sound propagation in a turbulent atmosphere is investigated. The axisymmetric PE method is a finite-difference method for solving a 2D parabolic wave equation, which follows from the 3D wave equation by the assumption of axial symmetry around the vertical axis through the source. It is found that this axisymmetric approximation has a considerable spurious effect on the fluctuations of the sound field. This is concluded from analytical expressions for the log-amplitude and phase variances, derived both for isotropic turbulence and for axisymmetric turbulence. The expressions for axisymmetric turbulence are compared with the results of numerical computations with the PE method. PMID:11051480

  3. Integrated modeling and parallel computation of laser-induced axisymmetric rod growth

    NASA Astrophysics Data System (ADS)

    Lan, Hong

    2005-07-01

    and Windows XP. Computation in the gas-phase domain is encapsulated in a C++ class, and it is convenient for users to choose either the integrated or the kinetic model to perform simulation of rod growth. Parallel implementation improves the computational performance. To demonstrate the capability of the integrated model, silane is chosen as the precursor to grow the axisymmetric rod with silicon as deposit and graphite as substrate. The integrated 3D LCVD model and the corresponding numerical methods are applied to simulate the gas-phase reaction process, and to predict heat transfer, molar ratio, initial and successive rod growths and growth time at each iteration. It is found that the diffusion-limited growth can affect the deposition process and must be taken into account when the temperature is higher than a certain threshold. The initial rod growth can affect the successive rod growth and its geometry. This modeling approach may provide a useful means for investigating the effect of different model parameters for optimizing the LCVD process.

  4. Star accretion onto supermassive black holes in axisymmetric galactic nuclei

    NASA Astrophysics Data System (ADS)

    Zhong, Shiyan; Berczik, Peter; Spurzem, Rainer

    2016-02-01

    Tidal Disruption (TD) of stars by supermassive central black holes from dense rotating star clusters is modeled by high-accuracy direct N-body simulation. We study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars. Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum J is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals bimodal features. We show that the bimodal structure can be explained by the presence of two families of regular orbits, namely short axis tube and saucer orbits.

  5. Modular Coils and Plasma Configurations for Quasi-axisymmetric Stellarators

    SciTech Connect

    L.P. Ku and A.H. Boozer

    2010-09-10

    Characteristics of modular coils for quasi-axisymmetric stellarators that are related to the plasma aspect ratio, number of field periods and rotational transform have been examined systematically. It is observed that, for a given plasma aspect ratio, the coil complexity tends to increase with the increased number of field periods. For a given number of field periods, the toroidal excursion of coil winding is reduced as the plasma aspect ratio is increased. It is also clear that the larger the coil-plasma separation is, the more complex the coils become. It is further demonstrated that it is possible to use other types of coils to complement modular coils to improve both the physics and the modular coil characteristics.

  6. Minimum weight design of a generic axisymmetric inlet

    NASA Technical Reports Server (NTRS)

    Nadell, Shari-Beth

    1996-01-01

    A new minimum weight design method for high-speed axisymmetric inlets was demonstrated on a generic inlet. The method uses Classical Beam Theory and shell buckling to determine the minimum required equivalent isotropic thickness for a stiffened shell based on prescribed structural design requirements and load conditions. The optimum spacing and equivalent isotropic thickness of ring frame supports are computed to prevent buckling. The method thus develops a preliminary structural design for the inlet and computes the structural weight. Finite element analyses were performed on the resulting inlet design to evaluate the analytical results. Comparisons between the analytical and finite element stresses and deflections identified areas needing improvement in the analytical method. The addition of the deflection due to shear and a torsional buckling failure mode to the new method brought its results in line with those from the finite element analyses. Final validation of the new method will be made using data from actual inlets.

  7. Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, Peter W.; Hall, Philip

    1988-01-01

    In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.

  8. Ideal saturated MHD helical structures in axisymmetric hybrid plasmas

    NASA Astrophysics Data System (ADS)

    Brunetti, D.; Graves, J. P.; Cooper, W. A.; Terranova, D.

    2014-06-01

    Kinked saturated m = 1 helical structures are frequently observed in tokamak hybrid plasmas and in reversed field pinches (RFP). These modes occur when an extremum in the safety factor is close to, but necessarily resonant with, a low order rational (typically qmin ≈ 1/1 in tokamaks, and qmax ≈ 1/7 in RFPs). If the exact resonance can be avoided, the essential character of these modes can be modelled assuming ideal nested magnetic flux surfaces. The methods used to characterize these structures include linear and nonlinear ideal magnetohydrodynamic stability calculations, which evaluate the departure from an axisymmetric plasma state, or equilibrium calculations using a 3D equilibrium code. The extent to which these approaches agree in tokamaks and reverse field pinches is investigated, and compared favourably for the first time with an analytic nonlinear treatment that is valid for arbitrary toroidal mode number.

  9. Development of Compact Quasi-Axisymmetric Stellarator Reactor Configurations

    SciTech Connect

    L.P. Ku; M. Zarnstorff; R.B. White; W.A. Cooper; R. Sanchez; H. Neilson; J.A. Schmidt

    2003-09-19

    We have started to examine the reactor potential of quasi-axisymmetric (QA) stellarators with an integrated approach that includes systems evaluation, engineering considerations, and plasma and coil optimizations. In this paper, we summarize the progress made so far in developing QA configurations with reduced alpha losses while retaining good MHD stability properties. The minimization of alpha losses is achieved by directly targeting the collisionless orbits to prolong the average resident times. Configurations with an overall energy loss rate of {approx}10% or less, including collisional contributions, have been found. To allow remotely maintaining coils and machine components in a reactor environment, there is a desire to simplify to the extent possible the coil design. To this end, finding a configuration that is optimized not only for the alpha confinement and MHD stability but also for the good coil and reactor performance, remains to be a challenging task.

  10. Axisymmetric buckling of laminated thick annular spherical cap

    NASA Astrophysics Data System (ADS)

    Dumir, P. C.; Dube, G. P.; Mallick, A.

    2005-03-01

    Axisymmetric buckling analysis is presented for moderately thick laminated shallow annular spherical cap under transverse load. Buckling under central ring load and uniformly distributed transverse load, applied statically or as a step function load is considered. The central circular opening is either free or plugged by a rigid central mass or reinforced by a rigid ring. Annular spherical caps have been analysed for clamped and simple supports with movable and immovable inplane edge conditions. The governing equations of the Marguerre-type, first order shear deformation shallow shell theory (FSDT), formulated in terms of transverse deflection w, the rotation ψ of the normal to the midsurface and the stress function Φ, are solved by the orthogonal point collocation method. Typical numerical results for static and dynamic buckling loads for FSDT are compared with the classical lamination theory and the dependence of the effect of the shear deformation on the thickness parameter for various boundary conditions is investigated.

  11. Time and 'angular' dependent backgrounds from stationary axisymmetric solutions

    SciTech Connect

    Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.

    2004-09-15

    Backgrounds depending on time and on angular variable, namely, polarized and unpolarized S{sup 1}xS{sup 2} Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary D-branes, iD-branes allow one to find S-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzschild and the Kerr metrics. The possibility of studying the i-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized S-branes depending not only on time but also on an angular variable.

  12. Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

    SciTech Connect

    Artun, M.; Tang, W.M.

    1994-03-01

    The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.

  13. Fluidic Control of Aerodynamic Forces on an Axisymmetric Body

    NASA Astrophysics Data System (ADS)

    Abramson, Philip; Vukasinovic, Bojan; Glezer, Ari

    2007-11-01

    The aerodynamic forces and moments on a wind tunnel model of an axisymmetric bluff body are modified by induced local vectoring of the separated base flow. Control is effected by an array of four integrated aft-facing synthetic jets that emanate from narrow, azimuthally-segmented slots, equally distributed around the perimeter of the circular tail end within a small backward facing step that extends into a Coanda surface. The model is suspended in the wind tunnel by eight thin wires for minimal support interference with the wake. Fluidic actuation results in a localized, segmented vectoring of the separated base flow along the rear Coanda surface and induces asymmetric aerodynamic forces and moments to effect maneuvering during flight. The aerodynamic effects associated with quasi-steady and transitory differential, asymmetric activation of the Coanda effect are characterized using direct force and PIV measurements.

  14. Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

    NASA Astrophysics Data System (ADS)

    Gourgoulhon, Eric; Markakis, Charalampos; Uryū, Kōji; Eriguchi, Yoshiharu

    2011-05-01

    A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

  15. Numerical study of axisymmetric collapses of submarine granular > columns

    NASA Astrophysics Data System (ADS)

    Monsorno, Davide; Varsakelis, Christos

    2014-11-01

    In this talk, we report on the results of a numerical study of the axisymmetric collapse of subaqueous granular columns. Our study is based on a 2-pressure, 2-velocity continuum flow model for fluid-saturated granular materials. This model is integrated via a multi-phase projection method that incorporates a regularization method for the treatment of material interfaces. In our simulations, a dense column of a granular material immersed in water is placed on a horizontal plane and is allowed to collapse and spread due to its weight. Emphasis is placed on the run-out distance and the termination height and their correlation with the aspect ratio, the volume fraction and the diameter of the grains. Comparisons against experimental measurements and previous numerical predictions are also performed. Finally, in order to examine and quantify the role of the interstitial fluid, we compare our numerical predictions against experimental results from column collapses of dry granular materials.

  16. An analytical and numerical study of axisymmetric flow around spheroids

    NASA Astrophysics Data System (ADS)

    Chang, Chien-Cheng; Liou, Biing-Horng; Chern, Ruey-Ling

    1992-01-01

    Axisymmetric viscous flow around ellipsoids of circular section is examined in detail using a matched asymptotic analysis and a deterministic hybrid vortex method. The hybrid vortex method solves the viscous vorticity equation by combining a finite-difference method for diffusion and a vortex-in-cell method for convection and stretching. The numerical study was carried out for an ellipsoid of axis ratio 2:1 and the limiting case of a sphere at Reynolds numbers between 100 and 3000. Particular attention is given to evaluation of the drag coefficient using three different approaches. Numerical and asymptotic results at small times are found to be in good agreement. Separation angles, wake lengths, and stationary drag coefficients for the sphere are also in good agreement with previous results obtained by a finite-difference method and with the standard drag curve.

  17. Axisymmetric nonlinear waves and structures in Hall plasmas

    SciTech Connect

    Islam, Tanim

    2012-06-15

    In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.

  18. Steady axisymmetric vortex flows with swirl and shear

    NASA Astrophysics Data System (ADS)

    Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.

    A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.

  19. Viscous effects on the instability of an axisymmetric jet

    NASA Technical Reports Server (NTRS)

    Zaman, K. B. M. Q.; Seiner, J. M.

    1990-01-01

    The stability characteristics of a laminar, axisymmetric jet, issuing from fully developed Poiseuille flow, are investigated. The jet preferred frequency, as inferred from surveys of u'-spectra, is found to yield a Strouhal number (St) that depends on the Reynolds number (R); St and R are based on the jet diameter (D) and the average velocity (U sub av) at the jet origin. The value of St increases with increasing R in the range 400 less than approximately R less than approximately 4000, attaining an asymptotic value of about 0.45. Flow visualization confirms that the instability is primarily in a helical mode, as predicted by stability analyses. Analyses do predict a similar St versus R variation in approximately the correct St-range. However, the R-range where this is predicted is lower than that found experimentally.

  20. Effect of tabs on the evolution of an axisymmetric jet

    NASA Technical Reports Server (NTRS)

    Zaman, K. B. M. Q.; Samimy, M.; Reeder, M. F.

    1991-01-01

    The effect of vortex generators, in the form of small tabs at the nozzle exit, on the evolution of an axisymmetric jet was investigated experimentally over a jet Mach number range of 0.34 to 1.81. The effects of one, two, and four tabs were studied in comparison with the corresponding case without a tab. Each tab introduced an indentation in the shear layer, apparently through the action of streamwise vortices which appeared to be of the trailing vortex type originating from the tips of the tab rather that of the necklace vortex type originating from the base of the tab. The resultant effect of two tabs, placed at diametrically opposite locations, was to essentially bifurcate the jet. The influence of the tabs was essentially the same at subsonic and supersonic conditions indicating that compressibility has little to do with the effect.

  1. Numerical simulation of axisymmetric turbulent flow in combustors and diffusers

    NASA Technical Reports Server (NTRS)

    Yung, Chain-Nan; Keith, Theo G., Jr.; De Witt, Kenneth J.

    1989-01-01

    Numerical studies of turbulent flow in an axisymmetric 45-deg-expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-epsilon model were solved in a nonorthogonal curvilinear coordinate system. A zonal-grid method, where the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. Boundary overlap and interpolating techniques were used, and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite-differencing methods (hybrid, quadratic upwind, and skew upwind) were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.

  2. Finite Axisymmetric Charged Dust Disks Sources for Conformastatic Spacetimes

    NASA Astrophysics Data System (ADS)

    González, Guillermo A.; Gutiérrez-Piñeres, Antonio C.; Ospina, Paolo A.

    2009-05-01

    An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the electromagnetic potential and the metric potential in terms of a solution of the Laplace equation. We give solutions to the Einstein-Maxwell equations with disk sources of finite extension in which the charge density is proportional to the energy surface density. We apply the well-know ``inverse'' approach to the gravitational potential representing finite thin disks given by Gonzalez and Reina to generate conformastatic charged dust thin discs. Exact examples of conformastatic metrics with disk sources are worked out in full.

  3. A fast solver for systems of axisymmetric ring vortices

    NASA Astrophysics Data System (ADS)

    Strickland, James H.; Amos, Donald E.

    1990-09-01

    A method which is capable of efficient calculation of the axisymmetric flow field produced by a large system of ring vortices is presented in this report. The system of ring vortices can, in turn, be used to model body surfaces and wakes in incompressible unsteady axisymmetric flow fields. This method takes advantage of source point and field point series expansions which enables one to make calculations for interactions between groups of vortices which are in well separated spatial domains rather than having to consider interactions between every pair of vortices. In this work, series expansions for the stream function of the ring vortex system are obtained. Such expansions explicitly contain the radial and axial velocity components. A FORTRAN computer code RSOLV has been written to execute the fast solution technique to calculate the stream function and the axial and radial velocity components at points in the flow field. Test cases have been run to optimize the code and to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the stream function and total velocity field are on the order of 5 times 10(exp -5) and 3 times 10(exp -3) respectively. Single precision accuracy produces errors in these quantities up to about 1 times 10(exp -5). For 100 vortices in the field, there is virtually no CPU time savings with the fast solver. For 10,000 vortices in the flow, the fast solver obtains solutions in about 1 to 3 percent of the time required for the direct solution technique. Simulations of vortices with square and circular cores were run in order to obtain expressions for the self-induced velocities of such vortices.

  4. Camassa-Holm equations and vortexons for axisymmetric pipe flows

    NASA Astrophysics Data System (ADS)

    Fedele, Francesco; Dutykh, Denys

    2014-02-01

    In this paper, we study the nonlinear dynamics of an axisymmetric disturbance to the laminar state in non-rotating Poiseuille pipe flows. In particular, we show that the associated Navier-Stokes equations can be reduced to a set of coupled dispersive Camassa-Holm type equations. These support inviscid and smooth localized travelling waves, which are numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices that concentrate near the pipe boundaries (wall vortexons) or wrap around the pipe axis (centre vortexons) in agreement with the analytical soliton solutions derived by Fedele (2012 Fluid Dyn. Res. 44 45509) for small and long-wave disturbances. Inviscid singular vortexons with discontinuous radial velocities are also numerically discovered as associated to special travelling waves with a wedge-type singularity, viz. peakons. Their existence is confirmed by an analytical solution of exponentially shaped peakons that is obtained for the particular case of the uncoupled Camassa-Holm equations. The evolution of a perturbation is also investigated using an accurate Fourier-type spectral scheme. We observe that an initial vortical patch splits into a centre vortexon radiating vorticity in the form of wall vortexons. These can under go further splitting before viscosity dissipates them, leading to a slug of centre vortexons. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with Eyink (2008 Physica D 237 1956-68). The inviscid and smooth vortexon is similar to the nonlinear neutral structures derived by Walton (2011 J. Fluid Mech. 684 284-315) and it may be a precursor to puffs and slugs observed at transition, since most likely it is unstable to non-axisymmetric disturbances.

  5. Geometry and Cloaking Devices

    NASA Astrophysics Data System (ADS)

    Ochiai, T.; Nacher, J. C.

    2011-09-01

    Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

  6. Control of supersonic axisymmetric base flows using passive splitter plates and pulsed plasma actuators

    NASA Astrophysics Data System (ADS)

    Reedy, Todd Mitchell

    decreasing pressure. Implementing an array of eight electric arcs circumferentially around the base near the corner expansion, the LAFPA actuators were shown to produce significant disturbances to the separating shear layer of the base flow and cause modest influences on the base pressure when actuated over a range of high frequencies (O(kHz)), forcing modes, duty cycles, and electrical currents. To tailor the plasma actuator toward the specific flow control application of the separated base flow, several actuator geometries and energy additions were evaluated. Displaying the ability to produce disturbances in the shear layer, an open cavity actuator design outperformed the other geometries consisting of a confined cavity with an exhaust orifice. Increases in duty cycle (between 2% and 6%) and in plasma current (1/4 to 4 amps) were shown to produce large velocity disturbances causing a decrease in average base pressure. At 4 amps and a maximum duty cycle of 6%, the largest measured change in area-weighted base pressure, near -1.5%, was observed for the axisymmetric forcing mode. Positive changes in base pressure were experienced (as much as 1% increase from the no-control) for the vertical and horizontal flapping modes.

  7. Students Discovering Spherical Geometry Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Guven, Bulent; Karatas, Ilhan

    2009-01-01

    Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

  8. Synthesis, characterization, X-ray crystal structure and conductometry studying of a number of new Schiff base complexes; a new example of binuclear square pyramidal geometry of Cu(II) complex bridged with an oxo group

    NASA Astrophysics Data System (ADS)

    Golbedaghi, Reza; Alavipour, Ehsan

    2015-11-01

    Three new binuclear Cu(II), Mn(II), Co(II) complexes [Cu2(L) (ClO4)](ClO4)2 (1), [Mn2(L) (ClO4)](ClO4)2 (2), and [Co2(L) (ClO4)](ClO4)2 (3), {L = 1,3-bis(2-((Z)-(2-aminopropylimino)methyl)phenoxy)propan-2-ol} have been synthesized. Single crystal X-ray structure analysis of complex 1 showed that the complex is binuclear and all nitrogen and oxygen atoms of ligand (N4O3) are coordinated to two Cu(II) center ions. In addition, the crystal structure studying shows, a perchlorate ion has been bridged to the Cu(II) metal centers. However, two distorted square pyramidal Cu(II) ions are bridged asymmetrically by a perchlorate ion and oxygen of hydroxyl group of Schiff base ligand. In addition, the conductometry behaviors of all complexes were studied in acetonitrile solution.

  9. Axisymmetric whole pin life modelling of advanced gas-cooled reactor nuclear fuel

    NASA Astrophysics Data System (ADS)

    Mella, R.; Wenman, M. R.

    2013-06-01

    Thermo-mechanical contributions to pellet-clad interaction (PCI) in advanced gas-cooled reactors (AGRs) are modelled in the ABAQUS finite element (FE) code. User supplied sub-routines permit the modelling of the non-linear behaviour of AGR fuel through life. Through utilisation of ABAQUS's well-developed pre- and post-processing ability, the behaviour of the axially constrained steel clad fuel was modelled. The 2D axisymmetric model includes thermo-mechanical behaviour of the fuel with time and condition dependent material properties. Pellet cladding gap dynamics and thermal behaviour are also modelled. The model treats heat up as a fully coupled temperature-displacement study. Dwell time and direct power cycling was applied to model the impact of online refuelling, a key feature of the AGR. The model includes the visco-plastic behaviour of the fuel under the stress and irradiation conditions within an AGR core and a non-linear heat transfer model. A multiscale fission gas release model is applied to compute pin pressure; this model is coupled to the PCI gap model through an explicit fission gas inventory code. Whole pin, whole life, models are able to show the impact of the fuel on all segments of cladding including weld end caps and cladding pellet locking mechanisms (unique to AGR fuel). The development of this model in a commercial FE package shows that the development of a potentially verified and future-proof fuel performance code can be created and used. The usability of a FE based fuel performance code would be an enhancement over past codes. Pre- and post-processors have lowered the entry barrier for the development of a fuel performance model to permit the ability to model complicated systems. Typical runtimes for a 5 year axisymmetric model takes less than one hour on a single core workstation. The current model has implemented: Non-linear fuel thermal behaviour, including a complex description of heat flow in the fuel. Coupled with a variety of

  10. The Helen of Geometry

    ERIC Educational Resources Information Center

    Martin, John

    2010-01-01

    The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.

  11. The Geometry of Viruses.

    ERIC Educational Resources Information Center

    Case, Christine L.

    1991-01-01

    Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)

  12. Gravity is Geometry.

    ERIC Educational Resources Information Center

    MacKeown, P. K.

    1984-01-01

    Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

  13. Sliding vane geometry turbines

    DOEpatents

    Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R

    2014-12-30

    Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.

  14. Making Solid Geometry Solid.

    ERIC Educational Resources Information Center

    Hartz, Viggo

    1981-01-01

    Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)

  15. Fractal geometry of music.

    PubMed Central

    Hsü, K J; Hsü, A J

    1990-01-01

    Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

  16. Geometry and physics

    PubMed Central

    Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

    2010-01-01

    We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

  17. GEOMETRY, TENTATIVE GUIDES.

    ERIC Educational Resources Information Center

    KLIER, KATHERINE M.

    PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…

  18. Geometry of spinor regularization

    NASA Technical Reports Server (NTRS)

    Hestenes, D.; Lounesto, P.

    1983-01-01

    The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.

  19. Listening to Geometry

    ERIC Educational Resources Information Center

    Cooper, Brett D.; Barger, Rita

    2009-01-01

    The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…

  20. Geoid Anomalies and Dynamic Topography from Time Dependent, Spherical Axisymmetric Mantle Convection

    NASA Technical Reports Server (NTRS)

    Kiefer, Walter S.; Kellogg, Louise H.

    1998-01-01

    Geoid anomalies and dynamic topography are two important diagnostics of mantle convection. We present geoid and topography results for several time-dependent convection models in spherical axisymmetric geometry for Rayleigh numbers between 10(exp 6) and 10(exp 7) with depth-dependent viscosity and mixtures of bottom and internal heating. The models are strongly chaotic, with boundary layer instabilities erupting out of both thermal boundary layers. In some instances, instabilities from one boundary layer influence the development of instabilities in the other boundary layer. Such coupling between events at the top and bottom of the mantle has been suggested to play a role in a mid-Cretaceous episode of enhanced volcanism in the Pacific. These boundary layer instabilities produce large temporal variations in the geoid anomalies and dynamic nd to the topography associated with the convection. The amplitudes of these fluctuations depend on the detailed model parameter,.% it of this but fluctuations of 30-50% relative to the time-averaged geoid and topography are common. The convective planform is strongly sensitive to the specific initial conditions. Convection cells with larger aspect ratio tend to have larger fractional fluctuations in their geoid and topography amplitudes, because boundary layer instabilities have more time to develop in long cells. In some instances, we observe low-amplitude topographic highs adjacent to the topographic lows produced by cold downwellings. We discuss applications of these results to several situations, including the temporal variability of m basis. hotspots such as Hawaii, the topography of subduction zone outer rises, and the topography of coronae on Venus.

  1. Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas

    SciTech Connect

    Lyons, B. C.; Jardin, S. C.; Ramos, J. J.

    2012-08-15

    A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f) in the conventional banana regime for both ions and electrons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h). We work in a 4D phase space in which {psi} defines a flux surface, {theta} is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and {lambda} is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and {lambda}. The Rosenbluth potentials, {Phi} and {Psi}, which define the integral part of the collision operator, are expanded in Legendre series in cos{chi}, where {chi} is the pitch angle, Fourier series in cos{theta}, and finite elements in v. At each {psi}, we solve a block tridiagonal system for h{sub i} (independent of f{sub e}), then solve another block tridiagonal system for h{sub e} (dependent on f{sub i}). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia et al., J. Comput. Phys. 37, 183-204 (1980)] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C{sup 1}[S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).

  2. Approximate Methods for Analyzing and Controlling Axisymmetric Instabilities of Elongated Tokamak Plasmas.

    NASA Astrophysics Data System (ADS)

    Frantz, Eric Randall

    Elongation and shaping of the tokamak plasma cross -section can allow increased beta and other favorable improvements. As the cross-section is made non-circular, however, the plasma can become unstable against axisymmetric motions, the most predominant one being a nearly uniform displacement in the direction of elongation. Without additional stabilizing mechanisms, this instability has growth rates typically (TURN)10('6)sec('-1). With passive and active feedback from external conductors, the plasma can be significantly slowed down and controlled. In this work, a mathematical formulism for analyzing the vertical instability is developed in which the external conductors are treated (or broken -up) as discrete coils. The circuit equations for the plasma induced currents can be included within the same mathematical framework. The plasma equation of motion and the circuit equations are combined and manipulated into a diagonalized form that can be graphically analyzed to determine the growth rate. An effective mode approximation (EMA) to the dispersion relation in introduced to simplify and approximate the growth rate of the more exact case. Controller voltage equations for active feedback are generalized to include position and velocity feedback and time delay. A position cut-off displacement is added to model finite spatial resolution of the position detectors or a dead-band voltage level. Stability criteria are studied for EMA and the more exact case. The time dependent responses for plasma position controller voltages, and currents are determined from the Laplace transformations. Slow responses are separated from the fast ones (dependent on plasma inertia) using a typical tokamak ordering approximation. The methods developed are applied in numerous examples for the machine geometry and plasma of TNS, an inside-D configuration plasma resembling JET, INTOR, or FED.

  3. Numerical Calculation of Neoclassical Distribution Functions and Current Profiles in Low Collisionality, Axisymmetric Plasmas

    SciTech Connect

    B.C. Lyons, S.C. Jardin, and J.J. Ramos

    2012-06-28

    A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials, φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).

  4. An introduction to Minkowski geometries

    NASA Astrophysics Data System (ADS)

    Farnsworth, David L.

    2016-07-01

    The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.

  5. MODELING MID-INFRARED VARIABILITY OF CIRCUMSTELLAR DISKS WITH NON-AXISYMMETRIC STRUCTURE

    SciTech Connect

    Flaherty, K. M.; Muzerolle, J.

    2010-08-20

    Recent mid-infrared observations of young stellar objects have found significant variations possibly indicative of changes in the structure of the circumstellar disk. Previous models of this variability have been restricted to axisymmetric perturbations in the disk. We consider simple models of a non-axisymmetric variation in the inner disk, such as a warp or a spiral wave. We find that the precession of these non-axisymmetric structures produces negligible flux variations but a change in the height of these structures can lead to significant changes in the mid-infrared flux. Applying these models to observations of the young stellar object LRLL 31 suggests that the observed variability could be explained by a warped inner disk with variable scale height. This suggests that some of the variability observed in young stellar objects could be explained by non-axisymmetric disturbances in the inner disk and this variability would be easily observable in future studies.

  6. Computation of compressible quasi-axisymmetric slender vortex flow and breakdown

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.; Kandil, Hamdy A.

    1991-01-01

    The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux difference splitting finite volume scheme. The developed three dimensional solver was verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic, quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown were captured. The problem was also calculated using the Euler solver of the same code; the results were compared with those of the Navier-Stokes solver. The effect of the initial swirl was investigated.

  7. Micro vortex generator control of axisymmetric high-speed laminar boundary layer separation

    NASA Astrophysics Data System (ADS)

    Estruch-Samper, D.; Vanstone, L.; Hillier, R.; Ganapathisubramani, B.

    2015-09-01

    Interest in the development of micro vortex generators (MVGs) to control high-speed flow separation has grown in the last decade. In contrast to conventional vortex generators, MVGs are fully submerged in the boundary layer and have the potential of inducing surface flow mixing with marginal drag penalty when suitably designed. Also, they do not result in undesired reduced mass flow such as with suction methods. The flow mechanisms at the location of MVGs are not yet fully understood, and optimal designs are difficult to establish given that both numerical predictions and experiments are particularly challenged for short element heights, yet optimal MVGs are generally expected to be at least shorter than half the local boundary layer thickness. The present work aims at investigating experimentally the fundamental flow physics concerning an individual MVG element (of `canonical' or simplified geometry) at a range of near-wall heights. A fully laminar base flow is considered so as to isolate the effect of incoming turbulence as well as the more complex physics that may occur when specific and/or multiple elements are used. Tests were performed in a gun tunnel at a freestream Mach number of 8.9 and Reynolds number of /m, and the basic test model consisted of a blunt-nosed cylinder which produced an axisymmetric laminar boundary layer with an edge Mach number of 3.4 and Reynolds number of /m at the MVG location. A laminar shock-wave/boundary layer interaction with separation was induced by a flare located further downstream on the model. Measurements consisted of time-resolved surface heat transfer obtained in the axial direction immediately downstream of the MVG and along the interaction, together with simultaneous high-speed schlieren imaging. The height () of the MVG element used in a `diamond' configuration (square planform with one vertex facing the flow) was adjusted between tests ranging from = 0.03 to 0.58, where the local undisturbed boundary layer thickness

  8. Simulations of ion beams for NDCX-II

    NASA Astrophysics Data System (ADS)

    Grote, D. P.; Friedman, A.; Sharp, W. M.

    2014-01-01

    NDCX-II, the second neutralized drift compression experiment, is a moderate energy, high current accelerator designed to drive targets for warm dense matter and IFE-relevant energy coupling studies, and to serve as a testbed for high current accelerator physics. As part of the design process, studies were carried out to assess the sensitivities of the accelerator to errors, and to further optimize the design in concert with the evolving pulsed power engineering. The Warp code was used to carry out detailed simulations in both axisymmetric and full 3-D geometry. Ensembles of simulations were carried out to characterize the effects of errors, such as timing jitter and noise on the accelerator waveforms, noise on the source waveform, and solenoid and source offsets. In some cases, the ensemble studies resulted in better designs, revealing operating points with improved performance and showing possible means for further improvement. These studies also revealed a new non-paraxial effect of the final focus solenoid on the beam, which must be taken into account in designing an optimal final focusing system.

  9. Reversed Field Pinch Dynamics in Toroidal and Cylindrical Geometries

    NASA Astrophysics Data System (ADS)

    Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.

    2014-10-01

    The effect of the curvature of the imposed magnetic field on Reversed Field Pinch dynamics is investigated by comparing the flow of a magnetofluid in a torus with aspect ratio 1.83, with the flow in a periodic cylinder. It is found that an axisymmetric toroidal mode is always present in the toroidal, but absent in the cylindrical configuration. In particular, in contrast to the cylinder, the toroidal case presents a double poloidal recirculation cell with a shear localized at the plasma edge. Quasi-single-helicity states are found to be more persistent in toroidal than in periodic cylinder geometry. This work was supported by the contract SiCoMHD (ANR-Blanc 2011-045), computing time was supplied by IDRIS, project 22206.

  10. Physics and geometry

    NASA Astrophysics Data System (ADS)

    Souriau, Jean-Marie

    1983-01-01

    Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality. This holds at every level: The concept of “connexion,” for instance, is used in the construction of models of the universe as well as in the description of the interior of the proton. Nothing is apparently more contrary to the wisdom of physicists; all the same, “it works.” The pages that follow show the conceptual role played by this geometry in some examples—without entering into technical details. In order to achieve this, we shall often have to abandon the complete mathematical rigor and even full definitions; however, we shall be able to give a precise description of the connection of ideas thanks to some elements of group theory.

  11. Puzzle geometry and rigidity

    NASA Astrophysics Data System (ADS)

    Smania, Daniel

    2007-07-01

    We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admit a topological conjugacy, quasiconformal outside the filled-in Julia set, are indeed quasiconformally conjugate. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen and Koskela and of Kallunki and Koskela, optimized for applications in complex dynamics. We prove, as the first application of this new method, that, for even criticalities distinct from two, the period two cycle of the Fibonacci renormalization operator is hyperbolic with 1 -dimensional unstable manifold.

  12. Failures of information geometry

    NASA Astrophysics Data System (ADS)

    Skilling, John

    2015-01-01

    Information H is a unique relationship between probabilities, based on the property of independence which is central to scientific methodology. Information Geometry makes the tempting but fallacious assumption that a local metric (conventionally based on information) can be used to endow the space of probability distributions with a preferred global Riemannian metric. No such global metric can conform to H, which is "from-to" asymmetric whereas geometrical length is by definition symmetric. Accordingly, any Riemannian metric will contradict the required structure of the very distributions which are supposedly being triangulated. It follows that probabilities do not form a metric space. We give counter-examples in which alternative formulations of information, and the use of information geometry, lead to unacceptable results.

  13. Cylindrical geometry hall thruster

    DOEpatents

    Raitses, Yevgeny; Fisch, Nathaniel J.

    2002-01-01

    An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.

  14. Internal performance characteristics of thrust-vectored axisymmetric ejector nozzles

    NASA Technical Reports Server (NTRS)

    Lamb, Milton

    1995-01-01

    A series of thrust-vectored axisymmetric ejector nozzles were designed and experimentally tested for internal performance and pumping characteristics at the Langley research center. This study indicated that discontinuities in the performance occurred at low primary nozzle pressure ratios and that these discontinuities were mitigated by decreasing expansion area ratio. The addition of secondary flow increased the performance of the nozzles. The mid-to-high range of secondary flow provided the most overall improvements, and the greatest improvements were seen for the largest ejector area ratio. Thrust vectoring the ejector nozzles caused a reduction in performance and discharge coefficient. With or without secondary flow, the vectored ejector nozzles produced thrust vector angles that were equivalent to or greater than the geometric turning angle. With or without secondary flow, spacing ratio (ejector passage symmetry) had little effect on performance (gross thrust ratio), discharge coefficient, or thrust vector angle. For the unvectored ejectors, a small amount of secondary flow was sufficient to reduce the pressure levels on the shroud to provide cooling, but for the vectored ejector nozzles, a larger amount of secondary air was required to reduce the pressure levels to provide cooling.

  15. Axisymmetric equilibria with pressure anisotropy and plasma flow

    NASA Astrophysics Data System (ADS)

    Throumoulopoulos, George; Evangelias, Achilleas

    2015-11-01

    A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a free boundary and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018.

  16. Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields

    NASA Technical Reports Server (NTRS)

    Tweedt, Daniel L.; Chima, Rodrick V.

    1995-01-01

    A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

  17. Axisymmetric toroidal modes of general relativistic magnetized neutron star models

    SciTech Connect

    Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp

    2014-07-20

    We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.

  18. Experimental evaluation of a Mach 3.5 axisymmetric inlet

    NASA Technical Reports Server (NTRS)

    Syberg, J.; Koncsek, J. L.

    1975-01-01

    Wind tunnel test results for a large scale inlet model designed for Mach 3.5 are presented and compared with analytical predictions. The inlet is an axisymmetric mixed-compression type with a lip diameter of 49.723 cm. The inlet design was developed using analytical procedures. Data are shown for freestream Mach numbers from 0.6 to 3.5. The test results indicate that boundary layer bleed requirements can be accurately predicted. Good agreement was obtained with analytical predictions of the flowfield structure and boundary layer development in the supersonic diffuser yielding high performance at the design Mach number. The highest engine face total pressure recovery at Mach 3.5 was 85.8%; this was obtained at 0.05 Mach tolerance with only 2.8% total pressure distortion and 13.4% bleed. In the started Mach number range from 1.6 to 3.5, the total pressure recovery in the throat, downstream of the terminal normal shock, ranged between 91% and 95%. Total pressure losses in the subsonic diffuser varied from 3% to 13%. The higher losses occuring between Mach 2.5 and 3.2 were believed to be caused by the rapid rate of increase in the area of the diffuser just downstream of the throat, possibly coupled with inadequate centerbody throat bleed. In the unstarted mode at transonic speeds, the maximum inlet flow was over 99% of the theoretical maximum capture mass-flow.

  19. An axisymmetric multiple-relaxation-time lattice Boltzmann scheme

    NASA Astrophysics Data System (ADS)

    Xie, Wenjun

    2015-01-01

    A multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme developed for axisymmetric flows recovers the complete continuity and Navier-Stokes equations. This scheme follows the strategy of the standard D2Q9 model by using a single particle distribution function and a simple "collision-streaming" updating rule. The extra terms related to axisymmetry in the macroscopic equations are recovered by adding source terms into the LB equation, which are simple and involve no gradients. The compressible effect retained in the Navier-Stokes equations is recovered by introducing a term related to the reversed transformation matrix for MRT collision operator, so as to produce a correct bulk viscosity, making it suitable for compressible flows with high frequency and low Mach number. The validity of the scheme is demonstrated by testing the Hagen-Poiseuille flow and 3D Womersley flow, as well as the standing acoustic waves in a closed cylindrical chamber. The numerical experiments show desirable stability at low viscosities, enabling to simulate a standing ultrasound field in centimeters space.

  20. Quasi-axisymmetric circulation and superrotation in planetary atmospheres

    NASA Astrophysics Data System (ADS)

    Mayr, H. G.; Harris, I.

    1983-05-01

    Atmospheric superrotation is ubiquitous in the solar system, and numerous theoretical models have been proposed to describe the effect. However, no model is fully accepted. Problems are primarily related to an understanding of the angular momentum and the energy budgets. In connection with the present investigation, attention is given to hybrid models, where three-dimensional models may describe eddy processes and two-dimensional symmetric models may describe the global scale circulation in the framework of a viscous medium. It is believed that the concept of an axisymmetric circulation is still useful. It is the main purpose of the current investigation to explore some of the properties of the circulation in planetary atmospheres. It is assumed that the eddy transports are downgradient or diffusive in nature. Energy and momentum are perceived to cascade from the global scale circulation driven by the sun to the smaller scale eddies which in turn determine the diffusive properties. A numerical model of the Venusian circulation is presented, and results are discussed for different conditions of static stability.

  1. Roll forming technology for manufacturing axisymmetric automotive components

    SciTech Connect

    Syn, C.K.; Lesuer, D.R.; Bieh, T.G.; Yang, H.s.; Brown, K.R.; Kaibyshev, R.O.; Petrov, E.N.

    1997-10-28

    A unique roll forming technology that permits complex axisymmetric components, such as automobile wheels and turbine disks, to be formed in a single forming operation, has been developed by two Russian Institute, the Institute of Technical Physics of the Russian Federal Nuclear Center and the Institute for Metals Superplasticity Problems. This process was used to fabricate automobile wheels from a Russian AVT alloy, a 6010 aluminum alloy equivalent. The process included steps of isothermal roll forming of preforms into wheels shapes, all at 430C for the AVT alloy. The microstructure and mechanical properties were evaluated at various locations in the finished wheels by optical metallography and tensile testing at elevated temperatures. Tensile properties were obtained by stain-rate change tests and tensile tests to failure at high strain rates. Microstructure and mechanical propertied of the preforms and blanks were also evaluated. The results indicate that dynamically recovered microstructures were developed during the processing, which showed relatively high strain rate sensitivity and rendered sufficiently plasticity at the elevated temperature for wheel fabrication process.

  2. Experimental and Theoretical Studies of Axisymmetric Free Jets

    NASA Technical Reports Server (NTRS)

    Love, Eugene S.; Grigsby, Carl E.; Lee, Louise P.; Woodling, Mildred J.

    1959-01-01

    Some experimental and theoretical studies have been made of axisymmetric free jets exhausting from sonic and supersonic nozzles into still air and into supersonic streams with a view toward problems associated with propulsive jets and the investigation of these problems. For jets exhausting into still air, consideration is given to the effects of jet Mach number, nozzle divergence angle, and jet static pressure ratio upon jet structure, jet wavelength, and the shape and curvature of the jet boundary. Studies of the effects of the ratio of specific heats of the jets are included are observations pertaining to jet noise and jet simulation. For jets exhausting into supersonic streams, an attempt has been made to present primarily theoretical certain jet interference effects and in formulating experimental studies. The primary variables considered are jet Mach number, free stream Mach number, jet static pressure ratio, ratio of specific heats of the jet, nozzle exit angle, and boattail angle. The simulation problem and the case of a hypothetical hypersonic vehicle are examined, A few experimental observations are included.

  3. Computing Axisymmetric Jet Screech Tones using Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Loh, Ching Y.

    2003-01-01

    The purpose of this paper is to show that computations with an aeroacoustic feedback loop, the jet screech noise, can be obtained using truly unstructured grid technology. Numerical results are presented for a nozzle with two different lip thicknesses which will be referred to in this paper as a thin and a thick lip nozzle respectively. The space-time conservation element and solution element (CE/SE) method is used to solve the conservation laws of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. Comparisons of numerical results with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

  4. Axisymmetric equilibria with pressure anisotropy and plasma flow

    NASA Astrophysics Data System (ADS)

    Evangelias, A.; Throumoulopoulos, G. N.

    2016-04-01

    A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones.

  5. Kinetic axisymmetric gravitational equilibria in collisionless accretion disk plasmas

    SciTech Connect

    Cremaschini, Claudio; Miller, John C.; Tessarotto, Massimo

    2010-07-15

    A theoretical treatment is presented of kinetic equilibria in accretion disks (AD) around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axisymmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily toroidal differential rotation and temperature anisotropy. It is conjectured that kinetic equilibria of this type can exist which are able to sustain both toroidal and poloidal electric current densities, the latter being produced via finite Larmor-radius effects associated with the temperature anisotropy. This leads to the possibility of existence of a new kinetic effect - referred to here as a 'kinetic dynamo effect - resulting in the self-generation of toroidal magnetic field even by a stationary plasma, without any net radial accretion flow being required. The conditions for these equilibria to occur, their basic theoretical features, and their physical properties are all discussed in detail.

  6. Non-axisymmetric Field Effects on Alcator C-Mod

    NASA Astrophysics Data System (ADS)

    Wolfe, S.; Hutchinson, I.; Granetz, R.; Rice, J.; Hubbard, A.; Irby, J.; Vieira, R.; Cochran, W.; Gwinn, D.; Rosati, J.; Lynn, A.

    2003-10-01

    A set of coils capable of producing non-axisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode (m) spectra has been installed on Alcator C-Mod. This coilset has been used to suppress locked modes during low density or high current operation and also to induce locked modes in normally stable configurations in order to study error field effects. Locked modes are observed to result in braking of core toroidal rotation, modification of sawtooth activity, and significant reduction in energy and particle confinement. The inferred value of the threshold perturbation for producing a locked mode is of order B_21/B_T ˜ 10-4, where B_21 is the helically resonant m/n=2/1 field evaluated at the q=2 surface. This value is comparable to extrapolations based on experiments on JET and DIII-D, but is inconsistent with stronger BT and size scaling inferred from Compass-D results(R. J. Buttery, et al., 17th Fusion Energy Conference, Oct. 1998, Yokohama (IAEA-CN-69) EX8/5). The C-Mod result therefore has favorable implications for the locked mode threshold in ITER.

  7. A 'turbulent spot' in an axisymmetric free shear layer. I

    NASA Astrophysics Data System (ADS)

    Sokolov, M.; Hussain, A. K. M. F.; Kleis, S. J.; Husain, Z. D.

    1980-05-01

    The paper discusses the evolution of the three-dimensionality in an axisymmetric mixing layer by studying a spark-induced spot in the layer. Even though the spot signature is buried in the large-amplitude random turbulent signal, it was possible to educe the spot signature at three streamwise stations through signal enhancement techniques; these involved relative alignment of individual realizations through a cross-correlation of low-pass filtered signals, rejection of realizations requiring excessive shifts, and phase averaging the aligned realizations. There is no evidence as to whether the spark induces a spot in the boundary layer preceding the nozzle lip which subsequently develops in the shear layer or produces a large pressure pulse which directly induces a disturbance in the shear layer. Finally, it is shown that the spot signature involves the entire mixing layer and that the spot produced turbulence, and it appears that the spot is an elongated vortical structure spanning the shear-layer width.

  8. Circulation Control on Axisymmetric Bodies using Synthetic Jets

    NASA Astrophysics Data System (ADS)

    Rinehart, Christopher; McMichael, James; Glezer, Ari

    2001-11-01

    The capability of fluidic actuation based on synthetic jets to modify the apparent aerodynamic shape of lifting surfaces and thereby modify the aerodynamic forces and moments has been demonstrated in a number of earlier investigations of stalled two-dimensional airfoils (e.g., Amitay et al., AIAA J., 39, 2001). The present work is a study of the fundamental ability of synthetic jets to favorably modify the flow over axisymmetric bodies at subsonic speeds. Aft-facing synthetic jets oriented tangentially to a circular Coanda surface at the base produce effective flow turning and lift generation, with ratios of lift to average jet momentum approaching values typical of conventional jet-based circulation control on two-dimensional airfoils. The result is interesting in that the body is not designed to be a lifting surface, and the actuation is effected over only a portion of the body’s circumference. The transient and steady global flow response to the actuation is demonstrated via phase- and time-averaged velocity measurements using particle image velocimetry (PIV).

  9. The development of an axisymmetric curved turbulent wall jet

    NASA Astrophysics Data System (ADS)

    Gregory-Smith, D. G.; Hawkins, M. J.

    1991-12-01

    An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.

  10. Unsteady Aerodynamic Flow Control of a Suspended Axisymmetric Moving Platform

    NASA Astrophysics Data System (ADS)

    Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari

    2011-11-01

    The aerodynamic forces on an axisymmetric wind tunnel model are altered by fluidic interaction of an azimuthal array of integrated synthetic jet actuators with the cross flow. Four-quadrant actuators are integrated into a Coanda surface on the aft section of the body, and the jets emanate from narrow, azimuthally segmented slots equally distributed around the model's perimeter. The model is suspended in the tunnel using eight wires each comprising miniature in-line force sensors and shape-memory-alloy (SMA) strands that are used to control the instantaneous forces and moments on the model and its orientation. The interaction of the actuation jets with the flow over the moving model is investigated using PIV and time-resolved force measurements to assess the transitory aerodynamic loading effected by coupling between the induced motion of the aerodynamic surface and the fluid dynamics that is driven by the actuation. It is shown that these interactions can lead to effective control of the aerodynamic forces and moments, and thereby of the model's motion. Supported by ARO.

  11. Synthetic Jet Control of a Yawing Axisymmetric Body

    NASA Astrophysics Data System (ADS)

    Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari

    2012-11-01

    The global aerodynamic forces and moments on an axisymmetric yawing body are controlled in wind tunnel experiments by exploiting the interaction of an array of synthetic jet actuators with the cross flow over the tail section of the body. The model is supported by a vertical wire through its aerodynamic center and is free to move in yaw. The baseline motion of the model is a yaw oscillation with amplitude and frequency that both monotonously increase with free stream velocity, characteristic of vortex shedding. The aft-facing control jet actuators emanate from narrow, azimuthally segmented slots around the perimeter of the tail section, and activation of the control jets effects the model's path through localized flow attachment on integrated Coanda surfaces. The control jets are used to control the yaw trajectory of the model using a closed loop PID controller. The baseline and controlled model motion is monitored using a laser vibrometer, and the flow evolution near the body and in its near wake is investigated using PIV. The coupled, time dependent response of the model to the actuation is investigated with emphasis on controlling its unstable modes. Supported by ARO.

  12. THE LOSS-CONE PROBLEM IN AXISYMMETRIC NUCLEI

    SciTech Connect

    Vasiliev, Eugene; Merritt, David E-mail: merritt@astro.rit.edu

    2013-09-01

    We consider the problem of consumption of stars by a supermassive black hole (SBH) at the center of an axisymmetric galaxy. Inside the SBH sphere of influence, motion of stars in the mean field is regular and can be described analytically in terms of three integrals of motion: the energy E, the z-component of angular momentum L{sub z} , and the secular Hamiltonian H. There exist two classes of orbits, tubes and saucers; saucers occupy the low-angular-momentum parts of phase space and their fraction is proportional to the degree of flattening of the nucleus. Perturbations due to gravitational encounters lead to diffusion of stars in integral space, which can be described using the Fokker-Planck equation. We calculate the diffusion coefficients and solve this equation in the two-dimensional phase space (L{sub z} , H), for various values of the capture radius and the degree of flattening. Capture rates are found to be modestly higher than in the spherical case, up to a factor of a few, and most captures take place from saucer orbits. We also carry out a set of collisional N-body simulations to confirm the predictions of the Fokker-Planck models. We discuss the implications of our results for rates of tidal disruption and capture in the Milky Way and external galaxies.

  13. Non-neutral plasma equilibria with weak axisymmetric magnetic perturbations

    SciTech Connect

    Kotelnikov, I. A.; Rome, M.; Kabantsev, A.

    2006-09-15

    The effect of weak axisymmetric magnetic and/or electrostatic perturbations on the equilibrium of a non-neutral plasma in a Malmberg-Penning trap is analyzed. Analytical and semianalytical solutions for the potential variations inside the trap are found in a paraxial limit of the perturbations for various radial density profiles of the plasma, including the case of global thermal equilibrium. It is shown that a magnetic perturbation produces a potential variation with a sign which is changing along the plasma radius. The fraction of magnetically and electrostatically trapped particles thus created is calculated explicitly for the case of a Maxwellian distribution function, and it is shown to be independent from the sign of the magnetic field perturbation. The analysis of the potential perturbation is extended to the case of an anisotropic distribution function, with an arbitrary ratio between the parallel and the perpendicular plasma temperature. Two-dimensional thermal equilibrium simulations for parameters relevant to the CamV device [A. A. Kabantsev, J. H. Yu, R. B. Lynch, and C. F. Driscoll, Phys. Plasmas 10, 1628 (2003)] confirm the predictions of the analytical theory for smooth and weak perturbations of the magnetic field.

  14. Transonic analysis and design of axisymmetric bodies in nonuniform flow

    NASA Technical Reports Server (NTRS)

    Chang, Jen-Fu; Lan, C. Edward

    1987-01-01

    An inviscid nonuniform axisymmetric transonic code was developed for applications in analysis and design. Propfan slipstream effect on pressure distribution for a body with and without sting was investigated. Results show that nonuniformity causes pressure coefficient to be more negative and shock strength to be stronger and more rearward. Sting attached to a body reduced the pressure peak and moves the rear shock forward. Extent and Mach profile shapes of the nonuniformity region appeared to have little effect on the pressure distribution. Increasing nonuniformity magnitude made pressure coefficient more negative and moved the shock rearward. Design study was conducted with the CONMIN optimizer for an ellipsoid and a body with the NACA-0012 counter. For the ellipsoid, the general trend showed that to reduce the pressure drag, the front portion of the body should be thinner and the contour of the rear portion should be flatter than the ellipsoid. For the design of a body with a sharp trailing edge in transonic flow with an initial shape given by the NACA-0012 contour, the pressure drag was reduced by decreasing the nose radius and increasing the thickness in the aft portion. Drag reduction percentages are given.

  15. Axisymmetric magnetorotational instability in ideal and viscous laboratory plasmas

    SciTech Connect

    Mikhailovskii, A. B.; Lominadze, J. G.; Churikov, A. P.; Erokhin, N. N.; Pustovitov, V. D.; Konovalov, S. V.

    2008-10-15

    The original analysis of the axisymmetric magnetorotational instability (MRI) by Velikhov (Sov. Phys. JETP 9, 995 (1959)) and Chandrasekhar (Proc. Nat. Acad. Sci. 46, 253 (1960)), applied to the ideally conducting magnetized medium in the laboratory conditions and restricted to the incompressible approximation, is extended by allowing for the compressibility. Thereby, two additional driving mechanisms of MRI are revealed in addition to the standard drive due to the negative medium rotation frequency gradient (the Velikhov effect). One is due to the squared medium pressure gradient and another is a combined effect of the pressure and density gradients. For laboratory applications, the expression for the MRI boundary with all the above driving mechanisms and the stabilizing magnetoacoustic effect is derived. The effects of parallel and perpendicular viscosities on the MRI in the laboratory plasma are investigated. It is shown that, for strong viscosity, there is a family of MRI driven for the same condition as the ideal one. It is also revealed that the presence of strong viscosity leads to additional family of instabilities called the viscosity-driven MRI. Then the parallel-viscositydriven MRI looks as an overstability (oscillatory instability) possessing both the growth rate and the real part of oscillation frequency, while the perpendicular-viscosity MRI is the aperiodical instability.

  16. Axisymmetric viscous gravity currents flowing over a deep porous medium

    NASA Astrophysics Data System (ADS)

    Spannuth, Melissa; Neufeld, Jerome; Wettlaufer, John S.; Grae Worster, M.

    2006-11-01

    When a viscous fluid flows over a porous substrate, it not only spreads but also seeps into the underlying medium. Such flows have relevance to the design of shingle beds for use as safety features around storage facilities of dense fluids and to flow through fissures in porous rocks. Whereas previous investigations have been confined to two-dimensional flows of fixed volume, we have investigated currents fed by a constant fluid flux flowing axisymmetrically over a deep porous bed. Our experimental system consisted of glycerin spreading over monodisperse glass spheres of known permeability and the data were analyzed using scaling analyses. We have also solved a mathematical model using the well-known equations for a viscous gravity current spreading due to the slope of its free surface augmented by a simple draining law. Its predictions agree well with our experimental results and quantify, in particular, the maximum distance to which the current spreads as a function of the material and input properties.

  17. Adhesion and detachment of a capsule in axisymmetric flow

    NASA Astrophysics Data System (ADS)

    Keh, M. P.; Leal, L. G.

    2016-05-01

    The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus Ks of the membrane. The nonzero shear modulus Gs for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same Ks, a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same Ks.

  18. Axisymmetric Time-Dependent Computations of Expansion Tube Flow

    NASA Technical Reports Server (NTRS)

    Wilson, Gregory J.; Arnold, James O. (Technical Monitor)

    1994-01-01

    The goal of this work is to add insight about the flow within expansion tubes by using computational fluid dynamics. This is accomplished by comparing the results of axisymmetric numerical simulations with finite-rate chemistry to data from the HYPULSE expansion tube facility which was previously the NASA Langley expansion tube. The numerical simulations begin at the opening of the primary diaphragm and compute the flow throughout the whole facility and, thus, are able to follow and assess the effect of many of the flow features created during operation of the facility. One particular issue that will be investigated is the effect of boundary layer formation in the acceleration tube on the test gas volume and test gas conditions. Both laminar and turbulent boundary layers will be implemented. The effect of momentary shock reflection off the secondary diaphragm will also be investigated. There is concern that such a reflection will stagnate the test gas and create high levels of dissociated molecules. This is particularly important in propulsion experiments where a freestream composition different from flight conditions may influence ignition and burning data. Several different models of diaphragm rupture will be implemented in order to help understand the importance of this issue.

  19. Hysteresis and the transition between axisymmetric flow and wave flow in the baroclinic annulus

    NASA Technical Reports Server (NTRS)

    Miller, Timothy L.; Butler, Karen A.

    1991-01-01

    A numerical model is employed to establish the transitions between axisymmetric flow and wave flow in the rotating, differentially heated annulus experiments of Fein for both rigid lid and free surface cases. It is shown that, for most of the transitions, the method of computing a steady axisymmetric flow and then testing its linear stability to wave disturbance results in good agreement with the experiments. Implications for the investigation of the dynamics of the earth's atmosphere are considered.

  20. Freezing in confined geometries

    NASA Technical Reports Server (NTRS)

    Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.

    1992-01-01

    Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.

  1. Integral geometry and holography

    DOE PAGESBeta

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less

  2. Emergent Complex Network Geometry

    NASA Astrophysics Data System (ADS)

    Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra

    2015-05-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.

  3. Emergent Complex Network Geometry

    PubMed Central

    Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra

    2015-01-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems. PMID:25985280

  4. Integral geometry and holography

    SciTech Connect

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

  5. Turbulence measurements in axisymmetric jets of air and helium. I - Air jet. II - Helium jet

    NASA Astrophysics Data System (ADS)

    Panchapakesan, N. R.; Lumley, J. L.

    1993-01-01

    Results are presented of measurements on turbulent round jets of air and of helium of the same nozzle momentum efflux, using, for the air jets, x-wire hot-wire probes mounted on a moving shuttle and, for He jets, a composite probe consisting of an interference probe of the Way-Libby type and an x-probe. Current models for scalar triple moments were evaluated. It was found that the performance of the model termed the Full model, which includes all terms except advection, was very good for both the air and the He jets.

  6. User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume II. Detailed ADD code description

    SciTech Connect

    Anderson, O.L.; Hankins, G.B. Jr.; Edwards, D.E.

    1982-02-01

    This section of the manual is intended for the special user who wishes to modify the ADD code or adopt the ADD code to a different computer. An overview of the code is provided in terms of the principal tasks. These principal tasks are clearly labeled in the main program ALTMN and agree with the tasks listed in the Global Task Chart and the Global Tree Structure. Internal flags, as opposed to input options, are described. These flags are set by the code and control the calculation flow between different subroutines. Flags used only within a subroutine are described in the detailed subroutine descriptions. Special problems associated with machine specific language are also described in this Section. The operation of a general I/O routine, which uses UNIVAC library I/O routine NTRAN, and a description of the data files is given. This general I/O routine has been developed to allow NTRAN compatibility with ANSI standard DEFINE FILE for easy conversion. The ADD code also uses a standard spline smoothing routine ICSVKU provided by International Mathematical and Statistical Libraries, Inc. The use of this subroutine is described. All labelled COMMON block and DIMENSION statements are set by INCLUDE statements. Block sizes and EQUIVALENCE statements are set by PARAMETER statements. The use of these in the code is described.

  7. Axisymmetric oscillation modes of a double droplet system

    SciTech Connect

    Ramalingam, Santhosh K.; Basaran, Osman A.

    2010-11-15

    A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) the pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR3. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are compared to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R3, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.

  8. Theoretical issues on the spontaneous rotation of axisymmetric plasmas

    NASA Astrophysics Data System (ADS)

    Coppi, B.; Zhou, T.

    2014-09-01

    An extensive series of experiments have confirmed that the observed ‘spontaneous rotation’ phenomenon in axisymmetric plasmas is related to the confinement properties of these plasmas and connected to the excitation of collective modes associated with these properties (Coppi 2000 18th IAEA Fusion Energy Conf. (Sorrento, Italy, 2000) THP 1/17, www-pub.iaea.org/MTCD/publications/PDF/csp_008c/html/node343.htm and Coppi 2002 Nucl. Fusion 42 1). In particular, radially localized modes can extract angular momentum from the plasma column from which they grow while the background plasma has to recoil in the direction opposite to that of the mode phase velocity. In the case of the excitation of the plasma modes at the edge, the loss of their angular momentum can be connected to the directed particle ejection to the surrounding medium. The recoil angular momentum is then redistributed inside the plasma column mainly by the combination of an effective viscous diffusion and an inward angular momentum transport velocity that is connected, for instance, to ion temperature gradient (ITG) driven modes. The linear and quasi-linear theories of the collisionless trapped electron modes and of the toroidal ITG driven modes are re-examined in the context of their influence on angular momentum transport. Internal modes that produce magnetic reconnection and are electromagnetic in nature, acquire characteristic phase velocity directions in high temperature regimes and become relevant to the ‘generation’ of angular momentum. The drift-tearing mode, the ‘complex’ reconnecting mode and the m0 = 1 internal mode belong to this category, the last mode acquiring different features depending on the strength of its driving factor. Toroidal velocity profiles that reproduce the experimental observations are obtained considering a global angular momentum balance equation that includes the localized sources associated with the excited internal electrostatic and electromagnetic modes

  9. Radial Ion Transport in a Limited Axisymmetric Ecr Plasma.

    NASA Astrophysics Data System (ADS)

    Gibson, Gerald Warren, Jr.

    1995-01-01

    An experimental study of the radial transport of ions in the presence of a limiter for an axisymmetric plasma sustained by the resonant absorption of 2.45 GHz whistler waves is presented. In steady state, approximately 30% of the particles ionized in the core plasma flow radially into the scrape-off layer. The magnitude of radial ion flux is observed to be bounded from below by the radial electron transport rate and from above by the classical collisional ion transport rate of the cold edge ions. The system proves to be susceptible to a Kelvin-Helmholtz instability. The transport experiments were performed at a set input power of 300 W and over the neutral pressure range of 1-3 mTorr in Argon gas. The bulk ions possess a typical temperature of 1eV and do not obey a diffusion equation in the core plasma. Strong radial electric fields are observed and appear to provide the principal means by which radial ion diffusion is controlled. The presence of strongly sheared electric fields in this system excites a hydrodynamic instability of the Kelvin-Helmholtz type. The most frequently observed mode is driven by a region of depressed potential at the plasma edge. A theory for instability in the presence of a localized inverted Gaussian radial potential is presented and compared with experimental measurements. The convection of edge plasma into the core under influence of this mode leads to an increased edge temperature and, hence, enhanced axial losses from the scrape-off layer, thereby modifying the radial profile of the scrape-off layer. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

  10. Axisymmetric oscillation modes of a double droplet system

    DOE PAGESBeta

    Ramalingam, Santhosh K.; Basaran, Osman A.

    2010-11-15

    A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) themore » pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR3. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are compared to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R3, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.« less

  11. Graded geometry and Poisson reduction

    SciTech Connect

    Cattaneo, A. S.; Zambon, M.

    2009-02-02

    The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.

  12. Geometry Career Unit: Junior High.

    ERIC Educational Resources Information Center

    Jensen, Daniel

    The guide, the product of an exemplary career education program for junior high school students, was developed to show how geometry can be applied to real-life career-oriented areas and to bring a practical approach to the teaching of geometry. It is designed to show how some of the theorems or postulates in geometry are used in different careers.…

  13. Geometry: Grades 10-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    Behavioral objectives, each accompanied by six sample test items, for secondary school geometry are presented. Objectives were determined by surveying the most widely used secondary school geometry textbooks, and cover 14 major categories of geometry, with sections on set theory and introductory trigonometry. Answers are provided. Categories…

  14. Computer-Aided Geometry Modeling

    NASA Technical Reports Server (NTRS)

    Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)

    1984-01-01

    Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.

  15. Geometry of Quantum States

    NASA Astrophysics Data System (ADS)

    Bengtsson, Ingemar; Zyczkowski, Karol

    2006-05-01

    Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists

  16. Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products

    NASA Astrophysics Data System (ADS)

    Park, Dong Hwan; Yarlagadda, Prasad K. D. V.

    2004-06-01

    In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.

  17. The theoretical polarization of pure scattering axisymmetric circumstellar envelopes

    NASA Technical Reports Server (NTRS)

    Fox, G. K.

    1994-01-01

    The Sobolev approach to the scattering of starlight through a pure scattering circumstellar envelope is developed. The theoretical polarization due to electron scattering in Be star envelopes is calculated for two geometries (an equatorially enhanced envelope and a spheroidal envelope). Only the disk-type envelope is found to yield a maximum polarization consistent with the observed range for Be stars. A lower limit, analytical approximation to the theoretical polarization from a pure scattering envelope is obtained.

  18. Large Deformation and Adhesive Contact Studies of Axisymmetric Membranes

    PubMed Central

    Laprade, Evan J.; Long, Rong; Pham, Jonathan; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred; Hui, Chung-Yuen; Shull, Kenneth R.

    2013-01-01

    A model membrane contact system consisting of an acrylic copolymer membrane and polydimethyl-siloxane substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during non-contact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. A time dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. A displacement controlled geometry was more easily modeled than the pressure controlled geometry, the applicability of the analysis was limited by wrinkling instabilities. The substantial viscoelastic behavior of these membranes made it difficult to describe the entire membrane with a single modulus, given the nonuniform deformation history of the membranes. Given the difficulty in determining membrane tension from the measured pressure and profile fits using the model, the peel energy was used as a simpler measure of adhesion. Using an analytical balance in the displacement controlled geometry, the membrane tension at the contact line was directly measured. Coupled with contact angle imaging, the peel energy was determined. For the model membranes studied, this peel energy described the membrane/substrate adhesive interactions quite well, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644

  19. TEMP-STRESS---A thermomechanical finite element program for the analysis of plane and axisymmetric reinforced/prestressed concrete structures: User`s manual

    SciTech Connect

    Kennedy, J. M.; Pfeiffer, P. A.; Marchertas, A. H.

    1989-01-01

    TEMP-STRESS has been developed to improve the understanding of the behavior of concrete subjected to mechanical loadings and high temperatures simulating the effects of coolant spills, molten debris, etc. The capability to model concrete structures subjected to static and dynamic overpressures, such as LWR and LMR containments with complex axisymmetric geometries, can be solved. The computer code is a finite element program which has a weakly coupled thermomechanical formulation. It can handle transient and steady state problems through the use of explicit time integration and dynamic relaxation. There is a plane or axisymmetric continuum element and flexural beam and shell elements for concrete discretization. The continuum element is a four node quadrilateral using numerical integration and elastic hourglass control. Variable material properties as a function of temperature are available. Thermal and/or mechanical loading can be handled. The concrete material model has the following characteristics: (a) elastic-plastic response, (b) variable loading surface capability, (c) cracking normal to maximum principal strain at specified failure surface, (d) post-failure element treatment, and (e) variable temperature dependence. Concrete can be reinforced and/or prestressed. 15 refs., 33 figs., 24 tabs.

  20. A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

    NASA Technical Reports Server (NTRS)

    Zoby, E. V.; Graves, R. A., Jr.

    1973-01-01

    A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

  1. Effect of magnetic island geometry on ECRH/ECCD and consequences to the NTM stabilization dynamics

    NASA Astrophysics Data System (ADS)

    Chatziantonaki, I.; Tsironis, C.; Isliker, H.; Vlahos, L.

    2012-09-01

    In the majority of codes that model ECCD-based NTM stabilization, the analysis of the EC propagation and absorption is performed in terms of the axisymmetric magnetic field, ignoring effects due to the island topology. In this paper, we analyze the wave propagation, absorption and current drive in the presence of NTMs, as well as the ECCD-driven island growth, focusing on the effect of the island geometry on the wave de-position. A primary evaluation of the consequences of these effects on the NTM evolution is also made in terms of the modified Rutherford equation.

  2. Optically defined mechanical geometry

    NASA Astrophysics Data System (ADS)

    Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.

    2016-05-01

    In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.

  3. Critique of information geometry

    SciTech Connect

    Skilling, John

    2014-12-05

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  4. Geometry from Gauge Theory

    NASA Astrophysics Data System (ADS)

    Correa, Diego H.; Silva, Guillermo A.

    2008-07-01

    We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

  5. Geometry from Gauge Theory

    SciTech Connect

    Correa, Diego H.; Silva, Guillermo A.

    2008-07-28

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

  6. Critique of information geometry

    NASA Astrophysics Data System (ADS)

    Skilling, John

    2014-12-01

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  7. Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle

    NASA Astrophysics Data System (ADS)

    Du, Lili; Duan, Ben

    2016-04-01

    This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813-847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813-847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli's function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813-847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.

  8. A variational principle for the axisymmetric stability of rotating relativistic stars

    NASA Astrophysics Data System (ADS)

    Prabhu, Kartik; Schiffrin, Joshua S.; Wald, Robert M.

    2016-09-01

    It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.

  9. Comparative study of soot formation on the centerline of axisymmetric laminar diffusion flames: Fuel and temperature effects

    SciTech Connect

    Gomez, A.; Littman, M.G.; Glassman, I.

    1987-11-01

    The appearance of soot on the centerline aof axisymmetric laminar diffusion flames has been studied by monitoring (i) the gas temperature by thermocouples; (ii) the soot particle field by laser scattering/extinction; (iii) the presence of polycyclic aromatic hydrocarbons (PCAH) by laser induced fluorescence. Four fuels were used: butene, acetylene, butadiene, and benzene. All but one flame were at the smoke height condition and were characterized by different levels of N/sub 2/ dilution aimed at controlling the temperature field. It was observed that (i) soot nucleation occurs at the centerline; (ii) the soot onset on the centerline occurs when a characteristic temperature of 1350K is measured, regardless of fuel type or level of dilution; (iii) butene and benzene have similar fluorescence patterns, in contrast with premixed flame environments. These last two observations are consistent with the proposal that, though the extent of conversion of fuel into soot may significantly change from fuel to fuel, there is a common mechanism of soot formation for all fuels. Results are discussed.

  10. Turbulence measurements in axisymmetric jets of air and helium

    NASA Astrophysics Data System (ADS)

    Panchapakesan, N. R.

    Turbulent axisymmetric jets of air helium with the same nozzle momentum flux were studied experimentally using hot-wire probes. An X-wire hot-wire probe was used in the air jet and a composite probe consisting of an X-wire and an interference probe of the Way-Libby type was used in the helium jet to measure the helium concentration and two velocity components. Moments of turbulent fluctuations, up to fourth order, were calculated to characterize turbulent transport in the jet and to evaluate current models for triple moments that occur in the Reynolds stress equation. In the air jet, the momentum flux across the jet was found to be within +/- 5 percent of the nozzle input and the integral of the radial diffusive flux of the turbulent kinetic energy across the jet was found to be close to zero indicating consistency of measurements with the equations of motion. The fourth moments were very well described in terms of the second moments by the quasi-Gaussian approximation across the entire jet. Profiles of third moments were found to be significantly different from earlier measurements - (u(v exp 2)) (u(w exp 2)) and ((u exp 2)v) were found to be negative near the axis of the jet. The measurements in the helium jet were in the intermediate region between the non-buoyant jet and the plume regions. The helium mass flux across the jet was found to be within +/- 0 percent of the nozzle input. The far field behavior was in accord with the expected plume scalings. The near field behavior of the mean velocity along the axis of the jet follows the scaling expressed by the effective diameter but the mean concentration decay has a different density ratio dependence. The radical profiles of mean velocity and concentration indicate a turbulent Schmidt number of 0.7, the same as for passive scalars in round jets. Turbulent intensity of axial velocity fluctuations was significantly higher than that observed in the air jet while the radial and azimuthal intensities are virtually

  11. The effects of capillary forces on the axisymmetric propagation of two-phase, constant-flux gravity currents in porous media

    NASA Astrophysics Data System (ADS)

    Golding, Madeleine J.; Huppert, Herbert E.; Neufeld, Jerome A.

    2013-03-01

    The effects of capillary forces on the propagation of two-phase, constant-flux gravity currents in a porous medium are studied analytically and numerically in an axisymmetric geometry. The fluid within a two-phase current generally only partially saturates the pore space it invades. For long, thin currents, the saturation distribution is set by the vertical balance between gravitational and capillary forces. The capillary pressure and relative permeability of the fluid in the current depend on this saturation. The action of capillary forces reduces the average saturation, thereby decreasing the relative permeability throughout the current. This results in a thicker current, which provides a steeper gradient to drive flow, and a more blunt-nose profile. The relative strength of gravity and capillary forces remains constant within a two-phase gravity current fed by a constant flux and spreading radially, due to mass conservation. For this reason, we use an axisymmetric representation of the framework developed by Golding et al. ["Two-phase gravity currents in porous media," J. Fluid Mech. 678, 248-270 (2011)], 10.1017/jfm.2011.110, to investigate the effect on propagation of varying the magnitude of capillary forces and the pore-size distribution. Scaling analysis indicates that axisymmetric two-phase gravity currents fed by a constant flux propagate like t1/2, similar to their single-phase counterparts [S. Lyle, H. E. Huppert, M. Hallworth, M. Bickle, and A. Chadwick, "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)], 10.1017/S0022112005006713, with the effects of capillary forces encapsulated in the constant of proportionality. As a practical application of our new concepts and quantitative evaluations, we discuss the implications of our results for the process of carbon dioxide (CO2) sequestration, during which gravity currents consisting of supercritical CO2 propagate in rock saturated with aqueous brine. We apply our two

  12. RAXJET- TRANSONIC, AXISYMMETRIC FLOW OVER NOZZLE AFTERBODIES WITH SUPERSONIC JET EXHAUSTS

    NASA Technical Reports Server (NTRS)

    Wilmoth, R. G.

    1994-01-01

    The nozzle afterbody is one of the main drag-producing components of an aircraft propulsion system. Thus, considerable effort has been devoted to developing techniques for predicting the afterbody flow field and drag. The RAXJET computer program was developed to predict the transonic, axisymmetric flow over nozzle afterbodies with supersonic jet exhausts and includes the effects of boundary-layer displacement, separation, jet entrainment, and inviscid jet plume blockage. RAXJET iteratively combines the South-Jameson relaxation procedure, the Reshotko-Tucker boundary-layer solution, the Presz separation model, the Dash-Pergament mixing model, and the Dash-Thorpe inviscid plume model into a single, comprehensive model. The approach taken in the RAXJET program requires considerably less computational time than the Navier-Stokes solutions and generally yields results of comparable accuracy. In RAXJET, the viscous-inviscid interaction model is constructed by dividing the afterbody flow field into six separate computational regions: (1) The inviscid external flow solution is based on the relaxation procedure of South and Jameson for solving the exact nonlinear potential flow equation in nonconservative form. (2) The flow field in the inviscid jet exhaust is solved by explicit spatial marching of the conservative finite-difference form of the inviscid flow equations for a uniform composition gas mixture. (3) The properties in the attached boundary-layer region are solved by a modified version of the Reshotko-Tucker integral method for turbulent flows. (4) The analysis of the separated flow region consists of predicting the separation location and calculating the discriminating streamline shape. (5) The jet wake region is determined by either a simple extrapolation model or by an integral method that accounts for entrainment effects. (6) The displacement-thickness distribution arising from entrainment into the jet mixing layer is calculated by the overlaid mixing model

  13. Numerical simulation of the flow and fuel-air mixing in an axisymmetric piston-cylinder arrangement

    NASA Technical Reports Server (NTRS)

    Shih, T. I. P.; Smith, G. E.; Springer, G. S.

    1982-01-01

    The implicit factored method of Beam and Warming was employed to describe the flow and the fuel-air mixing in an axisymmetric piston-cylinder configuration during the intake and compression strokes. The governing equations were established on the basis of laminar flow. The increased mixing due to turbulence was simulated by appropriately chosen effective transport properties. Calculations were performed for single-component gases and for two-component gases and for two-component gas mixtures. The flow field was calculated as functions of time and position for different geometries, piston speeds, intake-charge-to-residual-gas-pressure ratios, and species mass fractions of the intake charge. Results are presented in graphical form which show the formation, growth, and break-up of those vortices which form during the intake stroke and the mixing of fuel and air throughout the intake and compression strokes. It is shown that at bore-to-stroke ratio of less than unity, the vortices may break-up during the intake stroke. It is also shown that vortices which do not break-up during the intake stroke coalesce during the compression stroke. The results generated were compared to existing numerical solutions and to available experimental data.

  14. Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas; Krejsa, Eugene A.; Kim, Chan M.

    1991-01-01

    The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

  15. The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

    NASA Technical Reports Server (NTRS)

    Nemeth, Michael P.; Schultz, Marc R.

    2012-01-01

    A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

  16. An Approximate Axisymmetric Viscous Shock Layer Aeroheating Method for Three-Dimensional Bodies

    NASA Technical Reports Server (NTRS)

    Brykina, Irina G.; Scott, Carl D.

    1998-01-01

    A technique is implemented for computing hypersonic aeroheating, shear stress, and other flow properties on the windward side of a three-dimensional (3D) blunt body. The technique uses a 2D/axisymmetric flow solver modified by scale factors for a, corresponding equivalent axisymmetric body. Examples are given in which a 2D solver is used to calculate the flow at selected meridional planes on elliptic paraboloids in reentry flight. The report describes the equations and the codes used to convert the body surface parameters into input used to scale the 2D viscous shock layer equations in the axisymmetric viscous shock layer code. Very good agreement is obtained with solutions to finite rate chemistry 3D thin viscous shock layer equations for a finite rate catalytic body.

  17. Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force

    NASA Astrophysics Data System (ADS)

    Zhao, Ren; Zhang, Li-Chun; Wu, Yue-Qin; Li, Huai-Fan

    2011-01-01

    We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton's law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.

  18. On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

    NASA Technical Reports Server (NTRS)

    Lerche, I.; Low, B. C.

    1980-01-01

    The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

  19. Modeling and Prediction of the Noise from Non-Axisymmetric Jets

    NASA Technical Reports Server (NTRS)

    Leib, Stewart J.

    2014-01-01

    mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant

  20. Planetary Image Geometry Library

    NASA Technical Reports Server (NTRS)

    Deen, Robert C.; Pariser, Oleg

    2010-01-01

    The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

  1. Status of Axisymmetric CFD of an Eleven Inch Diameter Hybrid Rocket Motor

    NASA Technical Reports Server (NTRS)

    Ruf, Joseph; Sullivan, Matthew R.; Wang, Ten See

    1993-01-01

    Current status of a steady state, axisymmetric analysis of an experimental 11 inch diameter hybrid rocket motor internal flow field is given. The objective of this effort is to develop a steady state axisymmetric model of the 11 inch hybrid rocket motor which can be used as a design and/or analytical tool. A test hardware description, modeling approach, and future plans are given. The analysis was performed with FDNS implementing several finite rate chemistry sets. A converged solution for a two equation and five species set on a 'fine' grid is shown.

  2. User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.

    1982-01-01

    This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

  3. Status of axisymmetric CFD of an eleven inch diameter hybrid rocket motor

    NASA Astrophysics Data System (ADS)

    Ruf, Joseph; Sullivan, Matthew R.; Wang, Ten See

    1993-07-01

    Current status of a steady state, axisymmetric analysis of an experimental 11 inch diameter hybrid rocket motor internal flow field is given. The objective of this effort is to develop a steady state axisymmetric model of the 11 inch hybrid rocket motor which can be used as a design and/or analytical tool. A test hardware description, modeling approach, and future plans are given. The analysis was performed with FDNS implementing several finite rate chemistry sets. A converged solution for a two equation and five species set on a 'fine' grid is shown.

  4. User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 3: ADD code coordinate generator

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.

    1982-01-01

    This User's Manual contains a complete description of the computer codes known as the Axisymmetric Diffuser Duct (ADD) code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.

  5. Axisymmetric transient thermal stress analysis of a multilayered composite hollow cylinder

    SciTech Connect

    Ootao, Y.; Tanigawa, Y.; Fukuda, T. Osaka Prefecture, University, Sakai Hitachi, Ltd., Yokohama )

    1991-06-01

    This article is concerned with axisymmetric, transient, thermal stress analysis of a hollow cylinder composed of multilayered composite laminates with temperature changes in the radial and axial directions due to axisymmetric heating from the outer and/or inner surfaces. The methods of Fourier cosine transform and Laplace transform are applied to the temperature field and the thermoelastic potential function, and Love's displacement function is applied to the thermoelastic field. Exact solutions are obtained for the temperature and thermal stress distributions in a transient state. Moreover, the theoretical developments proposed in the present article are applied to the analysis of a hollow cylinder with nonhomogeneous material properties, such as a functionally gradient material.

  6. High-frequency electromagnetic scarring in three-dimensional axisymmetric convex cavities

    DOE PAGESBeta

    Warne, Larry K.; Jorgenson, Roy E.

    2016-04-13

    Here, this article examines the localization of high-frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. When these orbits lead to unstable localized modes, they are known as scars. This article treats the case where the opposing sides, or mirrors, are convex. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as field point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation.

  7. On axisymmetric and stationary solutions of the self-gravitating Vlasov system

    NASA Astrophysics Data System (ADS)

    Ames, Ellery; Andréasson, Håkan; Logg, Anders

    2016-08-01

    Axisymmetric and stationary solutions are constructed to the Einstein–Vlasov and Vlasov–Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein–Vlasov system which contain ergoregions.

  8. Information geometry of Bayesian statistics

    NASA Astrophysics Data System (ADS)

    Matsuzoe, Hiroshi

    2015-01-01

    A survey of geometry of Bayesian statistics is given. From the viewpoint of differential geometry, a prior distribution in Bayesian statistics is regarded as a volume element on a statistical model. In this paper, properties of Bayesian estimators are studied by applying equiaffine structures of statistical manifolds. In addition, geometry of anomalous statistics is also studied. Deformed expectations and deformed independeces are important in anomalous statistics. After summarizing geometry of such deformed structues, a generalization of maximum likelihood method is given. A suitable weight on a parameter space is important in Bayesian statistics, whereas a suitable weight on a sample space is important in anomalous statistics.

  9. Spectral, IR and magnetic studies of Mn(II), Co(II), Ni(II) and Cu(II) complexes with pyrrole-2-carboxyaldehyde thiosemicarbazone (L)

    NASA Astrophysics Data System (ADS)

    Chandra, Sulekh; Kumar, Anil

    2007-11-01

    Mn(II), Co(II), Ni(II) and Cu(II) complexes are synthesized with thiosemicarbazone (L) derived from pyrrole-2-carboxyaldehyde. These complexes are characterized by elemental analysis, molar conductance, magnetic susceptibility measurement, mass, IR, electronic and EPR spectral studies. The molar conductance measurement of the complexes in DMSO indicates that the complexes are non-electrolyte except Co(L) 2(NO 3) 2 and Ni(L) 2(NO 3) 2 complexes which are 1:2 electrolyte. All the complexes are of high-spin type. On the basis of spectral studies an octahedral geometry may be assigned for Mn(II), Co(II) and Ni(II) complexes except Co(L) 2(NO 3) 2 and Ni(L) 2(NO 3) 2 which are of tetrahedral geometry. A tetragonal geometry may be suggested for Cu(II) complexes.

  10. Spectral simulations of an axisymmetric force-free pulsar magnetosphere

    NASA Astrophysics Data System (ADS)

    Cao, Gang; Zhang, Li; Sun, Sineng

    2016-02-01

    A pseudo-spectral method with an absorbing outer boundary is used to solve a set of time-dependent force-free equations. In this method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergence-free state of the magnetic field is enforced analytically by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be reproduced well by our pseudo-spectral code. Further, the method is used to present a time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well and the spin-down luminosity obtained in the steady state is in good agreement with the value given by Spitkovsky.

  11. The Application of Mechanics to Geometry. Popular Lectures in Mathematics.

    ERIC Educational Resources Information Center

    Kogan, B. Yu

    Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…

  12. MHD Modeling in Complex 3D Geometries: Towards Predictive Simulation of SIHI Current Drive

    NASA Astrophysics Data System (ADS)

    Hansen, Christopher James

    The HIT-SI experiment studies Steady Inductive Helicity Injection (SIHI) for the purpose of forming and sustaining a spheromak plasma. A spheromak is formed in a nearly axisymmetric flux conserver, with a bow tie cross section, by means of two semi-toroidal injectors. The plasma-facing surfaces of the device, which are made of copper for its low resistivity, are covered in an insulating coating in order to operate in a purely inductive manner. Following formation, the spheromak flux and current are increased during a quiescent period marked by a decrease in the global mode activity. A proposed mechanism, Imposed Dynamo Current Drive (IDCD), is expected to be responsible for this phase of quiescent current drive. Due to the geometric complexity of the experiment, previous numerical modeling efforts have used a simplified geometry that excludes the injector volumes from the simulated domain. The effect of helicity injection is then modeled by boundary conditions on this reduced plasma volume. The work presented here has explored and developed more complete computational models of the HIT-SI device. This work is separated into 3 distinct but complementary areas: 1) Development of a 3D MHD equilibrium code that can incorporate the non-axisymmetric injector fields present in HIT-SI and investigation of equilibria of interest during spheromak sustainment. 2) A 2D axisymmetric MHD equilibrium code that was used to explore reduced order models for mean-field evolution using equations derived from IDCD theory including coupling to 3D equilibria. 3) A 3D time-dependent non-linear MHD code that is capable of modeling the entire plasma volume including dynamics within the injectors. Although HIT-SI was the motivation for, and experiment studied in this research, the tools and methods developed are general --- allowing their application to a broad range of magnetic confinement experiments. These tools constitute a significant advance for modeling plasma dynamics in devices with

  13. GPS: Geometry, Probability, and Statistics

    ERIC Educational Resources Information Center

    Field, Mike

    2012-01-01

    It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

  14. Achievement in Writing Geometry Proofs.

    ERIC Educational Resources Information Center

    Senk, Sharon L.

    In 1981 a nationwide assessment of achievement in writing geometry proofs was conducted by the Cognitive Development and Achievement in Secondary School Geometry project. Over 1,500 students in 11 schools in 5 states participated. This paper describes the sample, instruments, grading procedures, and selected results. Results include: (1) at the…

  15. Limits of downstream hydraulic geometry

    NASA Astrophysics Data System (ADS)

    Wohl, Ellen

    2004-10-01

    Adjustments to flow width, depth, and velocity in response to changes in discharge are commonly characterized by using downstream hydraulic geometry relationships. The spatial limits of these relationships within a drainage basin have not been systematically quantified. Where the erosional resistance of the channel substrate is sufficiently large, hydraulic driving forces presumably will be unable to adjust channel form. Data sets from 10 mountain rivers in the United States, Panama, Nepal, and New Zealand are used in this study to explore the limits of downstream hydraulic geometry relationships. Where the ratio of stream power to sediment size (Ω/D84) exceeds 10,000 kg/s3, downstream hydraulic geometry is well developed; where the ratio falls below 10,000 kg/s3, downstream hydraulic geometry relationships are poorly developed. These limitations on downstream hydraulic geometry have important implications for channel engineering and simulations of landscape change.

  16. Lobachevsky's Geometry and Research of Geometry of the Universe

    NASA Astrophysics Data System (ADS)

    Brylevskaya, L. I.

    2008-10-01

    For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.

  17. Experimental and Computational Study fo CH, CH*, and OH* in an Axisymmetric Laminar Diffusion Flame

    NASA Technical Reports Server (NTRS)

    Walsh, K. T.

    1998-01-01

    In this study, we extend the results of previous combined numerical and experimental investigations of an axisymmetric laminar diffusion flame in which difference Raman spectroscopy, laser-induced fluorescence (LIF), and a multidimensional flame model were used to generate profiles of the temperature and major and minor species. A procedure is outlined by which the number densities of ground-state CH (X(sup 2)II) excited-state CH (A(sup 2)Delta, denoted CH*), and excited-state OH (A(sup 2)Sigma, denoted OH*) are measured and modeled. CH* and OH* number densities are deconvoluted from line-of-sight flame-emission measurements. Ground-state CH is measured using linear LIF. The computations are done with GRI Mech 2.11 as well as an alternate hydrocarbon mechanism. In both cases, additional reactions for the production and consumption of CH* and OH* are added from recent kinetic studies. Collisional quenching and spontaneous emission are responsible for the de-excitation of the excited-state radicals. As with our previous investigations, GRI Mech 2.11 continues to produce very good agreement with the overall flame length observed in the experiments, while significantly under predicting the flame lift-off height. The alternate kinetic scheme is much more accurate in predicting lift-off height but overpredicts the over-all flame length. Ground-state CH profiles predicted with GRI Mech 2.11 are in excellent agreement with the corresponding measurements, regarding both spatial distribution and absolute concentration (measured at 4 ppm) of the CH radical. Calculations of the excited-state species show reasonable agreement with the measurements as far as spatial distribution and overall characteristics are concerned. For OH*, the measured peak mole fraction, 1.3 x 10(exp -8), compared well with computed peaks, while the measured peak level for CH*, 2 x 10(exp -9), was severely underpredicted by both kinetic schemes, indicating that the formation and destruction kinetics

  18. Electomagnetic field due to a non-axisymmetric current loop around Kerr blackhole

    NASA Astrophysics Data System (ADS)

    Pandey, U. S.; Dubey, G. S.

    1983-12-01

    The authors derive expressions for the electromagnetic field of a non-axisymmetric current loop around a Kerr blackhole. Complete solution for the "inside" as well as the "outside" regions of the current loop are determined using vacuum solutions of King (1977). A particular solution, the electromagnetic field of an equatorial current loop, is explicitly derived.

  19. The direct numerical simulations of the turbulent wakes of axisymmetric bodies

    NASA Technical Reports Server (NTRS)

    Riley, J. J.; Metcalfe, R. W.

    1978-01-01

    Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.

  20. Influence of the initial conditions of the flow in axisymmetric slipstreams

    NASA Astrophysics Data System (ADS)

    Navoznov, O. I.; Pavelev, A. A.

    1980-08-01

    The paper deals with an experimental investigation of the flow in the initial portion of axisymmetric helium, air, and Freon-12 jets in turbulent mixing layers. Measurements of the mean and pulsation velocities and temperature are presented, along with flow pattern photographs.

  1. Influence of the initial conditions on axisymmetric jets in a parallel flow

    NASA Astrophysics Data System (ADS)

    Navoznov, O. I.; Pavelev, A. A.

    1980-07-01

    The paper deals with an experimental investigation of the flow in the initial portion of axisymmetric helium, air, and Freon-12 jets in turbulent mixing layers. Measurements of the mean and pulsation velocities and temperature are presented, along with flow pattern photographs.

  2. Velocity gradient method for calulating velocities in an axisymmetric annular duct

    NASA Technical Reports Server (NTRS)

    Katsanis, T.

    1982-01-01

    The velocity distribution along an arbitrary line between the inner and outer walls of an annular duct with axisymmetric swirling flow is calculated. The velocity gradient equation is used with an assumed variation of meridional streamline curvature. Upstream flow conditions can vary between the inner and outer walls, and an assumed total pressure distribution can be specified.

  3. Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Greenberg, P. S.

    1994-01-01

    Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

  4. Transport of absolute angular momentum in quasi-axisymmetric equatorial jet streams

    NASA Technical Reports Server (NTRS)

    Read, P. L.

    1986-01-01

    It is well known that prograde equatorial jet stresses cannot occur in an axisymmetric inviscid fluid, owing to the constraints of local angular momentum conservation. For a viscous fluid, the constraints of mass conservation prevent the formation of any local maximum of absolute angular momentum (m) without a means of transferring m against its gradient (delta m) in the meridional plane. The circumstances under which m can be diffused up-gradient by normal molecular viscosity are derived, and illustrated with reference to numerical simulations of axisymmetric flows in a cylindrical annulus. Viscosity is shown to act so as to tend to expel m from the interior outwards from the rotation axis. Such an effect can produce local super-rotation even in a mechanically isolated fluid. The tendency of viscosity to result in the expulsion of m is shown to be analogous in certain respects to a vorticity-mixing hypothesis for the effects of non-axisymmetric eddies of the zonally-averaged flow. It is shown how the advective and diffusive transport of m by non-axisymmetric eddies can be represented by the Transformed Eulerian Mean meridional circulation and the Eliassen-Palm (EP) flux of Andrews and McIntyre respectively, in the zonal mean. Constraints on the form and direction of the EP flux in an advective/diffusive flow for such eddies are derived, by analogy with similar constraints on the diffusive flux of m due to viscosity.

  5. Reconstruction of velocity profiles in axisymmetric and asymmetric flows using an electromagnetic flow meter

    NASA Astrophysics Data System (ADS)

    Kollár, László E.; Lucas, Gary P.; Meng, Yiqing

    2015-05-01

    An analytical method that was developed formerly for the reconstruction of velocity profiles in asymmetric flows is improved to be applicable for both axisymmetric and asymmetric flows. The method is implemented in Matlab, and predicts the velocity profile from measured electrical potential distributions obtained around the boundary of a multi-electrode electromagnetic flow meter (EMFM). Potential distributions are measured in uniform and non-uniform magnetic fields, and the velocity is assumed as a sum of axisymmetric and polynomial components. The procedure requires three steps. First, the discrete Fourier transform (DFT) is applied to the potential distribution obtained in a uniform magnetic field. Since the direction of polynomial components of order greater than two in the plane of the pipe cross section is not unique multiple solutions exist, therefore all possible polynomial velocity profiles are determined. Then, the DFT is applied to the potential distribution obtained in a specific non-uniform magnetic field, and used to calculate the exponent in a power-law representation of the axisymmetric component. Finally, the potential distribution in the non-uniform magnetic field is calculated for all of the possible velocity profile solutions using weight values, and the velocity profile with the calculated potential distribution which is closest to the measured one provides the optimum solution. The method is validated by reconstructing two quartic velocity profiles, one of which includes an axisymmetric component. The potential distributions are obtained from simulations using COMSOL Multiphysics where a model of the EMFM is constructed. The reconstructed velocity profiles show satisfactory agreement with the input velocity profiles. The main benefits of the method described in this paper are that it provides a velocity distribution in the circular cross section of a pipe as an analytical function of the spatial coordinates which is suitable for both

  6. Microwave and optical ray geometry

    NASA Astrophysics Data System (ADS)

    Cornbleet, S.

    The laws of refraction and reflection are examined, and the zero-distance phase front is discussed, taking into account aspects of definition and general derivation, refraction in a circular interface, reflection in a circle, reflection in a general curve, geometrical constructions, and caustic approximations. Other subjects explored are related to the inversion theorem of Damien, the mechanical description of optical surfaces, ray-tracing in nonuniform media, rays in linear and cylindrical media, rays in spherical and axisymmetric media, geodesics, rays and trajectories, curves and their formulae, derived curves, applications of Abel's integral, and the radiation patterns of Luneburg lenses. Attention is given to a geometrical method of optical design, lens bending, the general two-surface reflector system, the ray-tracing equations, expansions of the ray equations, transformations of the spherical lenses, and rays in an angular variable medium.

  7. 2D axisymmetric analysis of SRM ignition transient

    NASA Astrophysics Data System (ADS)

    Bai, S. D.; Han, Samuel S.; Pardue, B. A.

    1993-06-01

    To analyze ignition transient of Space Shuttle solid rocket motor, a transient two-dimensional numerical model based on turbulent compressible Navier-Stokes equations in a generalized coordinate system was developed. One-dimensional numerical models (Peretz et al., 1973; Han, 1992; Pardue and Han, 1992) with empirical correlations data obtained from steady turbulent boundary layer flows agrees reasonably well with test rocket data by adjusting a few parameters. However, a 1D model can not provide a physical insight into the complex multidimensional thermal fields and flowfields in the chamber and the converging-diverging rocket nozzle. As an interim step, a 2D model was developed and compared with test data. A modified version of SIMPLE algorithm was used for the numerical model, and the standard k-epsilon model with a wall function was used for turbulence closure. Transient flowfields and thermal fields in the combustion chamber and the attached nozzle were obtained for a selected rocket geometry and propellant. Transient behaviors of the flow and thermal fields were analyzed, and were found to be in good agreement with physical expectations.

  8. Parametric Geometry, Structured Grid Generation, and Initial Design Study for REST-Class Hypersonic Inlets

    NASA Technical Reports Server (NTRS)

    Ferlemann, Paul G.; Gollan, Rowan J.

    2010-01-01

    Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.

  9. Quantum Consequences of Parameterizing Geometry

    NASA Astrophysics Data System (ADS)

    Wanas, M. I.

    2002-12-01

    The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.

  10. Distance geometry and geometric algebra

    NASA Astrophysics Data System (ADS)

    Dress, Andreas W. M.; Havel, Timothy F.

    1993-10-01

    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

  11. On The Explosion Geometry of Red Supergiant Stars

    NASA Astrophysics Data System (ADS)

    Leonard, Douglas C.; Supernova Spectropolarimetry Project (SNSPOL)

    2016-06-01

    From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars, establishing the most homogeneous --- and well understood --- progenitor class of any type of core-collapse supernova. The physical process by which these stars explode, however, remains a mystery. A fundamental clue to the nature of the explosion mechanism is explosion geometry: In short, are supernovae round? Because young supernova atmospheres are electron-scattering dominated, their net linear polarization provides a direct probe of early-time supernova geometry, with higher degrees of polarization generally indicating greater departures from spherical symmetry. This presentation will describe the ongoing work being carried out on RSG explosion geometry by the SuperNova SpectroPOLarimetry project (SNSPOL), with a particular focus on SN 2013ej -- an SN II-P that exhibited remarkably high polarization just days after the explosion, and for which twelve epochs of spectropolarimetry trace an intriguing tale about its geometry deep into the nebular phase.We acknowledge support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out.

  12. The Dilemma of Descriptive Geometry

    ERIC Educational Resources Information Center

    Boleslavski, Moshe

    1977-01-01

    Proposes that engineering students undergo a preparatory summer school training program in fundamentals of engineering drawing, descriptive geometry, and mathematics prior to being admitted to regular engineering studies. (SL)

  13. Emergent geometry from quantized spacetime

    SciTech Connect

    Yang, Hyun Seok; Sivakumar, M.

    2010-08-15

    We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.

  14. Interaction of morphogens with geometry

    NASA Astrophysics Data System (ADS)

    Cummings, F. W.

    2005-09-01

    Morphogen patterns are viewed as being affected by epithelial sheet geometry in early development. As the total area of the (closed) sheet changes, the changing geometry acts back in turn to change the morphogen pattern. A number of constraints are given on the functional form of the Gauss and Mean curvatures, considered as functions of the morphogen concentrations and their derivatives. It is shown that the constraints are sufficient to motivate a convincing dependence of the two curvatures on the morphogen concentrations.

  15. The Common Geometry Module (CGM).

    SciTech Connect

    Tautges, Timothy James

    2004-12-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

  16. The Development of Explosions in Axisymmetric Ab Initio Core-collapse Supernova Simulations of 12-25 M Stars

    NASA Astrophysics Data System (ADS)

    Bruenn, Stephen W.; Lentz, Eric J.; Hix, W. Raphael; Mezzacappa, Anthony; Harris, J. Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; Marronetti, Pedro; Yakunin, Konstantin N.

    2016-02-01

    We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 {M}⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. We compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ {10}51 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 {\\text{B s}}-1, respectively, for the 12, 15, 20, and 25 {M}⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 {M}⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. We compare our results for the explosion energies and ejected {}56{Ni} masses against some observational standards despite the large error bars in both models and observations.

  17. The development of explosions in axisymmetric ab initio core-collapse supernova simulations of 12–25 M⊙ stars

    DOE PAGESBeta

    Bruenn, Stephen W.; Lentz, Eric J.; Hix, William Raphael; Mezzacappa, Anthony; Harris, James Austin; Messer, O. E. Bronson; Endeve, Eirik; Blondin, John M.; Chertkow, Merek Austin; Lingerfelt, Eric J.; et al

    2016-02-16

    We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. Wemore » compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ 1051 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 BS–1, respectively, for the 12, 15, 20, and 25 M⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. In conclusion, we compare our results for the explosion energies and ejected 56Ni masses against some observational standards despite the large error bars in both models and observations.« less

  18. A FORTRAN code for the calculation of probe volume geometry changes in a laser anemometry system caused by window refraction

    NASA Technical Reports Server (NTRS)

    Owen, Albert K.

    1987-01-01

    A computer code was written which utilizes ray tracing techniques to predict the changes in position and geometry of a laser Doppler velocimeter probe volume resulting from refraction effects. The code predicts the position change, changes in beam crossing angle, and the amount of uncrossing that occur when the beams traverse a region with a changed index of refraction, such as a glass window. The code calculates the changes for flat plate, cylinder, general axisymmetric and general surface windows and is currently operational on a VAX 8600 computer system.

  19. Black holes and large order quantum geometry

    SciTech Connect

    Huang Minxin; Klemm, Albrecht; Marino, Marcos; Tavanfar, Alireza

    2009-03-15

    We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations--which seem necessary to resolve the so-called entropy enigma in the Ooguri-Strominger-Vafa conjecture--do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.

  20. Realism, positivism, instrumentalism, and quantum geometry

    NASA Astrophysics Data System (ADS)

    Prugovečki, Eduard

    1992-02-01

    The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.

  1. An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus.

    PubMed

    Wirth, Benedikt; Sobey, Ian

    2006-12-01

    We formulate in general terms the equations for axisymmetric and fully 3D models of a hydrocephalic brain. The model is developed using small strain poroelasticity that includes non-linear permeability. The axisymmetric model is solved for four ventricle shapes, an ellipsoid, a 'peanut' shape, a 'cross' shape and a 'bone' shape. The distribution of fluid pressure, velocity and content in the deformed parenchyma for a blocked aqueduct provides new qualitative insight into hydrocepahlus. Some observations are offered for two forms of cerebrospinal fluid flow abnormality, normal pressure hydrocephalus and idiopathic intracranial hypertension. The model is extended to include a gravitational term in the governing equations and the effect of hydrostatic pressure variation is considered. Results of a fully 3D simulations are described for two horn-like lateral ventricles and one case with two lateral ventricles and a third ventricle. PMID:16740629

  2. On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, P. W.; Hall, P.

    1988-01-01

    Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

  3. On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, P. W.; Hall, P.

    1989-01-01

    Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub O. At values of the radius above a sub O all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

  4. A multi-machine analysis of non-axisymmetric and rotating halo currents

    NASA Astrophysics Data System (ADS)

    Myers, Clayton E.; Gerhardt, S. P.; Eidietis, N. W.; Granetz, R. S.; Pautasso, G.; ITPA Working Group on Non-Axisymmetric Halo Currents Collaboration

    2015-11-01

    Halo currents measured during tokamak disruptions exhibit non-axisymmetric and rotating features in several machines including Alcator C-Mod, ASDEX Upgrade, and NSTX. Such non-axisymmetries are of great interest to ITER because they can increase mechanical stresses during a disruption, especially if the rotation resonates with the natural frequencies of the vessel. This paper presents an ITPA-initiated multi-machine analysis of these phenomena. The ITPA non-axisymmetric halo current database presently includes data from NSTX, DIII-D, AUG, and C-Mod. These data are analyzed here within a common numerical framework. Emphasis is placed on the evolution of the n = 1 component of the halo current over the course of the disruption, as well as on how the non-axisymmetries and rotation depend on the equilibrium plasma parameters at the start of the disruption. This research is supported by DoE Contract Number DE-AC02-09CH11466.

  5. Measurement of density in axisymmetric jets using a novel background-oriented schlieren (BOS) technique

    NASA Astrophysics Data System (ADS)

    Tan, Dominic James; Edgington-Mitchell, Daniel; Honnery, Damon

    2015-11-01

    A novel application of the adaptive Fourier-Hankel (AFH) Abel algorithm to reconstruct the radial density distribution of axisymmetric jets is presented. The fluid is imaged using the non-intrusive path-integrated background-oriented schlieren (BOS) technique. BOS images are cross-correlated to obtain background displacements that are proportional to the first derivative of the refractive index. The critical step is deconvolving the projected displacements. The AFH method is applied to simulated displacement data to validate the use of averaged turbulent fluctuations that approximate an axisymmetric field. The influence of experimental noise and variations in the flow on the accuracy of the method is discussed. The limitations of the system are demonstrated by applying it to low- and high-Reynolds ( Re) number jets. The high- Re jets are produced from a high-pressure fuel injector operating at nozzle pressure ratios of 2, 3, and 4.

  6. Temperature measurements in an axisymmetric methane-air flame using Talbot images

    NASA Astrophysics Data System (ADS)

    Khramtsov, P. P.; Penyazkov, O. G.; Shatan, I. N.

    2015-02-01

    The paper discusses the principles of optical testing of transparent objects using the Talbot images method and its applicability to diagnostic of flames. The experimental study was performed for premixed methane -air flame formed by an axisymmetric nozzle. The local deflection angles of the probe radiation were determined from measurements of the relative displacements of intensity maxima of the Talbot image which is caused by passing of light through the flame. The Abel integral equation was solved to reconstruct the refractive index distribution in the flame. Calculation of the temperature field from the refractive index data was based on neglecting the spatial variation of the component composition. Inaccuracy of the calculations was evaluated by comparing the results with the thermocouple measurements. The results demonstrate that the Talbot images method can be used to measure the temperature distribution in axisymmetric reacting gas flows with high spatial resolution.

  7. Spin Stability Criteria for Axisymmetric Spinning Body with Large Flexible Membrane

    NASA Astrophysics Data System (ADS)

    Tsuda, Yuichi

    Stability of the dynamics of spinning spacecraft equipped with a large flexible membrane is discussed. The spin stability of an object having a flexible structure is deteriorated from that of a rigid object with the same shape in general, which makes a significant impact on the design of such spacecraft systems. This paper provides a fully analytical solution for the stability criteria of axisymmetric spinner spacecraft equipped with a large flexible membrane. Distinct from past studies, this paper does not impose restrictions on axial offset of the membrane attachment, and provides a stability condition using energy-angular momentum analysis when the membrane is subject only to an outer-plane first-order mode deformation. These criteria can be applied to the design of such missions as spinner solar sail spacecraft, large solar power satellite and other general spacecraft with large axisymmetric structures.

  8. A RANS/DES Numerical Procedure for Axisymmetric Flows with and without Strong Rotation

    SciTech Connect

    Andrade, A J

    2007-10-30

    A RANS/DES numerical procedure with an extended Lax-Wendroff control-volume scheme and turbulence model is described for the accurate simulation of internal/external axisymmetric flow with and without strong rotation. This new procedure is an extension, from Cartesian to cylindrical coordinates, of (1) a second order accurate multi-grid, control-volume integration scheme, and (2) a k-{omega} turbulence model. This paper outlines both the axisymmetric corrections to the mentioned numerical schemes and the developments of techniques pertaining to numerical dissipation, multi-block connectivity, parallelization, etc. Furthermore, analytical and experimental case studies are presented to demonstrate accuracy and computational efficiency. Notes are also made toward numerical stability of highly rotational flows.

  9. Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator

    SciTech Connect

    S.R. Hudson; C.C. Hegna

    2003-09-15

    A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present.

  10. Axisymmetric shell analysis of the Space Shuttle solid rocket booster field joint

    NASA Technical Reports Server (NTRS)

    Nemeth, Michael P.; Anderson, Melvin S.

    1989-01-01

    The Space Shuttle Challenger (STS 51-L) accident led to an intense investigation of the structural behavior of the solid rocket booster (SRB) tang and clevis field joints. The presence of structural deformations between the clevis inner leg and the tang, substantial enough to prevent the O-ring seals from eliminating hot gas flow through the joints, has emerged as a likely cause of the vehicle failure. This paper presents results of axisymmetric shell analyses that parametrically assess the structural behavior of SRB field joints subjected to quasi-steady-state internal pressure loading for both the original joint flown on mission STS 51-L and the redesigned joint recently flown on the Space Shuttle Discovery. Discussion of axisymmetric shell modeling issues and details is presented and a generic method for simulating contact between adjacent shells of revolution is described. Results are presented that identify the performance trends of the joints for a wide range of joint parameters.

  11. Stationary axisymmetric and slowly rotating spacetimes in Hořava-Lifshitz gravity.

    PubMed

    Wang, Anzhong

    2013-03-01

    Stationary, axisymmetric, and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and it is shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary, and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution. This is in contrast to the claim of Barausse and Sotiriou [Phys. Rev. Lett. 109, 181101 (2012)], in which slowly rotating black holes were reported (incorrectly) not to exist in the infrared limit of the nonprojectable HL theory. PMID:23496699

  12. Turbine Engine Stability/Instability With Rub Forces Axisymmetric Rotor-Support Stiffness

    NASA Technical Reports Server (NTRS)

    Gallardo, Vicente; Lawrence, Charles

    2004-01-01

    The stability/instability condition of a turbine rotor with axisymmetric supports is determined in the presence of gyroscopic loads and rub-induced destabilizing forces. A modal representation of the turbine engine is used, with one mode in each of the vertical and horizontal planes. The use of non-spinning rotor modes permits an explicit treatment of gyroscopic effects. The two linearized modal equations of motion of a rotor with axisymmetric supports are reduced to a single equation in a complex variable. The resulting eigenvalues yield explicit expressions at the stability boundary, for the whirl frequency as well as the required damping for stability in the presence of the available rub-induced destabilization. Conversely, the allowable destabilization in the presence of the available damping is also given.

  13. Towards Simulating Non-Axisymmetric Influences on Aircraft Plumes for Signature Prediction

    NASA Technical Reports Server (NTRS)

    Kenzakowski, D. C.; Shipman, J. D.; Dash, S. M.

    2000-01-01

    A methodology for efficiently including three-dimensional effects on aircraft plume signature is presented. First, exploratory work on the use of passive mixing enhancement devices, namely chevrons and tabs, in IR signature reduction for external turbofan plumes is demonstrated numerically and experimentally. Such small attachments, when properly designed, cause an otherwise axisymmetric plume to have significant 3D structures, affecting signature prediction. Second, an approach for including non-axisymmetric and installation effects in plume signature prediction is discussed using unstructured methodology. Unstructured flow solvers, using advanced turbulence modeling and plume thermochemistry, facilitate the modeling of aircraft effects on plume structure that previously have been neglected due to gridding complexities. The capabilities of the CRUNCH unstructured Navier-Stokes solver for plume modeling is demonstrated for a passively mixed turbofan nozzle, a generic fighter nozzle, and a complete aircraft.

  14. On axisymmetric/diamond-like mode transitions in axially compressed core-shell cylinders

    NASA Astrophysics Data System (ADS)

    Xu, Fan; Potier-Ferry, Michel

    2016-09-01

    Recent interests in curvature- and stress-induced pattern formation and pattern selection motivate the present study. Surface morphological wrinkling of a cylindrical shell supported by a soft core subjected to axial compression is investigated based on a nonlinear 3D finite element model. The post-buckling behavior of core-shell cylinders beyond the first bifurcation often leads to complicated responses with surface mode transitions. The proposed finite element framework allows predicting and tracing these bifurcation portraits from a quantitative standpoint. The occurrence and evolution of 3D instability modes including sinusoidally deformed axisymmetric patterns and non-axisymmetric diamond-like modes will be highlighted according to critical dimensionless parameters. Besides, the phase diagram obtained from dimensional analyses and numerical results could be used to guide the design of core-shell cylindrical systems to achieve the desired instability patterns.

  15. Potential of the Galaxy from the Besançon galaxy model including non-axisymmetric components: Preliminary results

    NASA Astrophysics Data System (ADS)

    Fernández-Trincado, J. G.; Robin, A. C.; Bienaymé, O.; Reylé, C.; Valenzuela, O.; Pichardo, B.

    2014-07-01

    In this contributed poster we present a preliminary attempt to compute a non-axisymmetric potential together with previous axisymmetric potential of the Besançon galaxy model. The contribution by non-axisymmetric components are modeled by the superposition of inhomogeneous ellipsoids to approximate the triaxial bar and superposition of homogeneous oblate spheroids for a stellar halo, possibly triaxial. Finally, we have computed the potential and force field for these non-axisymmetric components in order to constraint the total mass of the Milky Way. We present preliminary results for the rotation curve and the contribution of the bar to it. This approach will allow future studies of dynamical constraints from comparisons of kinematical simulations with upcoming surveys such as RAVE, BRAVA, APOGEE, and GAIA in the near future. More details, are presented in https://gaia.ub.edu/Twiki/pub/GREATITNFC/ProgramFinalconference/Poster_JG.Fern%e1ndez.pdf.

  16. Dependence of the drag of a conical axisymmetric cavitation body on the cone angle and the cavitation number

    SciTech Connect

    Khomyakov, A.N.

    1995-11-01

    Numerical investigations of flow past axisymmetric conical cavitation bodies have shown that the drag coefficient of the cavitation body, calculated from the maximum cross-sectional area of the cavity (midsection), depends on the cavitation number and the cone angle.

  17. Deformable cells in confined geometries: From hemolysis to hydrodynamic interactions

    NASA Astrophysics Data System (ADS)

    Abkarian, Manouk; Faivre, Magalie; Stone, Howard A.

    2004-11-01

    Recent developments in microfluidics allow a wide range of possibilities for studying cellular-scale hydrodynamics. Here we use microfluidic technology to address several open questions in the blood flow literature where cell deformation and hydrodynamic interactions are significant. In particular, we investigate the pressure-driven flow of a dilute suspension in a channel and characterize the transition from steady axisymmetric cell shapes (for which numerical calculations exist) to asymmetric, highly extended shapes, which are precursors to hemolysis (i.e. destruction of the cell). In addition, we examine the influence of geometry on hydrodynamic interactions of deformable cells by contrasting one-dimensional motion of a train of particles in a channel with two-dimensional motions in a Hele-Shaw cell. This study can help to understand flow of cells in microcirculation from the unidirectional flow in capillaries to the two-dimensional flow in the lung alveoli and provides the basic steps to understand certain aspects of microcirculatory deseases like sickle cell anemia for example.

  18. Investigation of flowfields found in typical combustor geometries

    NASA Technical Reports Server (NTRS)

    Lilley, D. G.

    1985-01-01

    Activities undertaken during the entire course of research are summarized. Studies were concerned with experimental and theoretical research on 2-D axisymmetric geometries under low speed nonreacting, turbulent, swirling flow conditions typical of gas turbine and ramjet combustion chambers. They included recirculation zone characterization, time-mean and turbulence simulation in swirling recirculating flow, sudden and gradual expansion flowfields, and furher complexities and parameter influences. The study included the investigation of: a complete range of swirl strengths; swirler performance; downstream contraction nozzle sizes and locations; expansion ratios; and inlet side-wall angles. Their individual and combined effects on the test section flowfield were observed, measured and characterized. Experimental methods included flow visualization (with smoke and neutrally-buoyant helium-filled soap bubbles), five-hole pitot probe time-mean velocity field measurements, and single-, double-, and triple-wire hot-wire anemometry measurements of time-mean velocities, normal and shear Reynolds sresses. Computational methods included development of the STARPIC code from the primitive-variable TEACH computer code, and its use in flowfield prediction and turbulence model development.

  19. Turbulent boundary layer over porous surfaces with different surface geometries

    NASA Technical Reports Server (NTRS)

    Kong, F. Y.; Schetz, J. A.

    1982-01-01

    The turbulent boundary layer over three porous walls with different surface geometries was studied in order to investigate the individual influences of porosity and small roughness, as well as their combined effects, on turbulent boundary layer behavior. The tests were conducted in a 2 m x 2 m tunnel on a large axisymmetric model at speeds corresponding to Re(L) = 5,000,000-6,000,000. The development of the turbulent boundary layer was compared for that of sintered metal, bonded screening, and perforated sheet and then to that for the flow over a solid smooth wall and a solid, sand-roughened wall. The comparisons reveal that the effect of porosity is to shift the logarithmic region of the wall law down by a certain amount from the solid wall results and to increase the skin friction values by about 30-40%. The downward shift of the logarithmic region of the wall law and the increase of the skin friction value by the combined effects of small roughness and porosity are found to be roughly the sum of their individual effects.

  20. Two component laser velocimeter measurements of turbulence parameters downstream of an axisymmetric sudden expansion

    NASA Technical Reports Server (NTRS)

    Gould, Richard D.; Stevenson, Warren H.; Thompson, H. Doyle

    1986-01-01

    Simultaneous two-component laser velocimeter measurements were made in an axisymmetric sudden expansion flowfield. A specially designed correction lens was employed to correct optical aberrations introduced by the circular tube. This lens system allowed the accurate simultaneous measurement of axial and radial velocities in the test section. The experimental measurements were compared to predictions generated by a code which employed the k-epsilon turbulence model. Possible sources of differences observed between model predictions and the measurements are discussed.

  1. Stationary axisymmetric solutions involving a third order equation irreducible to Painlevé transcendents

    NASA Astrophysics Data System (ADS)

    Gariel, J.; Marcilhacy, G.; Santos, N. O.

    2008-02-01

    We extend the method of separation of variables, studied by Léauté and Marcilhacy [Ann. Inst. Henri Poincare, Sect. A 331, 363 (1979)], to obtain transcendent solutions of the field equations for stationary axisymmetric systems. These solutions depend on transcendent functions satisfying a third order differential equation. For some solutions this equation satisfies the necessary conditions, but not sufficient, to have fixed critical points.

  2. Static internal performance of an axisymmetric nozzle with multiaxis thrust-vectoring capability

    NASA Technical Reports Server (NTRS)

    Carson, George T., Jr.; Capone, Francis J.

    1991-01-01

    An investigation was conducted in the static test facility of the Langley 16 Foot Transonic Tunnel in order to determine the internal performance characteristics of a multiaxis thrust vectoring axisymmetric nozzle. Thrust vectoring for this nozzle was achieved by deflection of only the divergent section of this nozzle. The effects of nozzle power setting and divergent flap length were studied at nozzle deflection angles of 0 to 30 at nozzle pressure ratios up to 8.0.

  3. MHD Stability Calculations of High-Beta Quasi-Axisymmetric Stellarators

    SciTech Connect

    C. Kessel; G.Y. Fu; L.P. Ku; M.H. Redi; N. Pomphrey; et al

    1999-09-01

    The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size.

  4. CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction

    NASA Technical Reports Server (NTRS)

    Davis, David Owen

    2015-01-01

    Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/ boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. These results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.

  5. Emission of sound from axisymmetric turbulence convected by a mean flow with application to jet noise

    NASA Technical Reports Server (NTRS)

    Goldstein, M. E.; Rosenbaum, B. M.

    1972-01-01

    A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.

  6. A numerical determination of the bow shock wave in transonic axisymmetric flow about blunt bodies

    NASA Technical Reports Server (NTRS)

    Jones, D. J.; South, J. C., Jr.

    1975-01-01

    A numerical method was developed for calculating axisymmetric transonic (M greater than 1) flow about a blunt body; the bow shock wave location was investigated. A Rankine-Hugoniot jump was applied at the shock while relaxation on the isentropic equation of motion was used between shock and body. The shock wave is adjusted by a Newton type iteration scheme. Results are given for a sphere in the Mach number range 1.62 down to 1.02.

  7. Stationary axisymmetric four dimensional space-time endowed with Einstein metric

    SciTech Connect

    Hasanuddin; Azwar, A.; Gunara, B. E.

    2015-04-16

    In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time.

  8. Saturn's Very Axisymmetric Magnetic Field: Implication for the Interior of the Planet

    NASA Astrophysics Data System (ADS)

    Cao, Hao; Russell, C. T.; Christensen, U. R.; Dougherty, M. K.

    2010-10-01

    Saturn's intrinsic magnetic field is very spin-axisymmetric as found by Pioneer 11 and confirmed by the Voyager 1 and 2 flybys. Since 2004, the Cassini spacecraft has been providing continuous measurements of the magnetic field from Saturn orbit. Orbits with high inclination and low altitude provide a good dataset for the study of the intrinsic magnetic field of the planet. Our investigation shows no evidence for any detectable non-axisymmetric intrinsic magnetic field. The biggest possible dipole tilt we can find is 0.06 degree, which is the noise level of the analysis. Our axisymmetric model for Saturn's intrinsic magnetic field is characterized by Schmidt-normalized spherical harmonic coefficients g11 = 21191nT, g20 = 1586nT, g30 = 2374nT. No significant degree 4 or 5 terms can be determined from the current data. Compared with the SPV model, which fits the measurements from Pioneer 11, Voyager 1 and 2 equally well, the secular variation is found to be an order of magnitude smaller than for similar terms of the Earth's field for degree 1 and 2. This implies no fast decay of the Saturn's dipole moment, which is fundamentally different from the current secular variation of the Earth's field. The extremely high degree of axisymmetry of Saturn's magnetic field is challenging for dynamo theory. Our analysis of the magnetic measurement from Cassini requires a damping factor of 0.006 if the dipole tilt in the dynamo region is 10 degrees. To meet this damping factor, the stable layer must has significant thickness, L, is greater than or equal to 4,000km. This thicker stable layer is also favored by the prediction of Saturn's observed dipole moment from scaling theory. Numerical dynamo models with predicted damping factors are needed to determine possible limits to the degree of axisymmetrization by a conducting layer.

  9. Hydrodynamic analysis of the displacement conditions of formation fluids using an axisymmetric model

    NASA Astrophysics Data System (ADS)

    Chernoshchuk, I. B.

    2008-03-01

    The axisymmetric problem of the displacement of formation fluids by a drilling mud filtrate with filter cake formation is considered. An analysis is made of the distribution and variation of the main parameters of the process: filtrate volume, filter cake thickness, oil saturation, and pressure. The positions of the water-saturation and salt-concentration fronts are determined. The results are compared with the geophysical logging data for straight-hole drilling.

  10. Synthesis, Characterization and Biological Evaluation of Co(II), Cu(II), Ni(II) and Zn(II) Complexes With Cephradine

    PubMed Central

    Jaffery, Maimoon F.

    2000-01-01

    Some Co(II), Cu(II), Ni(II) and Zn(II) complexes of antibacterial drug cephradine have been prepared and characterized by their physical, spectral and analytical data. Cephradine acts as bidentate and the complexes have compositions, [M(L)2X2] where [M = Co(II), Ni(II) and Zn(II), L = cephradine and X = Cl2] showing octahedral geometry, and [M(L)2] where [M = Cu(II), L = cephradine] showing square planar geometry. In order to evaluate the effect of metal ions upon chelation, eephradine and its complexes have been screened for their antibacterial activity against bacterial strains, Escherichia coli, Staphylococcus aureus, and Pseudomonas aeruginosa. PMID:18475955

  11. The diffracted sound field from the transition region of an axisymmetric body in water

    NASA Astrophysics Data System (ADS)

    Li, Xue-Gang; Yang, Kun-De; Wang, Yong

    2011-07-01

    Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction. The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method. Based on the diffracted sound field, a simulation scheme for the noise correlation of the conformal array was presented. It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray. The flow noises of two models were compared and a rather optimum fore-body geometric shape was given. Furthermore, it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies. And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency, which is important for sonar system design.

  12. On the growth of enstrophy in axisymmetric 3D Euler flows with swirl

    NASA Astrophysics Data System (ADS)

    Ayala, Diego; Doering, Charles

    2015-11-01

    By numerically solving suitable PDE-constrained optimization problems, we study a family of axisymmetric vector fields, having the structure of a pair of vortex rings with swirl, that maximize the instantaneous production of enstrophy in the context of 3-dimensional (3D) incompressible Euler flows. The axisymmetric fields are parametrized by their energy K , enstrophy E and helicity H . The imposed symmetry is justified by the results from the seminal work of Doering & Lu (2008), recently confirmed independently by Ayala & Protas (2015), where highly localized pairs of colliding vortex rings were found to be instantaneously optimal for enstrophy production in 3D Navier-Stokes flows. The axial symmetry allows for an exhaustive exploration of the parameter space (K , E , H , as the 3D problem is effectively reduced to a 2-dimensional system of partial differential equations for the modified azimuthal vorticity and the azimuthal circulation density, with the corresponding reduction in computational complexity. Possible connections between these optimal axisymmetric fields with swirl and the ``blow-up'' problem are discussed.

  13. Influence of high-permeability discs in an axisymmetric model of the Cadarache dynamo experiment

    NASA Astrophysics Data System (ADS)

    Giesecke, A.; Nore, C.; Stefani, F.; Gerbeth, G.; Léorat, J.; Herreman, W.; Luddens, F.; Guermond, J.-L.

    2012-05-01

    Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-Kármán-sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability μr that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rmc for dynamo action of the first non-axisymmetric mode roughly scales like Rmcμr - Rmc∞∝μ-1/2r, i.e. the threshold decreases as μr increases. This scaling law suggests a skin effect mechanism in the soft iron discs. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high-permeability discs which becomes dominant for large μr. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disc interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of the high-permeability discs in the mode selection in the Cadarache dynamo experiment cannot be inferred from computations using idealized pseudo-vacuum boundary conditions (H × n = 0).

  14. Axisymmetrical separator for separating particulate matter from a fluid carrying medium

    DOEpatents

    Linhardt, Hans D.

    1984-09-04

    A separator for separating particles carried in a fluid carrying medium is disclosed. The separator includes an elongated duct and associated openings incorporated in a solid body. The duct is axisymmetrical relative to its longitudinal axis, and includes a curved wall portion having a curved cross-section taken along the longitudinal axis. An axisymmetrical opening located downstream of the curved wall portion leads from the duct into an axisymmetrical channel which is substantially radially disposed relative to the longitudinal axis. Continuation of the duct downstream of the opening is a discharge portion which is substantially colinear with the longitudinal axis. In operation, a substantial majority of the fluid carrying medium leaves the duct radially through the opening and channel in a state substantially free of particles. A remaining small portion of the fluid carrying medium and a substantial majority of the particles are channelled into the discharge portion by centrifugal forces arising due to travel of the particles along the curved walls. For industrial scale separation of particles from a fluid carrying medium, such as for the clean-up of stack gases, an array of several hundred to several thousand of the separators is provided.

  15. General parametrization of axisymmetric black holes in metric theories of gravity

    NASA Astrophysics Data System (ADS)

    Konoplya, Roman; Rezzolla, Luciano; Zhidenko, Alexander

    2016-03-01

    Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.

  16. On the nonlinear stability of a high-speed, axisymmetric boundary layer

    NASA Technical Reports Server (NTRS)

    Pruett, C. David; Ng, Lian L.; Erlebacher, Gordon

    1991-01-01

    The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

  17. An experimental study on characteristics of cavitation and ballistic of axisymmetric slender body underwater movement

    NASA Astrophysics Data System (ADS)

    Zhao, Cheng-Gong; Wang, Cong; Wei, Ying-Jie; Zhang, Xiao-Shi

    2015-12-01

    An experimental study of the axisymmetric slender body underwater movement was conducted using high-speed photography technology. From the results of the experiment, the characteristics of cavitation and ballistic of the axisymmetric, including the formation, development, evolution and collapse of the cavity, are presented in the paper. The experimental results show that the axisymmetric slender body moves in a supercavity, and the slender body rotate in the supercavity on its head at the same time due to the perturbation of launching. The supercavity wall is transparent and smooth except the tail itself. The impact between the tail of slender body and supercavity wall resulted from the slender body's rotation is termed as tail- slap which is one way to keep the stabilization of the movement. Series of different flow mechanisms and the relationship between ballistic characteristics and cavity characteristics with defferent initial velocities are discussed. The slender bodies have different accelerations and ballistics with different initial velocity which means they have different drag forces.

  18. High-Speed Unsteady Flows around Concave Axisymmetric Bodies: Flow Instabilities and their Suppression

    NASA Astrophysics Data System (ADS)

    Panaras, A.; Drikakis, D.

    2009-01-01

    The axisymmetric concave body, i.e. a body in which the normals to its surface intersect, is a typical configuration about which shock/shock interactions appear. Various shapes of axisymmetric concave bodies are used in a variety of applications in aeronautics. For exampe: axisymmetric jet inlets with conical centerbody, ballistic missiles drag reduction by spike, plasma or hot gas injection, parachutes for pilot-ejection capsules. However, it is well known that two distinct modes of instability appear around a concave body in the high-speed flow regime, for a certain range of geometric parameters. These instabilities can cause undesirable effects such as severe vibration of the structure, heating and pressure loads. According to the experimental evidence, the unsteady flow is characterized by periodic radial inflation and collapse of the conical separation bubble formed around the forebody (pulsation). Various explanations have been given for the driving mechanism of the instabilities. They are based on interpretation of experimental results or on numerical simulation of the related flows. A merging of the leading explanations is done, and basic rules for the passive suppression of the instabilities are applied, in order to enforce the proposed driving mechanism of the instabilities. Most of the analysis is based on numerical simulations.

  19. Earthquake cycles in complex geometries

    NASA Astrophysics Data System (ADS)

    Romanet, Pierre; Bhat, Harsha; Madariaga, Raul

    2016-04-01

    Our understanding of earthquake cycles, from a modelling perspective, comes mainly from theoretical, and numerical, work on a single straight fault. However, natural fault systems are geometrically complex. Modelling complex fault geometry (bends, kinks and multiple faults) is in itself a challenge as it is computationally intensive. To overcome this difficulty, we appeal to the Fast Multipole Method which was developed in the context of modelling N-body problems. This method is then used to model the quasi-dynamic response of multiple faults, with complex geometries, that are governed by rate and state friction laws. Our preliminary findings tell us that when stress interaction between faults, due to complex geometry, is accounted then even strongly rate-weakening faults (a-b)<0 show a complex spectrum of slow slip and dynamic ruptures.

  20. Quantum geometry and gravitational entropy

    SciTech Connect

    Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan

    2007-05-29

    Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.