Computation of recirculating compressible flow in axisymmetric geometries
Isaac, K.M.; Nejad, A.S.
1985-01-01
A computational study of compressible, turbulent, recirculating flow in axisymmetric geometries is reported in this paper. The SIMPLE algorithm was used in the differencing scheme and the k-epsilon model for turbulence was used for turbulence closure. Special attention was given to the specification of the boundary conditions. The study revealed the significant influence of the boundary conditions on the solution. The eddy length scale at the inlet to the solution domain was the most uncertain parameter in the specification of the boundary conditions. The predictions were compared with the recent data based on laser velocimetry. The two are seen to be in good agreement. The present study underscores the need to have a more reliable means of specifying the inlet boundary conditions for the k-epsilon turbulence model.
Numerical modeling in induction heating for axisymmetric geometries
Chaboudez, C.; Glardon, R.; Mari, D.; Clain, S.; Rappaz, J.; Swierkosz, M.
1997-01-01
Induction heating is widely used in today`s industry, in operations such as metal hardening, preheating for forging operations, or brazing. It is a complex process, involving both electromagnetic and thermal phenomena. Since the design and the investigation of an induction heating system usually relies upon a series of tedious, expensive and long experiments, numerical simulation can be a valuable help in this field. This paper deals with numerical simulation of induction heating for axisymmetric geometries. A mathematical model is presented, together with a numerical scheme based on the Finite Element Method. A numerical simulation code was implemented using the model presented in this paper. A comparison between results given by the code and experimental measurements is provided.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; 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.
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry
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.
Compact formulas for guiding-center orbits in axisymmetric tokamak geometry
Brizard, Alain J.
2011-02-15
Compact formulas for trapped-particle and passing-particle guiding-center orbits in axisymmetric tokamak geometry are given in terms of the Jacobi elliptic functions and complete elliptic integrals. These formulas can find applications in bounce-center kinetic theory as well as guiding-center Fokker-Planck kinetic theory.
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.
Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
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.
Reynolds number and geometry effects in laminar axisymmetric isothermal counterflows
NASA Astrophysics Data System (ADS)
Scribano, Gianfranco; Bisetti, Fabrizio
2016-12-01
The counterflow configuration is a canonical stagnation flow, featuring two opposed impinging round jets and a mixing layer across the stagnation plane. Although counterflows are used extensively in the study of reactive mixtures and other applications where mixing of two streams is required, quantitative data on the scaling properties of the flow field are lacking. The aim of this work is to characterize the velocity and mixing fields in isothermal counterflows over a wide range of conditions. The study features both experimental data from particle image velocimetry and results from detailed axisymmetric simulations. The scaling laws for the nondimensional velocity and mixture fraction are obtained as a function of an appropriate Reynolds number and the ratio of the separation distance of the nozzles to their diameter. In the range of flow configurations investigated, the nondimensional fields are found to depend primarily on the separation ratio and, to a lesser extent, the Reynolds number. The marked dependence of the velocity field with respect to the separation ratio is linked to a high pressure region at the stagnation point. On the other hand, Reynolds number effects highlight the role played by the wall boundary layer on the interior of the nozzles, which becomes less important as the separation ratio decreases. The normalized strain rate and scalar dissipation rate at the stagnation plane are found to attain limiting values only for high values of the Reynolds number. These asymptotic values depend markedly on the separation ratio and differ significantly from the values produced by analytical models. The scaling of the mixing field does not show a limiting behavior as the separation ratio decreases to the smallest practical value considered.
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.
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.
NASA Astrophysics Data System (ADS)
Alecian, G.; Stift, M. J.
2017-06-01
Numerical models for the atmospheres of magnetic ApBp stars have in the past dealt only with centred dipole magnetic field geometries. These models include atomic diffusion that stratifies the abundances of metals according to the local magnetic field strength and the direction with respect to the surface normal. The magnetic variations with rotational phase of most well observed stars, however, reveal that this assumption is far too simplistic. In this work, we establish for the first time a three-dimensional model with abundance stratifications arising from atomic diffusion of 16 metals, adopting a non-axisymmetric magnetic field geometry inspired by the configuration derived for a real ApBp star. We find that the chemical elements are distributed in complex patterns in all three dimensions, far from the simple rings that have been proposed as the dominant abundance structures from calculations that assume a perfectly centred dipolar magnetic geometry.
Full-field drift Hamiltonian particle orbits in axisymmetric tokamak geometry
Cooper, W. A.; Cooper, G. A.; Graves, J. P.; Isaev, M. Yu.
2011-05-15
A Hamiltonian/Lagrangian theory to describe guiding center orbit drift motion that is canonical in Boozer magnetic coordinates is developed to include full electrostatic and electromagnetic perturbed fields in axisymmetric tokamak geometry. Furthermore, the radial component of the equilibrium magnetic field in the covariant representation is retained and the background equilibrium state extends to anisotropic plasma pressure conditions. A gauge transformation on the perturbed vector potential is imposed to guarantee canonical structure in the Boozer frame. Perturbed field nonlinear wave-wave interactions affect only the evolution of the guiding center particle parallel gyroradius. The evolution of the particle coordinate positions retains only linear wave-particle interactions. For particle motion in magnetohydrodynamic (MHD) instability structures, the electrostatic potential is linked mainly to the binormal component of the perturbed displacement vector when finite {delta}A{sub perpendicular} components are included.
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.
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.
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.
Global axisymmetric simulations of two-fluid reconnection in an experimentally relevant geometry
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
New method for computing ideal MHD normal modes in axisymmetric toroidal geometry
Wysocki, F.; Grimm, R.C.
1984-11-01
Analytic elimination of the two magnetic surface components of the displacement vector permits the normal mode ideal MHD equations to be reduced to a scalar form. A Galerkin procedure, similar to that used in the PEST codes, is implemented to determine the normal modes computationally. The method retains the efficient stability capabilities of the PEST 2 energy principle code, while allowing computation of the normal mode frequencies and eigenfunctions, if desired. The procedure is illustrated by comparison with earlier various of PEST and by application to tilting modes in spheromaks, and to stable discrete Alfven waves in tokamak geometry.
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.
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.
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.
Co-current and counter-current imbibition in independent tubes of non-axisymmetric geometry.
Unsal, E; Mason, G; Morrow, N R; Ruth, D W
2007-02-01
Experiments that illustrate and quantify the basics of co- and counter-current spontaneous imbibition have been conducted in a series of simple model pore systems. The fundamental pore geometry is a rod in an angled round-bottomed slot with the rod touching a capping glass plate. The capillaries thus formed by the surfaces of the slot, rod and plate do not have circular cross-sections but more complicated geometric structures with angular corners. The tubes formed at each side of the rod connect at both ends. A viscous, refined oil was applied from one end. For co-current experiments, the opposite end was left open to the atmosphere and oil imbibed into both tubes. For counter-current experiments the opposite end was sealed and connected to a sensitive pressure transducer. Oil imbibed into the smaller capillary and expelled air as a series of bubbles from the end of the larger capillary. Bubble snap-off was observed to be rate-dependent and occurred at a lower curvature than that of the cylindrical meniscus that just fits inside the tube. Only the corners of the larger capillary filled with oil during counter-current imbibition. Meniscus curvatures were calculated using the Mayer and Stowe-Princen method and were compared with actual values by measuring the capillary rise in the tubes; agreement was close. A simple model for co-current and counter-current imbibition has also been developed and the predictions compared with the experimental results. The model results were in agreement with the experiments. The experiments demonstrate that the capillary back pressure generated by the interfaces and bubbles in counter-current imbibition can slow the process significantly.
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…
NASA Technical Reports Server (NTRS)
Chick, Kenneth M.; Gombosi, Tamas I.
1993-01-01
A numerical solution for the multiple light scattering in spherical axisymmetric geometry is applied to the simulation of images of a coma as it would appear to a near-flying satellite such as Giotto. The appearance of symmetric comas and dust jets is examined in detail; the nucleus visibility is studied; the effect of forward scattering is considered; and single and multiple scattering effects are quantified. Attention is given to simulated images of a coma with a hollow cone of dust, as predicted by dust-gas hydrodynamic modeling. The cone's appearance is very similar to the northern area of activity on Comet Halley, observed by the Giotto HMC.
NASA Technical Reports Server (NTRS)
Chick, Kenneth M.; Gombosi, Tamas I.
1993-01-01
A numerical solution for the multiple light scattering in spherical axisymmetric geometry is applied to the simulation of images of a coma as it would appear to a near-flying satellite such as Giotto. The appearance of symmetric comas and dust jets is examined in detail; the nucleus visibility is studied; the effect of forward scattering is considered; and single and multiple scattering effects are quantified. Attention is given to simulated images of a coma with a hollow cone of dust, as predicted by dust-gas hydrodynamic modeling. The cone's appearance is very similar to the northern area of activity on Comet Halley, observed by the Giotto HMC.
NASA Astrophysics Data System (ADS)
Heumann, Holger; Rapetti, Francesca
2017-04-01
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.
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.
NASA Technical Reports Server (NTRS)
Sohrab, Siavash H.
1999-01-01
Counterflow premixed flames play a significant role in the modeling of laminar flames. This is in part motivated by the fact that stretched premixed flames simulate local flamelet dynamics within turbulent premixed flames. In the present study, the modified form of the Navier-Stokes equation for reactive fields introduced earlier is employed to investigate the hydrodynamics of spherical flows embedded within counterflows. The geometry of premixed flames near the stagnation point is also determined. The predictions are in favorable agreement with the experimental observations and prior numerical studies.
Unified Field Theoretical Models from Generalized Affine Geometries II
NASA Astrophysics Data System (ADS)
Cirilo-Lombardo, Diego Julio
2011-06-01
The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288-1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗ O 3˜ R⊗ SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a( τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the "tratorial" form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.
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.
Modeling axisymmetric flow and transport.
Langevin, Christian D
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
Modeling axisymmetric flow and transport
Langevin, C.D.
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
NASA Astrophysics Data System (ADS)
Centeno, Felipe Roman; Brittes, Rogério; França, Francis. H. R.; Ezekoye, Ofodike A.
2015-05-01
The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer due to its relative simplicity, robustness and flexibility. This paper presents the computation of radiative heat transfer in a 2D axisymmetric chamber using two WSGG models to compute radiation in H2O and CO2 mixtures. The first model considers a fixed ratio between the molar concentrations of H2O and CO2, while the second allows the solution for arbitrary ratios. The correlations for both models are based on the HITEMP2010 database. The test case considers typical conditions found in turbulent methane flames, with steep variations in the temperature field as well as in the molar concentrations of the participating species. To assess the accuracy of the WSGG model, the results are compared with a solution obtained by line-by-line integration (LBL) of the spectrum.
Differential geometry based solvation model II: Lagrangian formulation.
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
Differential geometry based solvation model II: Lagrangian formulation
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
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.
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.
NASA Astrophysics Data System (ADS)
Hindman, R. G.
1985-09-01
Theoretical background and several basic test cases are presented for a new, time dependent Navier-Stokes solver for two-dimensional and axisymmetric flows. The goal of the effort is to invoke state-of-the-art computational fluid dynamics (CFD) technology to improve modeling of viscous phenomenal and to increase the robustness of CFD analysis. The original motivation was inadequate representation of supersonic ramp-induced separation by existing CFD codes. The present work addresses that inadequacy by using modern numerical methods which accurately model signal propagation in high-speed fluid flow. This technique solves the Navier-Stokes equations in general curvilinear coordinates in a four-sided domain bounded by a wall, and upper boundary opposite the wall, an inflow boundary, and an outflow boundary. The interior algorithm is a flux-difference splitting method similar to that of Yang, Lombard, and Bershader, but is blended into a second order, implicit factored delta form. With implicitly treated boundary conditions, the solution is performed using a block tridiagonal method followed by an explicit updating of the boundaries. The resulting scheme satisfies the global conversation requirement to within the order of accuracy of the algorithm. The grid is generated using a relaxation Poisson solver. A systematic and rigorous development of the complete method is presented. Initial steps in code validation include successful reproduction of Couette and Blasius solutions.
THREE-DIMENSIONAL GEOMETRIES AND THE ANALYSIS OF H II REGIONS
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.
Exact axisymmetric Taylor states for shaped plasmas
Cerfon, Antoine J. O'Neil, Michael
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Measurements of heat transfer to helium II at atmospheric pressure in a confined geometry
Warren, R.P.; Caspi, S.
1981-08-01
Recently the enhanced heat removal capability of unsaturated superfluid helium II has been exploited in fusion and accelerator dipole magnets. In superfluid the internal convection mechanism dominates the heat removal process and orientation with respect to gravity becomes of secondary importance. Heat transfer, however, can be influenced by the thermodynamic state of the liquid, especially with regard to possible phase transformations. The transformation from non-saturated He II must involve an He I state before the film boiling transition is experienced. Some steady state measurements of heat transfer to non-saturated He II have been previously reported. In typical magnet designs, cooling passages between turns result from gaps between the electrical insulation, and are typically on the order of a fraction of a millimeter. The purpose of the work reported here is to measure the attenuation of the heat transfer within such a restrictive geometry.
Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology
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.
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.
NASA Astrophysics Data System (ADS)
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-11-01
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. The principles used to provide supplemental
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.
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-10-01
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
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
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
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.
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.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-08-10
We present that third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. In conclusion, this made the effective shielding process for NSLS-II quite accurate and reliable. The principles
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; ...
2016-08-10
We present that third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and rampedmore » operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. In conclusion, this made the effective shielding process for NSLS-II quite accurate and reliable. The
NASA Astrophysics Data System (ADS)
Tanaka, Masaomi; Maeda, Keiichi; Mazzali, Paolo A.; Kawabata, Koji S.; Nomoto, Ken’ichi
2017-03-01
We present modeling of line polarization to study the multidimensional geometry of stripped-envelope core-collapse supernovae (SNe). We demonstrate that a purely axisymmetric, two-dimensional (2D) geometry cannot reproduce a loop in the Stokes Q ‑ U diagram, that is, a variation of the polarization angles along the velocities associated with the absorption lines. On the contrary, three-dimensional (3D) clumpy structures naturally reproduce the loop. The fact that the loop is commonly observed in stripped-envelope SNe suggests that SN ejecta generally have a 3D structure. We study the degree of line polarization as a function of the absorption depth for various 3D clumpy models with different clump sizes and covering factors. A comparison between the calculated and observed degree of line polarization indicates that a typical size of the clump is relatively large, ≳25% of the photospheric radius. Such large-scale clumps are similar to those observed in the SN remnant Cassiopeia A. Given the small size of the observed sample, the covering factor of the clumps is only weakly constrained (∼5%–80%). The presence of a large-scale clumpy structure suggests that the large-scale convection or standing accretion shock instability takes place at the onset of the explosion.
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.
Black holes in the Einstein-Gauss-Bonnet theory and the geometry of their thermodynamics—II
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata; Chakraborty, Subenoy
2010-03-01
In the present work we study (i) the charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as the Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
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
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.
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…
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.
NASA Technical Reports Server (NTRS)
Cohen, J.; Wygnanski, I.
1987-01-01
The modal distribution of coherent structures evolving near the nozzle of a circular jet was studied experimentally and theoretically, with particular attention given to the effects produced on the instability modes by transverse curvature, flow divergence, inhomogeneous inflow conditions, and the detailed shape of the mean velocity profile. Experiments were performed using a specially constructed air-jet facility; hot-wire anemometers were used in conjunction with Disa Model 55P11 sensors for flow measurements. The linear model used as a transfer function is capable of predicting the spectral distribution of the velocity perturbations in a jet. Consideration was also given to studies of leading nonlinear interactions generated by waves externally superimposed on an axisymmetric jet; theoretical predictions were verified experimentally.
Ni, Chengbao; Fettinger, James C; Long, Gary J; Power, Philip P
2010-11-28
Reaction of {Li(THF)Ar'MnI(2)}(2) (Ar' = C(6)H(3)-2,6-(C(6)H(2)-2,6-(i)Pr(3))(2)) with LiAr', LiC≡CR (R = (t)Bu or Ph), or (C(6)H(2)-2,4,6-(i)Pr(3))MgBr(THF)(2) afforded the diaryl MnAr'(2) (1), the alkynyl salts Ar'Mn(C≡C(t)Bu)(4){Li(THF)}(3) (2) and Ar'Mn(C≡CPh)(3)Li(3)(THF)(Et(2)O)(2)(μ(3)-I) (3), and the manganate salt {Li(THF)}Ar'Mn(μ-I)(C(6)H(2)-2,4,6-(i)Pr(3)) (4), respectively. Complex 4 reacted with one equivalent of (C(6)H(2)-2,4,6-(i)Pr(3))MgBr(THF)(2) to afford the homoleptic dimer {Mn(C(6)H(2)-2,4,6-(i)Pr(3))(μ-C(6)H(2)-2,4,6-(i)Pr(3))}(2) (5), which resulted from the displacement of the bulkier Ar' ligand in preference to the halogen. The reaction of the more crowded {Li(THF)Ar*MnI(2)}(2) (Ar* = C(6)H(3)-2,6-(C(6)H(2)-2,4,6-(i)Pr(3))(2)) with Li(t)Bu gave complex Ar*Mn(t)Bu (6). Complex 1 is a rare monomeric homoleptic two-coordinate diaryl Mn(II) complex; while 6 displays no tendency to eliminate β-hydrogens from the (t)Bu group because of the stabilization supplied by Ar*. Compounds 2 and 3 have cubane frameworks, which are constructed from a manganese, three carbons from three acetylide ligands, three lithiums, each coordinated by a donor, plus either a carbon from a further acetylide ligand (2) or an iodide (3). The Mn(II) atom in 4 has an unusual distorted T-shaped geometry while the dimeric 5 features trigonal planar manganese coordination. The chloride substituted complex Li(2)(THF)(3){Ar'MnCl(2)}(2) (7), which has a structure very similar to that of {Li(THF)Ar'MnI(2)}(2), was also prepared for use as a possible starting material. However, its generally lower solubility rendered it less useful than the iodo salt. Complexes 1-7 were characterized by X-ray crystallography and UV-vis spectroscopy. Magnetic studies of 2-4 and 6 showed that they have 3d(5) high-spin configurations.
Peng, Yan; Mereacre, Valeriu; Anson, Christopher E; Zhang, Yiquan; Bodenstein, Tilmann; Fink, Karin; Powell, Annie K
2017-06-05
Three air-stable Co(II) mononuclear complexes with different aromatic substituents have been prepared and structurally characterized by single-crystal X-ray diffraction. The mononuclear complexes [Co(H2L1)2]·2THF (1), [Co(HL2)2] (2), and [Co(H2L3)2]·CH2Cl2 (3) (where H3L1, H2L2, and H3L3 represent 3-hydroxy-naphthalene-2-carboxylic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, nicotinic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, and 2-hydroxy-benzoic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, respectively) feature a distorted mer octahedral coordination geometry. Detailed magnetic studies of 1-3 have been conducted using direct and alternating current magnetic susceptibility data. Field-induced slow magnetic relaxation was observed for these three complexes. There are few examples of such behavior in (distorted) octahedral coordination geometry (OC) Co(II) mononuclear complexes with uniaxial anisotropy. Analysis of the six-coordinate Co(II) mononuclear single-ion magnets (SIMs) in the literature using the SHAPE program revealed that they all show what is best described as distorted trigonal prismatic (TRP) coordination geometry, and in general, these show negative D zero-field splitting (ZFS) values. On the other hand, all the Co(II) mononuclear complexes displaying what is best approximated as distorted octahedral (OC) coordination geometry show positive D values. In the new Co(II) mononuclear complexes we describe here, there is an ambiguity, since the rigid tridentate ligands confer what is best described for an octahedral complex as a mer coordination geometry, but the actual shape of the first coordination sphere is between octahedral and trigonal prismatic. The negative D values observed experimentally and supported by high-level electronic structure calculations are thus in line with a trigonal prismatic geometry. However, a consideration of the rhombicity as indicated by the E value of the ZFS in conjunction with the
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.
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.
Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas
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.
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.…
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
Dahake, G; Gracewski, S M
1997-10-01
To understand better direct stress wave contributions to stone fragmentation during extracorporeal shock wave lithotripsy (ESWL), the numerical formulation developed in part I is applied to study the time evolution of stress wave fields produced inside submerged isotropic elastic solids having irregular geometries. Cut spheres are used to model stones that have already had an initial fracture. Ellipses are used to approximate other deviations from a spherical geometry. The propagation and focusing of the longitudinal (P) and shear (S) wave fronts are visualized by presenting internal strain contours. Internal strain measurements are obtained from strain gauges embedded inside plaster specimens to confirm the focusing effect obtained from the concave back surfaces of the stones. Fragmentation experiments indicate damage caused by spalling and direct stress wave focusing as well as a front surface pit presumably created by cavitation activity.
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).
Structure of axisymmetric mantle plumes
NASA Technical Reports Server (NTRS)
Olson, Peter; Schubert, Gerald; Anderson, Charles
1993-01-01
The structure of axisymmetric subsolidus thermal plumes in the earth's lower mantle is inferred from calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity. The velocity and temperature distribution is determined for axisymmetric convection above a heated disk in an incompressible fluid cylinder 2,400 km in height and 1,200 km in diameter. Several calculations of plumes with heat transport in the range 100-400 GW, similar to the advective heat transport at the Hawaiian hotspot, are presented. Hotspot formation by plumes originating at the base of the mantle requires both large viscosity variations and a minimum heat transport.
Multisource inverse-geometry CT. Part II. X-ray source design and prototype
Neculaes, V. Bogdan; Caiafa, Antonio; Cao, Yang; De Man, Bruno; Edic, Peter M.; Frutschy, Kristopher; Gunturi, Satish; Inzinna, Lou; Reynolds, Joseph; Vermilyea, Mark; Wagner, David; Zhang, Xi; Zou, Yun; Pelc, Norbert J.; Lounsberry, Brian
2016-01-01
Purpose: This paper summarizes the development of a high-power distributed x-ray source, or “multisource,” designed for inverse-geometry computed tomography (CT) applications [see B. De Man et al., “Multisource inverse-geometry CT. Part I. System concept and development,” Med. Phys. 43, 4607–4616 (2016)]. The paper presents the evolution of the source architecture, component design (anode, emitter, beam optics, control electronics, high voltage insulator), and experimental validation. Methods: Dispenser cathode emitters were chosen as electron sources. A modular design was adopted, with eight electron emitters (two rows of four emitters) per module, wherein tungsten targets were brazed onto copper anode blocks—one anode block per module. A specialized ceramic connector provided high voltage standoff capability and cooling oil flow to the anode. A matrix topology and low-noise electronic controls provided switching of the emitters. Results: Four modules (32 x-ray sources in two rows of 16) have been successfully integrated into a single vacuum vessel and operated on an inverse-geometry computed tomography system. Dispenser cathodes provided high beam current (>1000 mA) in pulse mode, and the electrostatic lenses focused the current beam to a small optical focal spot size (0.5 × 1.4 mm). Controlled emitter grid voltage allowed the beam current to be varied for each source, providing the ability to modulate beam current across the fan of the x-ray beam, denoted as a virtual bowtie filter. The custom designed controls achieved x-ray source switching in <1 μs. The cathode-grounded source was operated successfully up to 120 kV. Conclusions: A high-power, distributed x-ray source for inverse-geometry CT applications was successfully designed, fabricated, and operated. Future embodiments may increase the number of spots and utilize fast read out detectors to increase the x-ray flux magnitude further, while still staying within the stationary target inherent
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…
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…
CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES
Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood E-mail: k.holley@vanderbilt.edu
2015-09-20
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.
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.
Geometry of river networks. II. Distributions of component size and number
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.
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.
Axisymmetric Drop Shape Analysis (ADSA): An Outline.
Saad, Sameh M I; Neumann, A Wilhelm
2016-12-01
Drop shape techniques for the measurement of interfacial tension are powerful, versatile and flexible. The shape of the drop/bubble depends on the balance between surface tension and external forces, e.g. gravity. This balance is reflected mathematically in the Laplace equation of capillarity. Axisymmetric Drop Shape Analysis (ADSA) is a commonly used drop shape technique. A streamlined version of the development of ADSA over the past several decades is presented to illustrate its validity and range of utility. Several configurations of interest will be considered and presented systematically. Shape and surface tension will be linked to a shape parameter based on proper concepts of differential geometry. The resulting shape parameter will be shown to allow determination of the range of applicability of such a drop shape method.
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
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.
Fluidic Thrust Vectoring of an Axisymmetric Exhaust Nozzle at Static Conditions
NASA Technical Reports Server (NTRS)
Wing, David J.; Giuliano, Victor J.
1997-01-01
A sub-scale experimental static investigation of an axisymmetric nozzle with fluidic injection for thrust vectoring was conducted at the NASA Langley Jet Exit Test Facility. Fluidic injection was introduced through flush-mounted injection ports in the divergent section. Geometric variables included injection-port geometry and location. Test conditions included a range of nozzle pressure ratios from 2 to 10 and a range of injection total pressure ratio from no-flow to 1.5. The results indicate that fluidic injection in an axisymmetric nozzle operating at design conditions produced significant thrust-vector angles with less reduction in thrust efficiency than that of a fluidically-vectored rectangular jet. The axisymmetric geometry promoted a pressure relief mechanism around the injection slot, thereby reducing the strength of the oblique shock and the losses associated with it. Injection port geometry had minimal effect on thrust vectoring.
Numerical computation of gravitational field for general axisymmetric objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Distorted turbulence in axisymmetric flow
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1981-01-01
A solution to the rapid-distortion theory for small-scale turbulence in flow round an axisymmetric obstacle is derived. General formulae for velocity covariances and Eulerian time scales are obtained and are evaluated for the particular case of flow round a sphere. The large-scale limit for this flow is also discussed.
NASA Astrophysics Data System (ADS)
Balokovic, Mislav; Harrison, Fiona; Brightman, Murray
2017-08-01
The obscuring torus is one of the main components of the basic unified model of active galactic nuclei (AGN), needed to create anisotropy in obscuration as a function of the viewing angle. We present the first study of the geometrical properties of the AGN torus in a large and representative sample of type II Seyfert nuclei. The sample consists of 124 AGN selected in the hard X-ray band from the Swift/BAT 70-month catalog and observed simultaneously with NuSTAR and Swift/XRT. These data enable us to explore the constraints that observed spectra place on the properties of the obscuring torus in individual AGN and in the local population of Seyfert II nuclei. We make use of empirically motivated spectral models for X-ray reprocessing in approximately toroidal geometry for constraining the distribution of the average column density of the torus, and the distribution of the torus covering factor within this sample. We find that the torus-averaged column density is independent of the line-of-sight column density, with typical column density that is borderline Compton-thick, i.e., around the unity optical depth for Compton scattering. The distribution of torus covering factors is broad but shows a preference for high covering, peaking around the covering factor of 90%, with the median at 70%, in agreement with recent sample studies in the infrared band. We also examine the dependence of the covering factor on intrinsic luminosity, finding that the median covering factor peaks around the intrinsic X-ray luminosity of 10^42.5 erg/s and decreases toward both lower and higher luminosities.
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
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.
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.
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.
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.
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.
Optimal strokes for axisymmetric microswimmers
NASA Astrophysics Data System (ADS)
Alouges, F.; Desimone, A.; Lefebvre, A.
2009-03-01
We present a theory for low-Reynolds-number axisymmetric swimmers and a general strategy for the computation of strokes of maximal efficiency. An explicit equation characterizing optimal strokes is derived, and numerical strategies to obtain solutions are discussed. The merits of this approach are demonstrated by applying it to two concrete examples: the three linked spheres of Najafi and Golestanian and the pushmepullyou of Avron, Kenneth, and Oakmin.
A minimal axisymmetric hurricane model
NASA Astrophysics Data System (ADS)
Mai, Nguyen Chi; Smith, Roger K.; Zhu, Hongyan; Ulrich, Wolfgang
2002-10-01
Solutions of an axisymmetric version of the minimal three-dimensional numerical model of a tropical cyclone developed by Zhu et al. (2001) are described and compared with those of the three-dimensional model. Vortex evolution is similar in the two models during the early stages of intensification, but the period of rapid intensification occurs earlier in the axisymmetric model due to the higher effective resolution obtained using a staggered grid. There are marked differences at later times, when, in the three-dimensional model, asymmetric structures develop. The findings are compared with those of an earlier study by Anthes (1972). The axisymmetric model is used to investigate certain fundamental aspects of tropical-cyclone dynamics, including the emergence of a region of supergradient winds in the boundary layer and the evolution of regions satisfying necessary conditions for inertial and barotropic instability.Supergradient winds develop in the boundary layer within a radius of about 100 km of the vortex axis at an early stage of evolution and appear to be a natural feature of the vortex boundary layer. The development of flow regions satisfying necessary conditions for inertial and barotropic instability occur later, and may be attributed inter alia to the upward transfer of air with relatively high angular momentum, from the boundary layer to the middle and upper layers, by the secondary circulation of the vortex, and the downward transfer of air with relatively low angular momentum to the middle layer. A linear analysis of a two-layer slab-symmetric flow suggests why inertial instability does not occur in the axisymmetric model. Barotropic instability does not appear to be the mechanism responsible for the growth of asymmetries in the calculations using the three-dimensional version of the model.
Mean flowfields in axisymmetric combustor geometries with swirl
Rhode, D.L.; Lilley, D.G.
1982-01-01
Six flowfield configurations are investigated with sidewall angles of 90 and 45/sup 0/, and swirl vane angles of 0, 45, and 70/sup 0/. It is found that central recirculation zones occur for the swirling flow cases investigated, which extend from the inlet to x/D 1.7, where x is the axial polar coordinate, and D is the test section diameter. Five-hole pitot probe pressure measurements are used to determine time-mean velocities, and corresponding flow situations are predicted and compared to results of experimental data. Excellent agreement is found for the nonswirling flow, although poor agreement is found for swirling flow cases, especially near the inlet. The discrepancy is attributed to the lack of realism in the turbulence model, and/or to inaccurate specification of time-mean velocity and turbulence energy distributions at the inlet.
Mean flowfields in axisymmetric combustor geometries with swirl
NASA Technical Reports Server (NTRS)
Rhode, D. L.; Lilley, D. G.; Mclaughlin, D. K.
1982-01-01
Six flowfield configurations are investigated with sidewall angles of 90 and 45 deg, and swirl vane angles of 0, 45, and 70 deg. It is found that central recirculation zones occur for the swirling flow cases investigated, which extend from the inlet to x/D = 1.7, where x is the axial polar coordinate, and D is the test section diameter. Five-hole pitot probe pressure measurements are used to determine time-mean velocities, and corresponding flow situations are predicted and compared to results of experimental data. Excellent agreement is found for the nonswirling flow, although poor agreement is found for swirling flow cases, especially near the inlet. The discrepancy is attributed to the lack of realism in the turbulence model, and/or to inaccurate specification of time-mean velocity and turbulence energy distributions at the inlet.
Onset of dynamo action in an axisymmetric flow.
Tilgner, A
2002-07-01
Peffley, Cawthorne, and Lathrop [Phys. Rev. E 61, 5287 (2000)] have reported on an experiment using liquid sodium, which studies the approach toward a self-generating dynamo. Their results challenge the traditional views of kinematic dynamo theory because (i) the modes of the magnetic field with the smallest decay rates appear to be nearly axisymmetric and (ii) the observed decay rates vary spatially. This report shows how these observations can be reconciled with kinematic dynamo theory.
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.
Chatterjee, Ruchira; Milikisiyants, Sergey; Lakshmi, K V
2012-05-21
We use two-dimensional hyperfine sublevel correlation (HYSCORE) spectroscopy to investigate the coordination geometry of the nitrogen ligands of biomimetic models of the oxygen-evolving complex of photosystem II. In the 2D HYSCORE spectroscopy study, [(bpy)2Mn(III)(μ-O)2Mn(IV)(bpy)2](ClO4)3 (bpy, 2,2'-bipyridine) (1) and [H2O(terpy)Mn(III)(μ-O)2Mn(IV)(terpy)OH2](NO3)3 (terpy = 2,2':6',2″-terpyridine) (2) exhibit electron-nuclear hyperfine interactions that depend on both the oxidation state of the manganese ion and the geometry of the nitrogen ligand. We observe four types of (14)N hyperfine interactions corresponding to the Mn(iii) and Mn(iv) ion of each mixed-valence complex and the equatorial and axial geometry of the ligand, respectively. The strongest and the weakest hyperfine interactions arise from the axial and equatorial ligands of the Mn(iii) ion, respectively. The hyperfine interactions of intermediate strength are due to the axial and equatorial ligands of the Mn(iv) ion. Based on the results of this study, we assign the location and ligand geometry of the Mn(iii) ion of the tetranuclear manganese-calcium-oxo cluster in the S2 state of photosystem II.
2016-01-01
2-Alkenylphenols react with allenes, upon treatment with catalytic amounts of Pd(II) and Cu(II), to give benzoxepine products in high yields and with very good regio- and diastereoselectivities. This contrasts with the results obtained with Rh catalysts, which provided chromene-like products through a pathway involving a β-hydrogen elimination step. Computational studies suggest that the square planar geometry of the palladium is critical to favor the reductive elimination process required for the formation of the oxepine products. PMID:27807509
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
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.
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.
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.
Characterization of a cold flow non-axisymmetric supersonic ejector
NASA Astrophysics Data System (ADS)
Lineberry, David M.
Experimental investigations of dual and single nozzle non-axisymmetric strut based supersonic ejectors were carried out. The strut nozzles transitioned from a round throat to a square exit with an expansion ratio of 4.6. The ejector system entrained secondary air from the lab and exhausted to the lab at atmospheric pressure. The ejectors were operated at equivalent mass flow rates at primary chamber pressure to back pressure ratios ranging from 6.8 to 61.2 for the single nozzle strut and 3.4 to 30.6 for the dual nozzle strut. Under these conditions both struts demonstrated operation in three distinct regimes: mixed, saturated supersonic and supersonic. Secondary flow choking was demonstrated for both struts at equivalent primary mass flow rates. The mixing length was determined by pressure recovery or equalization with the back pressure. This length remained relatively constant at approximately 20 nozzle hydraulic diameters for the primary mass flow rates in the mixed regime. At higher mass flow rates, the pressure recovery length increased and appeared to be strongly affected by the primary nozzle exit pressure. Surveys of duct exit stagnation pressure indicated poor mixing at high mass flow rates with a supersonic core existing through the mixing duct. Shadow graph images revealed a complex shock structure in the recovery region of the mixing duct. Classical analytical models for axisymmetric ejectors were used to investigate the effect of non-axisymmetric geometry. Preliminary CFD simulations were performed to investigate ejector mixing.
Two-dimensional axisymmetric Child-Langmuir scaling law
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.
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.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-08-10
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. Lastly, the principles used to provide
Axisymmetric fully spectral code for hyperbolic equations
NASA Astrophysics Data System (ADS)
Panosso Macedo, Rodrigo; Ansorg, Marcus
2014-11-01
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.
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.
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.
Axisymmetric Magnetic Mirror Fusion-Fission Hybrid
Moir, R. W.; Martovetsky, N. N.; Molvik, A. W.; Ryutov, D. D.; Simonen, T. C.
2011-05-13
The achieved performance of the gas dynamic trap version of magnetic mirrors and today’s technology we believe are sufficient with modest further efforts for a neutron source for material testing (Q=P_{fusion}/P_{input}~0.1). The performance needed for commercial power production requires considerable further advances to achieve the necessary high Q>>10. An early application of the mirror, requiring intermediate performance and intermediate values of Q~1 are the hybrid applications. The Axisymmetric Mirror has a number of attractive features as a driver for a fusion-fission hybrid system: geometrical simplicity, inherently steady-state operation, and the presence of the natural divertors in the form of end tanks. This level of physics performance has the virtue of low risk and only modest R&D needed and its simplicity promises economy advantages. Operation at Q~1 allows for relatively low electron temperatures, in the range of 4 keV, for the DT injection energy ~ 80 keV. A simple mirror with the plasma diameter of 1 m and mirror-to-mirror length of 35 m is discussed. Simple circular superconducting coils are based on today’s technology. The positive ion neutral beams are similar to existing units but designed for steady state. A brief qualitative discussion of three groups of physics issues is presented: axial heat loss, MHD stability in the axisymmetric geometry, microstability of sloshing ions. Burning fission reactor wastes by fissioning actinides (transuranics: Pu, Np, Am, Cm, .. or just minor actinides: Np, Am, Cm, …) in the hybrid will multiply fusion’s energy by a factor of ~10 or more and diminish the Q needed to less than 1 to overcome the cost of recirculating power for good economics. The economic value of destroying actinides by fissioning is rather low based on either the cost of long-term storage or even deep geologic disposal so most of the revenues of hybrids will come from electrical power. Hybrids that obtain revenues from
NASA Astrophysics Data System (ADS)
Kojima, Takayuki; Sato, Tetsuya; Tanatsugu, Nobuhiro; Enomoto, Yoshinari
A control system of variable geometry mixed compression axisymmetric intake is experimentally studied at ONERA S3 supersonic wind tunnel. The acceleration/deceleration of the space plane is simulated by changing the free stream velocity. The intake is successfully controlled with 90% of the maximum total pressure recovery and mass capture ratio. In this experiment, two subjects about control of axisymmetric intake are also cleared. First, the effect of the trapping of the terminal shock by bleed holes causes the disturbances in the terminal shock control system. Second, a special compression form change operation is necessary when the intake compression form change from all external compression to mixed compression.
NASA Astrophysics Data System (ADS)
Golbedaghi, Reza; Azimi, Saeid; Molaei, Atefeh; Hatami, Masoud; Notash, Behrouz
2017-10-01
A new Schiff base ligand HL, 1,3-bis(2-((Z)-(2-aminoethylimino)methyl)phenoxy)ethylene di amine, has been synthesized from the reaction of a new aldehyde and ethylenediamine. After preparation the Schiff base, a new dinuclear Cu(II) complex with two different geometry for each metal ion was synthesized. Single crystal X-ray structure analysis of the complex Cu(II) showed that the complex is binuclear and all nitrogen and oxygen atoms of ligand (N4O3) are coordinated to two Cu(II) center ions. The crystal structure studying shows, a perchlorate ion has been coordinated to the two Cu(II) metal centers as bridged and another perchlorate coordinated to the one of Cu(II) ion as terminal. However, two interesting structures square pyramidal and distorted octahedral Cu(II) ions are bridged asymmetrically by a perchlorate ion and oxygen of hydroxyl group of Schiff base ligand. In addition, we had a theoretical study to have a comparison of experimental and theoretical results we determined the HOMO and LUMO orbitals.
On the existence of certain axisymmetric interior metrics
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.
Axisymmetric generalized harmonic evolution code
Sorkin, Evgeny
2010-04-15
We describe the first axisymmetric numerical code based on the generalized harmonic formulation of the Einstein equations, which is regular at the axis. We test the code by investigating gravitational collapse of distributions of complex scalar field in a Kaluza-Klein spacetime. One of the key issues of the harmonic formulation is the choice of the gauge source functions, and we conclude that a damped-wave gauge is remarkably robust in this case. Our preliminary study indicates that evolution of regular initial data leads to formation both of black holes with spherical and cylindrical horizon topologies. Intriguingly, we find evidence that near threshold for black hole formation the number of outcomes proliferates. Specifically, the collapsing matter splits into individual pulses, two of which travel in the opposite directions along the compact dimension and one which is ejected radially from the axis. Depending on the initial conditions, a curvature singularity develops inside the pulses.
Guided waves by axisymmetric and non-axisymmetric surface loading on hollow cylinders
Shin; Rose
1999-06-01
Guided waves generated by axisymmetric and non-axisymmetric surface loading on a hollow cylinder are studied. For the theoretical analysis of the superposed guided waves, a normal mode concept is employed. The amplitude factors of individual guided wave modes are studied with respect to varying surface pressure loading profiles. Both theoretical and experimental focus is given to the guided waves generated by both axisymmetric and non-axisymmetric excitation. For the experiments, a comb transducer and high power tone burst function generator system are used on a sample Inconel tube. Surface loading conditions, such as circumferential loading angles and axial loading lengths, are used with the frequency and phase velocity to control the axisymmetric and non-axisymmetric mode excitations. The experimental study demonstrates the use of a practical non-axisymmetric partial loading technique in generating axisymmetric modes, particularly useful in the inspection of tubing and piping with limited circumferential access. From both theoretical and experimental studies, it also could be said that the amount of flexural modes reflected from a defect contains information on the reflector's circumferential angle, as well as potentially other classification and sizing feature information. The axisymmetric and non-axisymmetric guided wave modes should both be carefully considered for improvement of the overall analysis of guided waves generated in hollow cylinders.
A relativistic axisymmetric approach to the galactic rotation curves problem
NASA Astrophysics Data System (ADS)
Herrera-Aguilar, A.; Nucamendi, U.
2014-11-01
It is known that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions (see [1] and [2] for details): i) that emitted photons come to us from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and ii) that these photons propagate to us along null geodesics. This relation can be established without appealing at all to a concrete theory of gravitational interaction. This kinematical spherically symmetric approach to the galactic rotation curves problem can be generalized to the stationary axisymmetric realm, which is precisely the symmetry that spiral galaxies possess [3]. Here we review the relativistic results obtained in the latter work. Namely, by making use of the most general stationary axisymmetric metric, we consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic red/blue shifts in terms of three arbitrary metric functions, clarifying the contribution of the rotation as well as the dragging of the gravitational field. This stationary axisymmetric approach distinguishes between red and blue shifts emitted by circularly orbiting receding and approaching stars, respectively, even when they are considered with respect to the center of a spiral galaxy, indicating the need of precise measurements in order to confront predictions with observations. We also point out the difficulties one encounters in the attempt of determining the metric functions from observations and list some potential strategies to overcome them.
Variable geometry for supersonic mixed-compression inlets
NASA Technical Reports Server (NTRS)
Sorensen, N. E.; Latham, E. A.; Smeltzer, D. B.
1974-01-01
Study of two-dimensional and axisymmetric supersonic mixed-compression inlet systems has shown that the geometry of both systems can be varied to provide adequate transonic airflow to satisfy the airflow demand of most jet engines. Collapsing geometry systems for both types of inlet systems provide a generous amount of transonic airflow for any design Mach number inlet system. However, the mechanical practicality of collapsing centerbodies for axisymmetric inlet systems is doubtful. Therefore, translating centerbody axisymmetric inlets with auxiliary airflow systems to augment the transonic airflow capability are an attractive alternative. Estimates show that the capture mass-flow ratio at Mach number 1.0 can be increased approximately 0.20 for a very short axisymmetric inlet system designed for Mach number 2.37. With this increase in mass-flow ratio, even variable-cycle engine transonic airflow demand can be matched without oversizing the inlet at the design Mach number.
Wachter, Erin; Zamora, Ana; Heidary, David K; Ruiz, José; Glazer, Edith C
2016-08-09
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.
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.
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.
Dynamo Models for Saturn's Axisymmetric Magnetic Field
NASA Astrophysics Data System (ADS)
Stanley, S.; Tajdaran, K.
2012-12-01
Magnetic field measurements by the Cassini mission have confirmed the earlier Pioneer 11 and Voyager missions' results that Saturn's observed magnetic field is extremely axisymmetric . For example, Saturn's dipole tilt is less than 0.06 degrees (Cao et al., 2011) . The nearly-perfect axisymmetry of Saturn's dipole is troubling because of Cowling's Theorem which states that an axisymmetric magnetic field cannot be maintained by a dynamo. However, Cowling's Theorem applies to the magnetic field generated inside the dynamo source region and we can avert any contradiction with Cowling's Theorem if we can find reason for a non-axisymmetric field generated inside the dynamo region to have an axisymmetrized potential field observed at satellite altitude. Stevenson (1980) proposed a mechanism for this axisymmetrization. He suggested that differential rotation in a stably-stratified electrically conducting layer (i.e. the helium rain-out layer) surrounding the dynamo could act to shear out the non-axisymmetry and hence produce an axisymmetric observed magnetic field. In previous work, we used three-dimensional self-consistent numerical dynamo models to demonstrate that a thin helium rain-out layer can produce a more axisymmetrized field (Stanley, 2010). We also found that the direction of the zonal flows in the layer is a crucial factor for magnetic field axisymmetry. Here we investigate the influence of the thickness of the helium rain-out layer and the intensity of the thermal winds on the axisymmetrization of the field. We search for optimal regions in parameter space for producing axisymmetric magnetic fields with similar spectral properties to the observed Saturnian field.
Beyond the Maltese Cross: Geometry of Turbulence Between 0.2 and 1 au
NASA Astrophysics Data System (ADS)
Verdini, Andrea; Grappin, Roland
2016-11-01
The spectral anisotropy of turbulent structures has been measured in the solar wind since 1990, relying on the assumption of axisymmetry about the mean magnetic field, B 0. However, several works indicate that this hypothesis might be partially wrong, thus raising two questions: (i) is it correct to interpret measurements at 1 au (the so-called Maltese cross) in term of a sum of slab and two-dimensional (2D) turbulence; and (ii) what information is really contained in the Maltese cross? We solve direct numerical simulations of the magnetohydrodynamic equations including the transverse stretching exerted by the solar wind flow and study the genuine 3D anisotropy of turbulence as well as that one resulting from the assumption of axisymmetry about B 0. We show that the evolution of the turbulent spectrum from 0.2 to 1 au depends strongly on its initial anisotropy. An axisymmetric spectrum with respect to B 0 keeps its axisymmetry, i.e., resists stretching perpendicular to radial, while an isotropic spectrum becomes essentially axisymmetric with respect to the radial direction. We conclude that close to the Sun, slow-wind turbulence has a spectrum that is axisymmetric around B 0 and the measured 2D component at 1 au describes the real shape of turbulent structures. In contrast, fast-wind turbulence has a more isotropic spectrum at the source and becomes radially symmetric at 1 au. Such structure is hidden by the symmetrization applied to the data that instead returns a slab geometry.
Pandey, Sharmila; Das, Partha Pratim; Singh, Akhilesh Kumar; Mukherjee, Rabindranath
2011-10-28
Using an acyclic hexadentate pyridine amide ligand, containing a -OCH(2)CH(2)O- spacer between two pyridine-2-carboxamide units (1,4-bis[o-(pyrydine-2-carboxamidophenyl)]-1,4-dioxabutane (H(2)L(9)), in its deprotonated form), four new complexes, [Co(II)(L(9))] (1) and its one-electron oxidized counterpart [Co(III)(L(9))][NO(3)]·2H(2)O (2), [Ni(II)(L(9))] (3) and [Cu(II)(L(9))] (4), have been synthesized. Structural analyses revealed that the Co(II) centre in 1 and the Ni(II) centre in 3 are six-coordinate, utilizing all the available donor sites and the Cu(II) centre in 4 is effectively five-coordinated (one of the ether O atoms does not participate in coordination). The structural parameters associated with the change in the metal coordination environment have been compared with corresponding complexes of thioether-containing hexadentate ligands. The μ(eff) values at 298 K of 1-4 correspond to S = 3/2, S = 0, S = 1 and S = 1/2, respectively. Absorption spectra for all the complexes have been investigated. EPR spectral properties of the copper(II) complex 4 have been investigated, simulated and analyzed. Cyclic voltammetric experiments in CH(2)Cl(2) reveal quasireversible Co(III)-Co(II), Ni(III)-Ni(II) and Cu(II)-Cu(I) redox processes. In going from ether O to thioether S coordination, the effect of the metal coordination environment on the redox potential values of Co(III)-Co(II) (here the effect of spin-state as well), Ni(III)-Ni(II) and Cu(II)-Cu(I) processes have been systematically analyzed.
Non-axisymmetric local magnetostatic equilibrium
Candy, Jefferey M.; Belli, Emily A.
2015-03-24
In this study, we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas. Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozer coordinates is clarified.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; ...
2016-08-10
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing thismore » dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. Lastly, the principles used to provide
Gil-Hernández, B; Calahorro, A J; Gili, P; Sanchiz, J
2017-04-05
Three new heterometallic metal-organic frameworks, namely, {(Ph4P)2[MnCu3(Hmesox)3Br(H2O)]·H2O}n (1), {(Ph4P)2[CoCu3(Hmesox)3Br]}n (2) and {(Ph4P)2[ZnCu3(Hmesox)3Br]·2.5H2O}n (3) were prepared and their structure and magnetic properties were investigated (H4mesox = mesoxalic acid, Ph4P(+) = tetraphenylphosphonium). The structure of all the compounds consist of two interpenetrating opposite-chirality supramolecular cationic and polymeric anionic 3-D (10,3)-a networks, which results in chiral compounds. The anionic network is formed from the polymerization of [Cu3(Hmesox)3Br](4-) units, working as three connectors, and M(ii) cations, working as three-connecting nodes, M = Mn(ii), Co(ii) and Zn(ii). The Ph4P(+) cations build the cationic chiral supramolecular network opposite to the anionic one. Compounds 1 and 2 exhibit long-range magnetic ordering with critical temperatures of 7.2 K and 6.9 K, respectively. However, compound 3 does not display long-range order, but shows ferromagnetic and antiferromagnetic coupling among the Cu(ii) ions. The magnetic interactions are studied by DFT calculations and compared with related Cu(ii)-mesoxalate compounds previously reported.
Axisymmetric and non-axisymmetric modulated MHD waves in magnetic flux tubes
NASA Astrophysics Data System (ADS)
Chargeishvili, B. B.; Japaridze, D. R.
2016-02-01
Nonlinear modulated both axisymmetric and non-axisymmetric MHD wave propagation in magnetic flux tubes is studied. In the cylindrical coordinates, ordinary differential equation with cubic nonlinearity is derived. In both cases of symmetry, the equation has solitary solutions. Modulation stability of the solutions is studied. The results of the study show that the propagation of axisymmetric soliton causes rising of plasma temperature in peripheral regions of a magnetic flux tube. In the non-axisymmetric case, it gives also temperature rising effect. Results of theoretical study are examined on idealized model of chromospheric spicule.
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).
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).
Bypassing Cowling's Theorem in Axisymmetric Fluid Dynamos
Gissinger, Christophe; Fauve, Stephan; Dormy, Emmanuel
2008-10-03
We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. We show that, even in the absence of nonaxisymmetric velocity fluctuations, a mean magnetic field with a dominant axisymmetric dipolar component can be generated via a secondary bifurcation from an equatorial dipole. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.
Numerical Simulation of Slinger Combustor Using 2-D Axisymmetric Computational Model
NASA Astrophysics Data System (ADS)
Lee, Semin; Park, Soo Hyung; Lee, Donghun
2010-06-01
Small-size turbojet engines have difficulties in maintaining the chemical reaction due to the limitation of chamber size. The combustion chamber is generally designed to improve the reaction efficiency by the generation of vortices in the chamber and to enhance air-fuel mixing characteristics. In the initial stage of designing the combustor, analysis of the 3-D full configuration is not practical due to the huge time consuming computation and grid generation followed by modifications of the geometry. In the present paper, an axisymmetric model maintaining geometric similarity and flow characteristic of 3-D configuration is developed. Based on numerical results from the full 3-D configuration, model reduction is achieved toward 2-D axisymmetric configuration. In the modeling process, the area and location of each hole in 3-D full configuration are considered reasonably and replaced to the 2-D axisymmetric model. By using the 2-D axisymmetric model, the factor that can affect the performance is investigated with the assumption that the flow is non-reacting and turbulent. Numerical results from the present model show a good agreement with numerical results from 3-D full configuration model such as existence of vortex pair in forward region and total pressure loss. By simplifying the complex 3-D model, computing time can be remarkably reduced and it makes easy to find effects of geometry modification.
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.
Mondal, Amit Kumar; Goswami, Tamal; Misra, Anirban; Konar, Sanjit
2017-06-19
In this work, the effects of ligand field strength as well as the metal coordination geometry on magnetic anisotropy of pentacoordinated Co(II) complexes have been investigated using a combined experimental and theoretical approach. For that, a strategic design and synthesis of three pentacoordinate Co(II) complexes [Co(bbp)Cl2]·(MeOH) (1), [Co(bbp)Br2]·(MeOH) (2), and [Co(bbp)(NCS)2] (3) has been achieved by using the tridentate coordination environment of the ligand in conjunction with the accommodating terminal ligands (i.e., chloride, bromide, and thiocyanate). Detailed magnetic studies disclose the occurrence of slow magnetic relaxation behavior of Co(II) centers with an easy-plane magnetic anisotropy. A quantitative estimation of ZFS parameters has been successfully performed by density functional theory (DFT) calculations. Both the sign and magnitude of ZFS parameters are prophesied well by this DFT method. The theoretical results also reveal that the α → β (SOMO-SOMO) excitation contributes almost entirely to the total ZFS values for all complexes. It is worth noting that the excitation pertaining to the most positive contribution to the ZFS parameter is the dxy → dx(2)-y(2) excitation for complexes 1 and 2, whereas for complex 3 it is the dz(2) → dx(2)-y(2) excitation.
NASA Astrophysics Data System (ADS)
Shoji, Mitsuo; Isobe, Hiroshi; Nakajima, Takahito; Yamaguchi, Kizashi
2015-11-01
Full geometry optimizations of ([CaMn4O4(CH3COO)8(py)(CH3COOH)2], (py: pyridine) (1)) were performed at the UB3LYP theoretical level. 1 is a theoretical model for the synthetic model ([CaMn4O4(ButCOO)8(py)(ButCOOH)2], (But: t-butyl) (2)) which closely mimicks the native oxygen evolving complex (OEC) in photosystem II. It was shown that the X-ray structure of 2 was well reproduced by 1 in the (Mn1(III), Mn2(IV), Mn3(IV), Mn4(III)) valence state with the unprotonated O5 (O5 = O2-), and two different valence states were obtained in the one-electron oxidized state. Importance of the Jahn-Teller effect of the Mn(III) site for the structural deformations was presented.
NASA Astrophysics Data System (ADS)
Gilbert, D. C.; Dikanov, S. A.; Doetschman, D. C.; Smeija, J. A.
1999-12-01
Spin coupling with pyrrole nitrogens and NO geometry in pyridyl-NO-Fe(II) tetraphenyl- 15N4-porphyrin, examined with hyperfine sublevel correlation spectroscopy (HYSCORE), was studied because of renewed interest in diatomic molecule bound ferrous hemes, e.g. the physiologically important NO synthase. Dipolar coupling locates the effective electron spin position (0.109±0.008 nm from the ring center, 0.106±0.006 nm above the ring plane and projecting 37±2° from the nearest pyrrole nitrogen). The NO projection in an X-ray study of the 4-methyl piperidine complex is 38.6°. The negative pyrrole nitrogen spin densities induced by the NO obey a sinusoidal angular relationship.
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.
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.
Energetic Particle Transport in Compact Quasi-axisymmetric Stellarators
Redi, M.H.; Mynick, H.E.; Suewattana, M.; White, R.B.; Zarnstorff, M.C.; Isaev, M.Yu.; Mikhailov, M.I.; Subbotin, A.A.
1999-03-01
Hamiltonian coordinate, guiding-center code calculations of the confinement of suprathermal ions in quasi-axisymmetric stellarator (QAS) designs have been carried out to evaluate the attractiveness of compact configurations which are optimized for ballooning stability. A new stellarator particle-following code is used to predict ion loss rates and particle confinement for thermal and neutral beam ions in a small experiment with R = 145 cm, B = 1-2 T and for alpha particles in a reactor-size device. In contrast to tokamaks, it is found that high edge poloidal flux has limited value in improving ion confinement in QAS, since collisional pitch-angle scattering drives ions into ripple wells and stochastic field regions, where they are quickly lost. The necessity for reduced stellarator ripple fields is emphasized. The high neutral beam ion loss predicted for these configurations suggests that more interesting physics could be explored with an experiment of less constrained size and magnetic field geometry.
Two-Dimensional Axisymmetric Child-Langmuir Scaling Law
NASA Astrophysics Data System (ADS)
Ragan-Kelley, Benjamin; Verboncoeur, John
2007-11-01
The classical one-dimensional Child-Langmuir law has been extended to two dimensions by numerical simulation in planar geometries [1]. By considering an axisymmetric cylindrical system with emission radius r, outer radius R > r, and gap length L, we further examine the space charge limit in two dimensions. The ratio of the observed current density limit JCL2 to the theoretical one-dimensional value JCL1 is found to be a monotonically decreasing function of the ratio of emission area (r^2) to gap separation (L). This result is in agreement with the planar results, where the emission area is proportional to the cathode width (r) [1]. The simulations were run in the particle in cell code, OOPIC [2]. [1] J. W. Luginsland, Y. Y. Lau, and R. M. Gilgenbach, Phys. Rev. Lett. 77, 4668 (1996). [2] J. P. Verboncoeur, A. B. Langdon, and N. T. Gladd, Comp. Phys. Comm. 87, 199 (1995).
Peyrin, E; Guillaume, Y C; Guinchard, C
1999-01-01
Chiral recognition mechanism relationships for binding at site II on human serum albumin (HSA) were investigated using D, L dansyl amino acids. Sodium phosphate salt was used as a solute-HSA interaction modifier. A new model was developed using a biochromatographic approach to describe the variation in the transfer equilibrium constant with the salt concentration, i.e., the nature of the interactions. The solute binding was divided into two salt concentration ranges c. For the low c values, below 0.03 M, the nonstereoselective interactions constituted the preponderant contribution to the variation in the solute binding with the salt concentration. For the high c values, above 0.03 M, the solute binding was governed by the hydrophobic effect and the stereoselective interactions. The different contributions implied in the binding process provided an estimation of both the surface charge density (sigma/F) and the surface area of the site II binding cavity accessible to solvent, which were found to be equal to around 10.10(-7) mol/m(2) and 2 nm(2). As well, the excess of sodium ions excluded by the solute transfer from the surface area of the pocket were about(-0.7) for dansyl norvaline and (-0.8) for dansyl tryptophan. PMID:10465735
Non-axisymmetric local magnetostatic equilibrium
Candy, Jefferey M.; Belli, Emily A.
2015-03-24
In this study, we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas. Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozermore » coordinates is clarified.« less
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.
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).
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.
Observation of axisymmetric dark plasma excitations in a two-dimensional electron system
NASA Astrophysics Data System (ADS)
Muravev, V. M.; Andreev, I. V.; Belyanin, V. N.; Gubarev, S. I.; Kukushkin, I. V.
2017-07-01
Resonant microwave absorption of two-dimensional electron systems in AlGaAs/GaAs heterostructures with a single Corbino disk geometry has been studied. Axisymmetric dark plasmon modes have been excited using a near-field excitation technique, and their magnetodispersion have been determined in the presence of a perpendicular magnetic field. Plasma excitations observed have been compared to bright plasmon modes in a single disk of identical geometry. Dark plasmon modes have been found to have considerably longer lifetimes compared to bright plasmon modes due to the inhibition of superradiant losses.
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.
Nonaxisymmetric effects of stratified spin-up in an axisymmetric annular channel
NASA Astrophysics Data System (ADS)
Smirnov, S. A.; Boyer, D. L.; Baines, P. G.
2005-08-01
Laboratory experiments were conducted on spin-up of a linearly stratified fluid in a rotating axisymmetric annular channel formed by two cylindrical coaxial walls and a flat bottom. Secular as well as instantaneous variation in rotation speeds was investigated for a range of Rossby numbers ɛ =ΔΩ/Ω⩽1, where ΔΩ is the change in the rotation rate and Ω is the final rotation rate of the annulus. The experimental studies reported by Smirnov et al. [S. A. Smirnov, P. G. Baines, D. L. Boyer, S. I. Voropayev, and A. N. Srdic-Mitrovic, "Long-time evolution of linearly stratified spin-up flows in axisymmetric geometries," Phys. Fluids 17, 016601 (2005)] were extended to (i) explore the density structure of the corner regions formed adjacent to the inner and outer sidewalls of the annular channel during spin-up, and to (ii) investigate the role of the boundary conditions at the vertical sidewalls in the development of nonaxisymmetric disturbances and formation of large columnar eddies at late spin-up times. The latter was achieved by introducing roughness elements in the form of vertical prisms at the inner sidewall. Observations demonstrated that isopycnals (surfaces of constant density) experience large vertical displacements near the lateral boundaries during spin-up. The density gradient reduces to near zero in the corner regions, where the fluid is stirred, and increases above/below them near the outer/inner sidewalls, respectively. The relative height of the corner regions h /H (H is the depth of the fluid layer) was found to be determined only by the relative values of the Rossby (ɛ) and Burger (Bu) numbers and follows the experimental dependence h /H=0.54ɛ1/2/Bu. A flow stability regime diagram is presented as a function of the Rossby and Burger numbers. Introduction of roughness elements at the inner sidewall did not alter significantly the process and time scales of stratified spin-up, large eddy formation, and subsequent relaxation to the initial state
Kinetically Stabilized Axisymmetric Tandem Mirrors: Summary of Studies
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
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.
Prediction of Supersonic Jet Noise Radiated from Rectangular and Axi-Symmetric Plug Nozzles
NASA Astrophysics Data System (ADS)
荒木, 幹也; 佐野, 貴透; 今村, 宰; 小島, 孝之; 田口, 秀之; 後藤, 健; 八田, 博志; 志賀, 聖一
Effects of nozzle geometry, and total temperature on supersonic jet noise radiated from rectangular and axi-symmetric plug nozzles are investigated, experimentally. In JAXA (Japan Aerospace Exploration Agency), a pre-cooled turbojet engine for an HST (Hypersonic transport) is under development. In the present study, three kinds of subscale nozzle models are employed, namely two kinds of rectangular plug nozzles (RPN1 and RPN2) and an axi-symmetric plug nozzle (APN), and the jet noise data are acquired at aft angles of the jets by use of 1/4 inch high frequency microphones. The total pressure is set at 0.3MPa(a), which corresponds to the take-off condition of the vehicle, and the total temperature is varied from 290K to 860K. The jet noise spectra obtained are reduced to normalized spectra by use of a scaling law of heated jets (AU n law). It is shown that the normalized spectra collapse onto two lines according to each nozzle geometry, regardless of the total temperature. For APN, the peak SPL is smaller by about 8 to 14 dB when compared with that for RPN1 and RPN2, which implies that the axi-symmetric plug nozzle could be much quieter than rectangular plug nozzle.
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.
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.
NASA Astrophysics Data System (ADS)
Nbili, W.; Soudani, S.; Kaabi, K.; Wojtaś, M.; Ferretti, V.; Lefebvre, F.; Jelsch, C.; Ben Nasr, C.
2017-10-01
The crystal structure of the new complex [Co(C5H7N3O)2(H2O)4](NO3)2ṡ4H2O synthesized in aqueous solution has been determined by single crystal X-ray diffraction. The compound crystallizes in the triclinic space group P 1 bar with lattice parameters: a = 7.3056(2), b = 8.4065(2), c = 10.4724(3) Å, α = 103.9470(19), β = 105.6600(14), γ = 91.1350(18)°, V = 598.54(3) Å3 and Z = 1. The Co(II) central ion is in a slightly distorted octahedral coordination geometry formed by two nitrogen atoms of two 2-amino-6-methoxypyrimidine ligands and four oxygen atoms of coordinated water molecules. The crystal packing is stabilized by intermolecular Osbnd H⋯O, Nsbnd H⋯O and Csbnd H⋯O hydrogen bonds which link the molecules into a three-dimensional network. Intermolecular interactions were investigated by Hirshfeld surfaces. Electronic properties such as HOMO and LUMO energies were derived. The vibrational absorption bands were identified by infrared spectroscopy. The compound was characterized by thermal analysis to determine its thermal behavior with respect to temperature.
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.
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.
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
NASA Astrophysics Data System (ADS)
Khaykovich, B.; Gubarev, M. V.; Bagdasarova, Y.; Ramsey, B. D.; Moncton, D. E.
2011-03-01
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
AXISYMMETRIC, NONSTATIONARY BLACK HOLE MAGNETOSPHERES: REVISITED
Song, Yoo Geun; Park, Seok Jae E-mail: sjpark@kasi.re.kr
2015-10-10
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 and 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.
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.
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.
NASA Astrophysics Data System (ADS)
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
Direct numerical simulation of incompressible axisymmetric flows
NASA Technical Reports Server (NTRS)
Loulou, Patrick
1994-01-01
In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.
Stabilization of the vertical instability by non-axisymmetric coils
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
2016-07-05
In a published Physical Review Letter [A. Reiman, Physical Review Letters, 99, 135007 (2007)], 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 to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted, in a real DIII-D-like configuration. A four field period trapezoid-shaped coil set was developed in toroidal geometry and 3-D equilibria were computed using trapezium coil currents of ,10kA, 100kA, and 500kA. 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 500kA, 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. Lastly, 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 l_{i}β, and q_{95} would mitigate this but seem unlikely to change the
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.
Stabilization of the vertical instability by non-axisymmetric coils
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; ...
2016-07-05
In a published Physical Review Letter [A. Reiman, Physical Review Letters, 99, 135007 (2007)], 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 to provide a proofmore » of principal that 3-D fields can, in fact raise the elongation limits as predicted, in a real DIII-D-like configuration. A four field period trapezoid-shaped coil set was developed in toroidal geometry and 3-D equilibria were computed using trapezium coil currents of ,10kA, 100kA, and 500kA. 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 500kA, 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. Lastly, 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 liβ, and q95 would mitigate this but seem unlikely to change the conclusion.« less
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…
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…
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.
Stress Analysis of Laminated Composite Cylinders Under Non-Axisymmetric Loading
Starbuck, J.M.
1999-10-26
The use of thick-walled composite cylinders in structural applications has seen tremendous growth over the last decade. Applications include pressure vessels, flywheels, drive shafts, spoolable tubing, and production risers. In these applications, the geometry of a composite cylinder is axisymmetric but in many cases the applied loads are non-axisymmetric and more rigorous analytical tools are required for an accurate stress analysis. A closed-form solution is presented for determining the layer-by-layer stresses, strains, and displacements and first-ply failure in laminated composite cylinders subjected to non-axisymmetric loads. The applied loads include internal and external pressure, axial force, torque, axial bending moment, uniform temperature change, rotational velocity, and interference fits. The formulation is based on the theory of anisotropic elasticity and a state of generalized plane deformation along the axis of the composite cylinder. Parametric design trade studies can be easily and quickly computed using this closed-form solution. A computer program that was developed for performing the numerical calculations is described and results from specific case studies are presented.
NASA Astrophysics Data System (ADS)
Haya, Laura; Tavoularis, Stavros
2017-06-01
Flow characteristics past a bileaflet mechanical heart valve were measured under physiological flow conditions in a straight tube with an axisymmetric expansion, similar to vessels used in previous studies, and in an anatomical model of the aorta. We found that anatomical features, including the three-lobed sinus and the aorta's curvature affected significantly the flow characteristics. The turbulent and viscous stresses were presented and discussed as indicators for potential blood damage and thrombosis. Both types of stresses, averaged over the two axial measurement planes, were significantly lower in the anatomical model than in the axisymmetric one. This difference was attributed to the lower height-to-width ratio and more gradual contraction of the anatomical aortic sinus. The curvature of the aorta caused asymmetries in the velocity and stress distributions during forward flow. Secondary flows resulting from the aorta's curvature are thought to have redistributed the fluid stresses transversely, resulting in a more homogeneous stress distribution in the anatomical aortic root than in the axisymmetric root. The results of this study demonstrate the importance of modelling accurately the aortic geometry in experimental and computational studies of prosthetic devices. Moreover, our findings suggest that grafts used for aortic root replacement should approximate as closely as possible the shape of the natural sinuses.
Axisymmetric instability in a thinning electrified jet.
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.
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.
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.
A numerical solution method for acoustic radiation from axisymmetric bodies
NASA Technical Reports Server (NTRS)
Caruthers, John E.; Raviprakash, G. K.
1995-01-01
A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.
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.
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.
Kinematic dynamos in spheroidal geometries
NASA Astrophysics Data System (ADS)
Ivers, D. J.
2017-10-01
The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤a/c≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.
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).
Elastic clearance change in axisymmetric shearing process
NASA Astrophysics Data System (ADS)
Yoshida, Yoshinori
2016-10-01
An axisymmetric shearing experiment is conducted for a sheet of low carbon steel and stainless steel. Elastic change in the clearance between punch and die is measured. The increase of the clearance in shearing is confirmed and the influence of sheared material's flow stress on the clearance change is shown. Finite element analysis (FEA) of shearing with Gurson-Tvergaard-Needlman model (GTN model) is conducted for shearing of the carbon steels with rigid tools as a numerical experiment. Burr height is predicted in the FEA and the result is compared with the experimental result. In addition, the influence of the clearance on stress state in the material is investigated.
Super-collimation by axisymmetric photonic crystals
Purlys, V.; Gailevičius, D.; Peckus, M.; Gadonas, R.; Maigyte, L.; Staliunas, K.
2014-06-02
We propose and experimentally show the mechanism of beam super-collimation by axisymmetric photonic crystals, specifically by periodic (in propagation direction) structure of layers of concentric rings. The physical mechanism behind the effect is an inverse scattering cascade of diffracted wave components back into on- and near-axis angular field components, resulting in substantial enhancement of intensity of these components. We explore the super-collimation by numerical calculations and prove it experimentally. We demonstrate experimentally the axial field enhancement up to 7 times in terms of field intensity.
Isodynamic axisymmetric equilibrium near the magnetic axis
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)
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.
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.
Axisymmetric scrape-off plasma transport
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.
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.
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.
Axisymmetric photonic structures with PT-symmetry
NASA Astrophysics Data System (ADS)
Ahmed, Waqas W.; Herrero, Ramon; Botey, Muriel; Staliunas, Kestutis
2016-09-01
PT-symmetric structures in photonic crystals, combining refractive index and gain-loss modulations is becoming a research field with increasing interest due to the light directionality induced by these particular potentials. Here, we consider PT-symmetric potentials with axial symmetry to direct light to the crystal central point obtaining a localization effect. The axial and PT-symmetric potential intrinsically generates an exceptional central point in the photonic crystal by the merge of both symmetries. This particular point in the crystal lattice causes field amplitude gradients with exponential slopes around the crystal center. The field localization strongly depends on the phase of the central point and on the complex amplitude of the PT-potential. The presented work analyzes in a first stage 1D linear PT-axisymmetric crystals and the role of the central point phase that determines the defect character, i.e. refractive index defect, gain-loss defect or a combination of both. The interplay of the directional light effect induced by the PT-symmetry and the light localization around the central point through the axial symmetry enhances localization and allows higher field concentration for certain phases. The linearity of the studied crystals introduces an exponential growth of the field that mainly depends on the complex amplitude of the potential. The work is completed by the analysis of 2D PT-axisymmetric potentials showing different spatial slopes and growth rates caused by symmetry reasons.
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
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
DETAILED DECOMPOSITION OF GALAXY IMAGES. II. BEYOND AXISYMMETRIC MODELS
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.
Simmons, Charles J; Stratemeier, Horst; Hitchman, Michael A; Reinen, Dirk; Masters, Vanessa M; Riley, Mark J
2011-06-06
The crystal structures of trans-diaquabis(methoxyacetato)copper(II) and the isostructural nickel(II) complex have been determined over a wide temperature range. In conjunction with the reported behavior of the g-values, the structural data suggest that the copper(II) compound exhibits a thermal equilibrium between three structural forms, two having orthorhombically distorted, tetragonally elongated geometries but with the long and intermediate bonds to different atoms, and the third with a tetragonally compressed geometry. This is apparently the first reported example of a copper(II) complex undergoing an equilibrium between tetragonally elongated and compressed forms. The optical spectrum of single crystals of the copper(II) compound is used to obtain metal-ligand bonding parameters which yield the g-values of the compressed form of the complex and hence the proportions of the complex in each structural form at every temperature. When combined with estimates of the Jahn-Teller distortions of the different forms, the latter produce excellent agreement with the observed temperature dependence of the bond lengths. The behavior of an infrared combination band is consistent with such a thermal equilibrium, as is the temperature dependence of the thermal ellipsoid parameters and the XAFS. The potential surfaces of the different forms of the copper(II) complex have been calculated by a model based upon Jahn-Teller coupling. It is suggested that cooperative effects may cause the development of the population of tetragonally compressed complexes, and the crystal packing is consistent with this hypothesis, though the present model may oversimplify the diversity of structural forms present at high temperature. © 2011 American Chemical Society
Nonlinear Stability of a Viscous Axisymmetric Jet.
NASA Astrophysics Data System (ADS)
Horwitz, Judith Ann
The nonlinear temporal stability of a viscous axisymmetric jet using a hyperbolic tangent approximation to the actual mean flow is studied with respect to axisymmetric and helical disturbances. For the case of axisymmetric disturbances the weakly nonlinear Stuart-Watson perturbation expansion is used to study the self interaction of the fundamental in a neighborhood of the critical Reynolds number (R_{c}). The Landau constant is positive indicating there is a supercritical Hopf bifurcation. In order to extend these results past R ~ R_ {c}, a severely truncated Fourier model expansion using the Stuart-Watson functions to represent the r dependence, exponentials in z and unknown amplitudes in time is substituted into the Navier-Stokes equation. A projection onto an appropriate subspace leads to a low dimensional (five) system of amplitude equations for the disturbance of the fundamental, harmonic and distortion to the mean flow. The bifurcation package AUTO and Fourier spectrum are used to characterize the nature of the solutions for various values of R. Numerical results show that the periodic solution is stable for 55.3 < R < 72.3. There is a secondary bifurcation at R = 72.3 to a quasiperiodic solution with 2 incommensurate frequencies (Q_2) f_1 and f_2. Each peak in the Fourier spectrum can be indexed according to f = f_1 + nf_2 for n = 0,+/-1, +/-2,.... As R increases past R = 78 there is a transition through another periodic regime and then finally a transition to intermittency for 100 < R < 1000. In the case of helical disturbances the ten dimensional system of amplitude equations has a stable periodic solution for 21.75 < R < 33.2. For 33.2 < R < 37, there is a Q_2 solution. The Fourier spectrum contains two families of peaks: q _{n} = nf_1 - (n - 1)f_2 for n = 0,1,2, ... and w_{n} = nf_1 - (n + 1)f_2 for n = 1,2,3,.... As R increases f_2/f _1 increases and the limiting frequency w_1 --> 0 as f_2/f_1 -->.5 indicating a possible homoclinic orbit. No bounded
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.
A solvable model of axisymmetric and non-axisymmetric droplet bouncing.
Andrew, Matthew; Yeomans, Julia M; Pushkin, Dmitri O
2017-02-07
We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in terms of surface tension forces. Once the drop has an elliptical footprint the surface tension force acting on the longer sides is greater. Therefore the shorter axis retracts faster and, due to the incompressibility constraints, pumps fluid along the more extended droplet axis. This leads to a positive feedback, allowing the drop to jump in an elongated configuration, and more quickly.
Axisymmetric Column Collapse in a Rotating System
NASA Astrophysics Data System (ADS)
Warnett, Jay; Thomas, Peter; Dennisenko, Petr
2012-11-01
We discuss experimental and computational results of a study investigating the collapse of an initially axisymmetric cylindrical column of granular material within a rotating environment of air or liquids. In industry this type of granular column collapse that is subject to background rotation is encountered, for instance, in the context of the spreading of powders and fertilizers. In comparison to its non-rotating counterpart the physical characteristics of the column collapse in a rotating system are expected to be modified by effects arising from centrifugal forces and Coriolis forces. We compare our new results for the rotating flow to data available in the literature for the collapse of granular columns in non-rotating systems to highlight the differences observed.
Turbulence characteristics of an axisymmetric reacting flow
NASA Technical Reports Server (NTRS)
Gould, R. D.; Stevenson, W. H.; Thompson, H. D.
1984-01-01
Turbulent sudden expansion flows are of significant theoretical and practical importance. Such flows have been the subject of extensive analytical and experimental study for decades, but many issues are still unresolved. Detailed information on reacting sudden expansion flows is very limited, since suitable measurement techniques have only been available in recent years. The present study of reacting flow in an axisymmetric sudden expansion was initiated under NASA support in December 1983. It is an extension of a reacting flow program which has been carried out with Air Force support under Contract F33615-81-K-2003. Since the present effort has just begun, results are not yet available. Therefore a brief overview of results from the Air Force program will be presented to indicate the basis for the work to be carried out.
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M.; White, R.B.
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ``explicit`` velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer`s inductive terms.
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M. . Dipt. di Scienze Matematiche); White, R.B. . Plasma Physics Lab.)
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to explicit'' velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer's inductive terms.
Prediction of an axisymmetric combusting flow
NASA Technical Reports Server (NTRS)
Correa, S. M.
1983-01-01
A numerical model for turbulent, recirculating combusting flow is developed and applied to a research combustor. The model is based on the time-averaged Navier-Stokes equations with k-epsilon turbulence closure and the compositional fluctuations at each point are given probabilistically in terms of the mixture fraction. The probability density function is derived from transport equations for its first two moments along with an assumption regarding its shape. The resulting equations are solved using a standard line relaxation algorithm. It is found that the predictions of the model are in good agreement with data from an axisymmetric, bluff-body stabilized research combustor, while the major discrepancies are similar to those found in isothermal flow comparisons. The peculiar features of this flow which contribute to the errors are examined. The agreement between the theory and data deteriorates as the central jet velocity is increased which indicates an enhanced role for unsteady effects.
Compact neutron imaging system using axisymmetric mirrors
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.
Ideal ballooning modes in axisymmetric mirror machines
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.
Direct numerical simulation of axisymmetric turbulence
NASA Astrophysics Data System (ADS)
Qu, Bo; Bos, Wouter J. T.; Naso, Aurore
2017-09-01
The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.
Axisymmetric collapse of rotating, isothermal clouds
NASA Technical Reports Server (NTRS)
Boss, A. P.; Haber, J. G.
1982-01-01
The results of over 50 new models of the axisymmetric collapse of rotating, isothermal clouds are presented, with the following objectives: (1) to fully explore the initial conditions necessary for collapse from uniform density and uniform rotation, subject to constant volume and constant pressure boundary conditions; (2) to catalog the possible end states for cloud collapse from these initial conditions; and (3) to determine if there is a critical value of rotational energy/gravitational energy associated with ring formation, as appears to be the case for adiabatic clouds. Three end states are obtained: Bonnor-Ebert spheroids, rings and collapsing disks. The rings are formed with values of the ratio of rotational energy to the absolute value of the gravitational energy typically less than the Maclaurin spheroid value for dynamic instability to ring formation.
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.
Nonlinear axisymmetric liquid currents in spherical annuli
NASA Technical Reports Server (NTRS)
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
Axisymmetric Bending Oscillations of Stellar Disks
NASA Astrophysics Data System (ADS)
Sellwood, J. A.
1996-12-01
Self-gravitating stellar disks with random motion support both exponentially growing and, in some cases, purely oscillatory axisymmetric bending modes, unlike their cold disk counterparts. A razor-thin disk with even a very small degree of random motion in the plane is both unstable and possesses a discrete spectrum of neutral modes, irrespective of the sharpness of the edge. Random motion normal to the disk plane is stabilizing but at the same time allows bending waves to couple to the internal vibrations of the particles, which causes the formerly neutral modes to decay through Landau damping. Focusing first on instabilities, I here determine the degree of random motion normal to the plane needed to suppress global, axisymmetric, bending instabilities in a family of self-gravitating disks. As found previously, bending instabilities are suppressed only when the thickness exceeds that expected from a local criterion when the degree of pressure support within the disk plane is comparable to, or exceeds, the support from rotation. Nevertheless, a modest disk thickness would seem to be adequate for the bending stability of most disk galaxies, except perhaps near their centers. The discretization of the neutral spectrum in a zero-thickness disk is due to the existence of a turning point for bending waves in a warm disk, which is absent when the disk is cold. When the disk is given a finite thickness, the discrete neutral modes generally become strongly damped through wave-particle interactions. It is surprising therefore that I find some simulations of warm, stable disks can support (quasi-)neutral, large-scale, bending modes that decay very slowly, if at all.
Orientifolded locally AdS3 geometries
NASA Astrophysics Data System (ADS)
Loran, F.; Sheikh-Jabbari, M. M.
2011-01-01
Continuing the analysis of [Loran F and Sheikh-Jabbari M M 2010 Phys. Lett. B 693 184-7], we classify all locally AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity and show that they are obtained by applying certain orientifold projection on AdS3, BTZ or AdS3 self-dual orbifold, respectively, O-AdS3, O-BTZ and O-SDO geometries. Depending on the orientifold fixed surface, the O-surface, which is either a space-like 2D plane or a cylinder, or a light-like 2D plane or a cylinder, one can distinguish four distinct cases. For the space-like orientifold plane or cylinder cases, these geometries solve AdS3 Einstein equations and are hence locally AdS3 everywhere except at the O-surface, where there is a delta-function source. For the light-like cases, the geometry is a solution to Einstein equations even at the O-surface. We discuss the causal structure for static, extremal and general rotating O-BTZ and O-SDO cases as well as the geodesic motion on these geometries. We also discuss orientifolding Poincaré patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces and comment on the 2D CFT dual to the O-geometries.
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.
Evidence for axisymmetric halos: The case of IC 2006
NASA Astrophysics Data System (ADS)
Franx, Marijn; van Gorkom, J. H.; de Zeeuw, Tim
1994-12-01
We present a new method to derive the shape of the potential from the velocity field of a gas ring, or a gas disk with a flat rotation curve. The method is an extension of previous work by Binney and Teuben, and it can detect deviations from axisymmetry at the level of a few percent. The velocity field of the ring or disk is expanded into harmonics, and we present analytic expressions which relate these harmonic terms to the intrinsic parameters, and the viewing angles. We show that both the velocity field and the geometry of the ring are necessary to give complete information on the shape of the potential in the plane of the ring. The velocity field alone gives incomplete information for small ellipticities. We present new neutral hydrogen data on the H I ring around the early-type galaxy IC 2006, which was discovered by Schweizer, van Gorkom, & Seitzer (1989). The new data show that the ring is filled and has a remarkably regular velocity field. Application of our method to this gas ring shows that the halo must be close to perfectly axisymmetric. We detect a nonsignificant ellipticity of the potential of 0.012 +/- 0.026. The 95% confidence limit on the ellipticity is 0.05. This implies that the potential is nearly circular in the plane of the ring. The analysis indicates that the circular velocity is nearly constant from 0.5 Re to 6.5 Re. We confirm that the M/L ration in the outer parts increases (Schweizer et al. 1989). The stellar component probably has a strong disk. The data demonstrate that galaxies other than spiral galaxies have massive halos. The inferred shape of the halo can be contrasted to the strongly triaxial halos found in simulations of dissipationless halo formation. As suggested by Katz & Gunn (1991), the inclusion of baryonic matter in the simulations may be necessary to resolve this issue.
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
Design of an Axisymmetric Afterbody Test Case for CFD Validation
NASA Technical Reports Server (NTRS)
Disotell, Kevin J.; Rumsey, Christopher L.
2017-01-01
As identified in the CFD Vision 2030 Study commissioned by NASA, validation of advanced RANS models and scale-resolving methods for computing turbulent flow fields must be supported by continuous improvements in fundamental, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, the underpinnings of a new test platform referred to herein as the NASA Axisymmetric Afterbody are presented. The devised body-of-revolution is a modular platform consisting of a forebody section and afterbody section, allowing for a range of flow behaviors to be studied on interchangeable afterbody geometries. A body-of-revolution offers advantages in shape definition and fabrication, in avoiding direct contact with wind tunnel sidewalls, and in tail-sting integration to facilitate access to higher Reynolds number tunnels. The current work is focused on validation of smooth-body turbulent flow separation, for which a six-parameter body has been developed. A priori RANS computations are reported for a risk-reduction test configuration in order to demonstrate critical variation among turbulence model results for a given afterbody, ranging from barely-attached to mild separated flow. RANS studies of the effects of forebody nose (with/without) and wind tunnel boundary (slip/no-slip) on the selected afterbody are presented. Representative modeling issues that can be explored with this configuration are the effect of higher Reynolds number on separation behavior, flow physics of the progression from attached to increasingly-separated afterbody flows, and the effect of embedded longitudinal vortices on turbulence structure.
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.
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.
Enrichment Activities for Geometry.
ERIC Educational Resources Information Center
Usiskin, Zalman
1983-01-01
Enrichment activities that teach about geometry as they instruct in geometry are given for some significant topics. The facets of geometry included are tessellations, round robin tournaments, geometric theorems on triangles, and connections between geometry and complex numbers. (MNS)
Tanase, Stéfania; Tuna, Floriana; Guionneau, Philippe; Maris, Thierry; Rombaut, Guillaume; Mathonière, Corine; Andruh, Marius; Kahn, Olivier; Sutter, Jean-Pascal
2003-03-10
Two molecule-based magnets, [Mn(2)(tea)Mo(CN)(7)].H(2)O, 1, and [Mn(2)(tea)Mo(CN)(7)], 2 (tea stands for triethanolamine), formed with the 4d ion building block, [Mo(CN)(7)](4)(-), Mn(II) ions, and an additional ligand, tea, have been prepared and structurally characterized by single-crystal X-ray analyses. Whereas 1 is obtained by a self-assembling process in solution, compound 2 is quantitatively formed through a smooth thermal treatment of 1. Their magnetic properties revealed that these compounds exhibit magnetic ordering at T(c) = 75 and 106 K respectively for compounds 1 and 2. The difference for their critical temperature is attributed to the geometry of the coordination sphere of a Mn(II) site found to be square-pyramidal for 1 and tetrahedral for 2.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-05-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized into annular rings
Efficient material treatment by axi-symmetrically polarized laser radiation
NASA Astrophysics Data System (ADS)
Makin, V. S.; Pestov, Yu I.; Makin, R. S.
2016-08-01
Recent years the increased interest is to the problem of interaction of nontraditionally polarized laser radiation with condensed media. The experiments with axisymmetrical polarization attract more attention. The peculiarities of interaction of axisymmetrical laser radiation with condensed matter are considered in framework of universal polariton model. It is shown that more effective is interaction of radially polarized laser radiation with surface active media. The optical schemes for efficient material treatment by radially polarized radiation are sketched.
Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters
NASA Astrophysics Data System (ADS)
Zhang, Wan-chao; Liu, Heng-xu; Zhang, Liang; Zhang, Xue-wei
2016-12-01
The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber's hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.
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.
Particle acceleration in axisymmetric pulsar current sheets
NASA Astrophysics Data System (ADS)
Cerutti, Benoît; Philippov, Alexander; Parfrey, Kyle; Spitkovsky, Anatoly
2015-03-01
The equatorial current sheet in pulsar magnetospheres is often regarded as an ideal site for particle acceleration via relativistic reconnection. Using 2D spherical particle-in-cell simulations, we investigate particle acceleration in the axisymmetric pulsar magnetosphere as a function of the injected plasma multiplicity and magnetization. We observe a clear transition from a highly charge-separated magnetosphere for low plasma injection with little current and spin-down power, to a nearly force-free solution for high plasma multiplicity characterized by a prominent equatorial current sheet and high spin-down power. We find significant magnetic dissipation in the current sheet, up to 30 per cent within 5 light-cylinder radii in the high-multiplicity regime. The simulations unambiguously demonstrate that the dissipated Poynting flux is efficiently channelled to the particles in the sheet, close to the Y-point within about 1-2 light-cylinder radii from the star. The mean particle energy in the sheet is given by the upstream plasma magnetization at the light cylinder. The study of particle orbits shows that all energetic particles originate from the boundary layer between the open and the closed field lines. Energetic positrons always stream outwards, while high-energy electrons precipitate back towards the star through the sheet and along the separatrices, which may result in auroral-like emission. Our results suggest that the current sheet and the separatrices may be the main source of high-energy radiation in young pulsars.
Characteristics of an axisymmetric sudden expansion flow
NASA Technical Reports Server (NTRS)
Stevenson, W. H.; Thompson, H. D.
1985-01-01
A two-color, two component Laser Doppler Velocimeter (LDV) system operating in forward scatter has been developed in order to make simultaneous measurements of the axial and radial velocity components in an axisymmetric sudden expansion flow with and without combustion. The LDV system includes Bragg cell modulators in the four beam paths to allow a net frequency shift of 5MHz in both the green and blue beams. This permits an unambiguous measurement of negative velocities and also eliminates incomplete signal bias. The green beam probe volume has a waist diameter of 0.200 mm and is approximately 2mm long. The blue beam has a probe volume waist of 0.250 mm and is approximately 1 mm long. The scattered light from the probe volume is separated so that approximately 80% of each color passes to its respective photomultiplier tube by using a dichroic filter. Narrow bandpass filters are used to further filter unwanted signals before they are detected. A schematic diagram of the LDV system is shown.
Control of Thermoacoustic Axisymmetric and Helical Instabilities
NASA Astrophysics Data System (ADS)
Gutmark, Ephraim; Paschereit, Christian Oliver; Weisenstein, Wolfgang
1998-11-01
Unstable thermoacoustic modes were investigated and controlled in an experimental low-emission swirl stabilized combustor, in which the acoustic boundary conditions were modified to obtain combustion instability. Several axisymmetric and helical unstable modes were identified for fully premixed conditions. These unstable modes were associated with flow instabilities related to the recirculating wake-like region near the combustor axis and shear layer instabilities at the sudden expansion (dump plane). Open and closed loop active control systems were used to suppress the thermoacoustic pressure oscillations and to reduce undesired emissions of pollutants during premixed combustion. Pressure transducers and OH emission detection sensors monitored the combustion process and provide input to the processor of the control system. The actuators were high frequency valves, which were employed to superimpose modulations in the fuel stream. Symmetric and antisymmetric fuel injection schemes were tested. Suppression levels of up to 24 dB in the pressure oscillations were obtained. In some of the cases tested, concomitant reductions of NOx and CO emissions were achieved. The effect of the various pulsed fuel injection methods on the combustion structure was investigated.
Four motional invariants in axisymmetric tori equilibria
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}=
An annular superposition integral for axisymmetric radiators
Kelly, James F.; McGough, Robert J.
2007-01-01
A fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators. This method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the Rayleigh-Sommerfeld integral or the generalized King integral. Expressions are derived for plane circular pistons using both continuous wave and pulsed excitations. Several commonly used apodization schemes for the surface velocity distribution are considered, including polynomial functions and a “smooth piston” function. The effect of different apodization functions on the spectral content of the wave field is explored. Quantitative error and time comparisons between the new method, the Rayleigh-Sommerfeld integral, and the generalized King integral are discussed. At all error levels considered, the annular superposition method achieves a speed-up of at least a factor of 4 relative to the point-source method and a factor of 3 relative to the generalized King integral without increasing the computational complexity. PMID:17348500
Longitudinal wakefield for an axisymmetric collimator
Blednykh A.; Krinsky, S.
2012-05-25
We consider the longitudinal point-charge wakefield, w(s), for an axisymmetric collimator having inner radius b, outer radius d, inner length g, and taper length L. The taper angle {alpha} is defined by tan {alpha} = (d-b)/L. Using the electromagnetic simulation code ECHO, we explore the dependence of the wakefield on a collimator's geometric parameters over a wide range of profiles: from small-angle tapers to step-function transitions. The point-charge wakefield is determined using an approximation introduced by Podobedov and Stupakov. We have found it useful to exhibit the wakefield as a function of the scaled variable s/d{alpha}. For small taper angles, our results illustrate the satisfaction of the longitudinal scaling found by Stupakov, Bane, and Zagorodnov; and for larger taper angles, the breaking of this longitudinal scaling is clearly depicted. The use of the scaled variable s/d{alpha} turns out to be especially well suited to describing the wakefield for a collimator with step-function profile ({alpha} = {pi}/2).
Magnetic surfaces in an axisymmetric torus
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.
Design of a Quasi-Axisymmetric Stellarator
NASA Astrophysics Data System (ADS)
Reiman, A.; Ku, L.-P.; Boozer, A.; Brooks, A.; Goldston, R.; Johnson, J.; Monticello, D.; Mynick, H.; Nazikian, R.; Neilson, G. H.; Redi, M.; Sheffield, G.; Zarnstorff, M.
1997-11-01
We have been pursuing the design of a stellarator with the following properties: 1) magnetic field sufficiently close to quasi-axisymmetric that the neoclassical transport is small compared to the turbulent transport; 2) adequate ideal MHD stability β limit; 3) good equilibrium flux surfaces at β values of interest; 4) aspect ratio comparable to that of tokamaks. For our equilibrium and stability β limits, the goal is to exceed 5%. Equilibrium flux surfaces and magnetic island widths are evaluated using the PIES 3D equilibrium code. The assumed current profile corresponds to the self-consistent bootstrap current. Analytic estimates suggest that neoclassical currents will have a large effect on island widths, leading to the requirement that the ι profile be monotonically increasing. One option being considered for construction of the stellarator would be to use the present PBX toroidal field coils and vacuum vessel, building additional coils inside the vacuum vessel. Fifteen MW of neutral beam power are available, allowing a test of the β limit.
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.
NASA Astrophysics Data System (ADS)
Gmerek, Felix; Stuhlmann, Benjamin; Álvarez-Valtierra, Leonardo; Pratt, David W.; Schmitt, Michael
2016-02-01
We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.
NASA Astrophysics Data System (ADS)
Potter, William J.; Cotter, Garret
2013-02-01
In this paper we develop the jet model of Potter & Cotter to include a magnetically dominated accelerating parabolic base transitioning to a slowly decelerating conical jet with a geometry set by recent radio observations of M87. We conserve relativistic energy-momentum and particle number along the jet and calculate the observed synchrotron emission from the jet by calculating the integrated line-of-sight synchrotron opacity through the jet in the rest frame of each section of plasma. We calculate the inverse-Compton emission from synchrotron, cosmic microwave background (CMB), accretion disc, starlight, broad-line region (BLR), dusty torus and narrow-line region photons by transforming into the rest frame of the plasma along the jet. We fit our model to simultaneous multi-wavelength observations of the Compton-dominant FSRQ type blazar PKS 0227-369, with a jet geometry set by M87 and an accelerating bulk Lorentz factor consistent with simulations and theory. We investigate models in which the jet comes into equipartition at different distances along the jet and equipartition is maintained via the conversion of jet bulk kinetic energy into particle acceleration. We find that the jet must still be magnetically dominated within the BLR and cannot be in equipartition due to the severe radiative energy losses. The model fits the observations, including radio data, very well if the jet comes into equipartition outside the BLR within the dusty torus (1.5 pc) or at further distances (34 pc). The fits require a high-power jet with a large bulk Lorentz factor observed close to the line of sight, consistent with our expectations for a Compton-dominant blazar. We find that our fit in which the jet comes into equipartition furthest along the jet, which has a jet with the geometry of M87 scaled linearly with black hole mass, has an inferred black hole mass close to previous estimates. This implies that the jet of PKS 0227 might be well described by the same jet geometry as M87.
Gmerek, Felix; Stuhlmann, Benjamin; Álvarez-Valtierra, Leonardo; Pratt, David W; Schmitt, Michael
2016-02-28
We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.
ERIC Educational Resources Information Center
Scott, Paul
1988-01-01
Discusses the use of computer graphics in the teaching of geometry. Describes five types of geometry: Euclidean geometry, transformation geometry, coordinate geometry, three-dimensional geometry, and geometry of convex sets. (YP)
Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials
NASA Astrophysics Data System (ADS)
Taani, Ali; Vallejo, Juan C.
2017-06-01
We describe the dynamical behavior of isolated old ( ⩾ 1Gyr) objects-like Neutron Stars (NSs). These objects are evolved under smooth, time-independent, gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincaré section for comparing the influence of different birth velocities. The inspection of the maximal asymptotic Lyapunov (λ) exponent shows that dynamical behaviors of the selected orbits are nearly the same as the regular orbits with 2-DOF, both in axisymmetric and triaxial when (ϕ, qz )= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (ϕ, qz )= (90, 1.5). The tube orbits preserve direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincaré section shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of several prototypical orbits offer the means to identify the phase-space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.
The dynamics of axisymmetric swirling flows in a diverging or contracting circular pipe
NASA Astrophysics Data System (ADS)
Rusak, Zvi; Wang, Shixiao
2009-11-01
This paper describes a study of the effect of pipe divergence and contraction on the stability and breakdown of axisymmetric swirling flows in a long, finite-length, circular pipe. The work extends the theory of Wang & Rusak (1997). The approach is based on a rigorous analysis of the axisymmetric, steady and inviscid flow equations with non-periodic boundary conditions. The analysis firmly establishes the global bifurcation of flow states in the pipe (solutions of the Squire-Long PDE) by relating it to the bifurcation of solutions of the columnar flow problem (solutions of the resulting ODE) and using a new flow force relationship between the inlet and outlet states. This technique provides a simple, yet exact, method of analyzing the complex flow behavior including transitions from near-columnar vortex states to flow fields with large separation (stagnation) zones along the pipe centerline (breakdown states) or along the pipe wall (swirl induced wall separation). Bifurcation diagrams for base vortex models including the solid- body rotation and the Burgers vortex are presented. The stability characteristics of the various branches of solutions and the flow dynamics in the pipe under various perturbations are discussed. Results show that pipe divergence or contraction significantly modify the global flow behavior in a straight pipe and shed light on the effect of pipe geometry on the mechanism of vortex breakdown.
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.
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.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-12-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since
Fast electron bremsstrahlung in axisymmetric magnetic configuration
NASA Astrophysics Data System (ADS)
Peysson, Y.; Decker, J.
2008-09-01
The nonthermal bremsstrahlung is calculated in a plasma with arbitrary axisymmetric magnetic configuration, taking into account the relativistic angular anisotropy of the radiation cross section at high photon energies, the helical winding of the field lines on the magnetic flux surfaces, and the poloidal variation of the electron distribution function including particle trapping effects. The fast electron dynamics during current drive in tokamaks and reverse field pinches can be investigated in detail by coupling this calculation to a bounce-averaged relativistic Fokker-Planck solver, which calculates the electron distribution function. The asymmetry between high- and low-field side hard x-ray emission intensity that has been measured on the Tore-Supra tokamak [Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995) Vol. 1, IAEA-CN-60/A1-5 (Institute of Physics, Bristol, U.K., 1995), p. 105] is explained for the first time by the role of trapped electrons. A much stronger poloidal asymmetry is predicted for the line-integrated fast electron bremsstrahlung in the poloidal plane of the Madison Symmetric Torus [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)], since the helical winding of the magnetic field lines is much larger for a reverse field pinch configuration. In this case, the hard x-ray emission is no longer a flux surface quantity, which prevents local reconstructions using a standard Abel inversion, whatever the geometrical arrangement of the lines of sight.
Viallet, Guilhem; Sgard, Franck; Laville, Frédéric; Boutin, Jérôme
2013-12-01
The axisymmetric hypothesis of the earplug-ear canal system geometry is commonly used. The validity of this hypothesis is investigated numerically in the case of a simplified configuration where the system is embedded in a rigid baffle and for fixed boundary conditions on the earplug lateral walls. This investigation is discussed for both individual and averaged insertion loss predictions of molded silicon earplugs. The insertion losses of 15 earplug-ear canal systems with realistic geometries are calculated using three-dimensional (3D) finite element models and compared with the insertion losses provided by two-dimensional equivalent axisymmetric finite element models using 6 different geometry reconstruction methods [all the models are solved using COMSOL Multiphysics (COMSOL, Sweden)]. These methods are then compared in order to find the most reliable ones in terms of insertion loss predictions in this simplified configuration. Two methods have emerged: The usage of a variable cross section (with the same area values as the 3D case) or the usage of a constant cross section (with the same length and volume as the 3D case).
NASA Technical Reports Server (NTRS)
Tag, I. A.; Lumsdaine, E.
1978-01-01
The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.
NASA Technical Reports Server (NTRS)
Tag, I. A.; Lumsdaine, E.
1978-01-01
The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.
Numerical simulation of axisymmetric base flow on tactical missiles with propulsive jet
NASA Astrophysics Data System (ADS)
Thomas, P. D.; Reklis, R. P.; Roloff, R. R.; Conti, R. J.
1987-11-01
The axisymmetric Lockheed Viscous Implicit Solver (LVIS) Navier-Stokes computer code is modified to incorporate the capability for computing the flow in the base region of a tactical missile with propulsive jet. Modifications include generalization of the computational space to accommodate the geometry of the base and implementation of two turbulence models of the two-equation type (kappa-epsilon and k-W). Computer runs are made with both turbulence models. The results of these computations are similar, but some differences are observed in the recirculating near-wake flow and in the shear layers that separate it from the high-speed streams of the propulsive jet and of the external flow. These differences are attributed to the greater eddy viscosity predicted by the kappa-epsilon model.
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.
Axisymmetric instabilities in electrospinning of highly conducting, viscoelastic polymer solutions
NASA Astrophysics Data System (ADS)
Carroll, Colman P.; Joo, Yong Lak
2009-10-01
In this paper the axisymmetric instabilities observed during the electrospinning of highly electrically conducting, viscoelastic poly(ethylene oxide) (PEO)/water solutions are investigated. In our theoretical study, a linear stability analysis is coupled with a model for the stable electrospun jet. The combined model is used to calculate the expected bead growth rate and wave number for given electrospinning conditions. In the experimental section of the study, PEO/water solutions are electrospun and the formation of axisymmetric beads is captured using high-speed photography. Experimental values for the bead growth rate and wave number are extracted and compared with the model predictions. An energy analysis is then carried out on the stability results to investigate the mechanism of instability via the coupling between base flow and perturbation. The analysis reveals that the unstable axisymmetric mode for electrically driven, highly conducting jets is not a capillary mode, but is mainly driven by electrical forces due to the interaction of charges on the jet. We note that this axisymmetric, conducting mode often exhibits a growth rate too small to be observed during electrospinning. However, both our experiments and stability analysis demonstrate that the axisymmetric instability with a high growth rate can be seen in practice when the electrical force is effectively coupled with viscoelastic forces.
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.
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.
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
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.
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
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
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)].
NASA Astrophysics Data System (ADS)
Yoo, S.; Zeng, X. C.
2006-05-01
We performed a constrained search for the geometries of low-lying neutral germanium clusters GeN in the size range of 21⩽N⩽29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N ˜65.
On the calculation of ducted propeller performance in axisymmetric flows
NASA Astrophysics Data System (ADS)
Falcao de Campos, J. A. C.
Some of the most important influences on the performance of ducted propellers in uniform and nonuniform axisymmetric flows are demonstrated. The viscous flow past an axisymmetric duct is analyzed for uniform axial flow and for the case when the flow can be regarded as being a part of the ducted propeller. The flow past an annular airfoil and a ducted propeller in axisymmetric shear flow is considered, and approximate numerical solutions of Euler's equation are given using a discrete vortex method. These methods are then applied to the interaction problem of a ducted propeller behind a body of revolution. The design of ducted propellers is discussed, and the results of the basic flow models developed in the paper are verified by correlation with experimental results.
Gainsford, Graeme J; Bhuiyan, M Delower H; Kay, Andrew J
2008-04-01
The compounds N-[2-(4-cyano-5-dicyanomethylene-2,2-dimethyl-2,5-dihydrofuran-3-yl)vinyl]-N-phenylacetamide, C(20)H(16)N(4)O(2), (I), and 2-{3-cyano-5,5-dimethyl-4-[2-(piperidin-1-yl)vinyl]-2,5-dihydrofuran-2-ylidene}malononitrile 0.376-hydrate, C(17)H(18)N(4)O x 0.376 H(2)O, (II), are novel push-pull molecules. The significant bonding changes in the polyene chain compared with the parent molecule 2-dicyanomethylene-4,5,5-trimethyl-2,5-dihyrofuran-3-carbonitrile are consistent with the relative electron-donating properties of the acetanilido and piperidine groups. The packing of (I) utilizes one phenyl-cyano C-H...N and two phenyl-carbonyl C-H...O hydrogen bonds. Compound (II) crystallizes with a partial water molecule (0.376H(2)O), consistent with cell packing that is dominated by attractive C-H...N(cyano) interactions. These compounds are precursors to novel nonlinear optical chromophores, studied to assess the impact of donor strength and the extent of conjugation on bond-length alternation, crystal packing and aggregation.
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.
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.
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
Li, X; Suzuki, K; Kanaori, K; Tajima, K; Kashiwada, A; Hiroaki, H; Kohda, D; Tanaka, T
2000-07-01
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-stranded alpha-helix bundle, as revealed by circular dichroism (CD) spectroscopy and sedimentation equilibrium analysis. By titration with metal ions and monitoring the change in the intensity of the CD spectra at 222 nm, the dissociation constant Kd was determined to be 1.5 +/- 0.8 microM for Cd(II). The triple-stranded complex formed by the 113Cd(II) ion showed a single 113Cd NMR resonance at 572 ppm whose chemical shift was not affected by the presence of Cl- ions. The 113Cd NMR resonance was connected with the betaH protons of the cysteine residue by 1H-113Cd heteronuclear multiple quantum correlation spectroscopy. These NMR results indicate that the three cysteine residues are coordinated to the cadmium ion in a trigonal-planar complex. Hg(II) also induced the assembly of the peptide into a triple-stranded alpha-helical bundle below the Hg(II)/peptide ratio of 1/3. With excess Hg(II), however, the alpha-helicity of the peptide was decreased, with the change of the Hg(II) coordination state from three to two. Combining this construct with other functional domains should facilitate the production of artificial proteins with functions controlled by metal ions.
Li, X.; Suzuki, K.; Kanaori, K.; Tajima, K.; Kashiwada, A.; Hiroaki, H.; Kohda, D.; Tanaka, T.
2000-01-01
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-stranded alpha-helix bundle, as revealed by circular dichroism (CD) spectroscopy and sedimentation equilibrium analysis. By titration with metal ions and monitoring the change in the intensity of the CD spectra at 222 nm, the dissociation constant Kd was determined to be 1.5 +/- 0.8 microM for Cd(II). The triple-stranded complex formed by the 113Cd(II) ion showed a single 113Cd NMR resonance at 572 ppm whose chemical shift was not affected by the presence of Cl- ions. The 113Cd NMR resonance was connected with the betaH protons of the cysteine residue by 1H-113Cd heteronuclear multiple quantum correlation spectroscopy. These NMR results indicate that the three cysteine residues are coordinated to the cadmium ion in a trigonal-planar complex. Hg(II) also induced the assembly of the peptide into a triple-stranded alpha-helical bundle below the Hg(II)/peptide ratio of 1/3. With excess Hg(II), however, the alpha-helicity of the peptide was decreased, with the change of the Hg(II) coordination state from three to two. Combining this construct with other functional domains should facilitate the production of artificial proteins with functions controlled by metal ions. PMID:10933497
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.
Ju, Dehao; Shrimpton, John; Bowdrey, Moira; Hearn, Alex
2012-08-01
A breath activated, pressurized metered dose inhaler (pMDI) device (Oxette(®)) has been developed to replace the traditional cigarette. In this paper, internal and external spray characters are measured by high speed imaging along with sizing the residual droplets at the distance from the discharge orifice where the human oropharynx locates. Two different formulations with 95% and 98% mass fraction of HFA 134a and two prototype cigarette alternatives with different expansion chamber volumes have been analyzed. The internal and external flows issuing from early stage prototype Oxette(®) are discussed along with boiling and evaporation phenomena. The expansion and entrainment regions of the jet are observed and discussed with comparison to the turbulent round jet of a single phase. From the visualizations of internal flows in the earlier design, a small expansion chamber can hardly generate small bubbles, which is difficult to produce fine sprays. The larger the expansion chamber volume, the more room for the propellant evaporation, recirculation, bubble generation and growth, all of which produces finer sprays. Therefore the later prototype of Oxette(®) 2 made a significant improvement to produce fine sprays and facilitated development of the cigarette alternative. Furthermore, the characters of the spray generated by Oxette(®) are compared to that issuing from a pMDI by previous researchers, where the residual MMD is larger than that of a pMDI, because the Oxette(®) has a smaller expansion chamber and the geometry provides less opportunity for the recirculation due to restrictions of the design space. Although the formulation with higher mass fraction of HFA 134a can generate smaller droplets, it cannot produce steady puffs with relatively low mass flow rate. Copyright © 2012 Elsevier B.V. All rights reserved.
Gronski, P; Bauer, R; Bodenbender, L; Boland, P; Diderrich, G; Harthus, H P; Kanzy, E J; Kühn, K; Schmidt, K H; Walter, G
1988-04-01
Electron micrographs of a fraction containing dimers isolated from pooled human polyclonal immunoglobulin G (IgG) suggest essentially a cyclic geometry compatible with bivalently associated monomers. It is obvious that such a structure can be produced by idiotype (Id)--anti-idiotype (anti-Id) interactions where the latter are able to neutralize certain combining site related Id functions. Accordingly, antibody (ab) activities against tetanus toxoid (tt) and rubella antigen (ag) were found to be almost exclusively confined to the monomeric molecules in preparations composed of monomers and dimers only. Moreover, electron micrographs of complexes prepared from a murine monoclonal Id as well as anti-Id reveal the presence of ring complexes, especially of cyclic tetramers. Gel filtration patterns of mixtures containing equimolar concentrations (concns) of such abs (1.6 x 10(-6) M) show, correspondingly for 9 different Id--anti-Id pairs and therefore probably representing a more common feature, mainly the formation of even-numbered complexes, especially tetramers. That is basically in accordance to an equilibrium model developed by Archer and Krakauer but not from a quantitative point of view because non-ideality terms had not been originally included. Despite taking strain energies determined by Schumaker et al. for cyclic complexes of polyclonal rabbit abs and a bivalent hapten into account for computation of size distribution patterns, the predominant formation of dimers was, nevertheless, again predicted by the modified theory in contrast to the experimental results. Fundamental conformity could only be achieved by further decreasing one of the statistical factors, namely the ring closing factor, which theoretically influences the generation of cyclic dimers. Therefore, referring to the experimental results of Schumaker et al., we postulate a strain energy well above 700 cal/mol for cyclic dimers produced by interacting Ids and anti-Ids. In general, the findings
Response of axisymmetric separated flow to its spatially localized perturbation
NASA Astrophysics Data System (ADS)
Dovgal, A. V.; Zanin, B. Yu.; Sorokin, A. M.
2016-11-01
The flow past an axisymmetric body with laminar boundary-layer separation in a low-velocity air stream has been studied. The hot-wire technique was employed to identify the variation of velocity field induced by a local stationary perturbation of separation region at the stern of the experimental model. A large-scale influence upon the near-wall flow due to a cylinder roughness element provided on the model surface was observed. The obtained data substantiate the possibility of controlling the laminar boundary-layer separation on an axisymmetric body using a local external forcing.
A mixed method for axisymmetric div-curl systems
NASA Astrophysics Data System (ADS)
Copeland, Dylan M.; Gopalakrishnan, Jayadeep; Pasciak, Joseph E.
2008-12-01
We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.
Radiative configuration factors from cylinders to coaxial axisymmetric bodies
NASA Technical Reports Server (NTRS)
Saltiel, C.; Naraghi, M. H. N.
1990-01-01
Exact solutions are obtained for the radiative configuration factor between differential elements of arbitrary orientation and cylinders. A general method is then proposed for calculating the view factor from a cylinder to a coaxial axisymmetric body using only a single numerical integration. The method is illustrated for axisymmetric bodies with function generators described by a power law equation. The method may be useful in calculating radiative heat transfer between cylindrical bodies and high-density exhaust gases and between annular radiative fins and their bases.
Zestanakis, P. A.; Anastassiou, G.; Hizanidis, K.; Kominis, Y.
2016-03-15
The presence of non-axisymmetric perturbations in an axisymmetric magnetic field equilibrium renders the Guiding Center (GC) particle motion non-integrable and may result in particle, energy, and momentum redistribution, due to resonance mechanisms. We analyse these perturbations in terms of their spectrum, as observed by the particles in the frame of unperturbed GC motion. We calculate semi-analytically the exact locations and strength of resonant spectral components of multiple perturbations. The presented Orbital Spectrum Analysis method is based on an exact Action-Angle transform that fully takes into account Finite Orbit Width effects. The method provides insight into the particle dynamics and enables the prediction of the effect of any perturbation to all different types of particles and orbits in a given, analytically or numerically calculated, axisymmetric equilibrium.
Hancock, Robert D; Reibenspies, Joseph H; Maumela, Hulisani
2004-05-03
The synthesis and structures of [Pb(DOTAM)](ClO4)2.4.5H2O (1) and [Hg(DOTAM)](ClO4)2.0.5CH3OH.1.5H2O (2) are reported, where DOTAM is 1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane. Compound 1 is triclinic, space group P, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, alpha = 101.45(2) degrees, beta = 93.32(2) degrees, gamma = 90.53(2) degrees, Z = 4, R = 0.0500. Compound 2 is monoclinic, space group Cc, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, beta = 101.91(2) degrees, Z = 4, R = 0.0381. The Pb(II) ion in 1 has an average Pb-N = 2.63 A to four N-donors from the macrocyclic ring, and four O-donors (average Pb-O = 2.77 A) from the amide pendant donors of the macrocycle, with a water molecule placed with Pb-O = 3.52 A above the proposed site of the lone pair (Lp) on Pb. The Hg(II) in 2 appears to be only six-coordinate, with four Hg-N bond lengths averaging 2.44 A, and two Hg-O from pendant amide donors at 2.41 A. The other two amide donors appear to be noncoordinating, with Hg-O distances of 2.74 and 2.82 A. A water situated 3.52 A above the proposed site of the lone pair on Pb(II) in 1 is oriented in such a way that it might be thought to be forming a Pb-Lp.H-O-H hydrogen bond. It is concluded that that this is not an H-bond, but that the presence of the lone pair allows a closer approach of the hydrogens to Pb than would be true otherwise. The structural analogy in the VSEPR sense between Pb(II), which has the 5d(10)6s(2) outer electron structure, and the Hg(II) ion, which has the 5d10 structure, is examined. The tendency of Hg(II) toward linear coordination, with two short Hg-L bonds (L = ligand) at 180 degrees to each other, and other donor groups at roughly 90 degrees to this and at much longer bond distances, is paralleled by Pb(II). One of the short Hg-L bonds is replaced in the Pb(II) structures by the lone pair (Lp), which is opposite the short Pb-L bond, or in some cases 2-4 shorter Pb-L bonds.
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…
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…
Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks
Hanson, James D.; Anderson, D.T.; Cianciosa, M.; Franz, P.; Hartwell, G. H.; Hirshman, Steven Paul; Knowlton, Stephen F.; Lao, Lang L.; Lazarus, Edward Alan; Marrelli, L.; Maurer, D. A.; Schmitt, J. C.; Sontag, A. C.; Stevenson, B. A.; Terranova, D.
2013-01-01
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.
Gainsford, Graeme J; Bhuiyan, M Delower H; Kay, Andrew J
2008-11-01
The planar component of 2-{3-cyano-4-[3-(1-decyl-1,4-dihydroquinolin-4-ylidene)prop-1-enyl]-5,5-dimethyl-2,5-dihydrofuran-2-ylidene}malononitrile, C(32)H(46)N(4)O, (I), forms into layers parallel to the (\\overline{1}01) plane. The larger of the two spaces between layers is filled by the alkyl chains, giving a ;sandwich stack' appearance. The packing of 2-{3-cyano-4-[5-(1-decyl-1,4-dihydroquinolin-4-ylidene)penta-1,3-dienyl]-5,5-dimethyl-2,5-dihydrofuran-2-ylidene}malononitrile, C(34)H(38)N(4)O, (II), which has partial disorder in the 1-decyl group, utilizes weak C-H...N, C-H...O and C-N...pi interactions in a three-dimensional ;herring-bone' array with molecular segments parallel to the (111) and (\\overline{1}1\\overline{1}) planes. Different rotational isomers with respect to the polyene chain and the 5,5-dimethyl-2,5-dihydrofuran-2-ylidene link are observed in the two structures. The significance of the study lies in the delocalization of charge along the polyene chain and the supramolecular aggregation present, which highlight the difficulty in obtaining the noncentrosymmetric alignment required for high nonlinear optical (NLO) responses in zwitterionic chromophores.
Computer program provides improved longitudinal response analysis for axisymmetric launch vehicles
NASA Technical Reports Server (NTRS)
Smith, W. W.; Walton, W. C., Jr.
1967-01-01
Computer program calculates axisymmetric launch vehicle steady-state response to axisymmetric sinusoidal loads. A finite element technique is utilized to construct the total launch vehicle stiffness matrix and mass matrix by subdividing the prototype structure into a set of axisymmetric shell components, fluid components, and spring-mass components.
NASA Astrophysics Data System (ADS)
Fillingham, Patrick; Murali, Harikrishnan
2016-11-01
Wall shear stress is characterized for underexpanded axisymmetric impinging jets for the application of aerodynamic particle resuspension from a surface. Analysis of the flow field and the wall shear stress resulted from normally impinging axisymmetric jets is conducted using Computational Fluid Dynamics. A normally impinging jet is modeled with a constant area nozzle, while varying height to diameter ratio (H/D) and inlet pressures. Schlieren photography is used to visualize the density gradient of the flow field for validation of the CFD. The Dimensionless Jet Parameter (DJP) is developed to describe flow regimes and characterize the shear stress. The DJP is defined as being proportional to the jet pressure ratio divided by the H/D ratio squared. Maximum wall shear stress is examined as a function of DJP with three distinct regimes: (i) subsonic impingement (DJP<1), (ii) transitional (1
Solution of axisymmetric and two-dimensional inviscid flow over blunt bodies by the method of lines
NASA Technical Reports Server (NTRS)
Hamilton, H. H., II
1978-01-01
Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.
Thermal deformation of concentrators in an axisymmetric temperature field
NASA Technical Reports Server (NTRS)
Bairamov, R.; Machuev, Y. I.; Nazarov, A.; Sokolov, Y. V.; Solodovnikova, L. A.; Fokin, V. G.
1985-01-01
Axisymmetric thermal deformations of paraboloid mirrors, due to heating, are examined for a mirror with a optical axis oriented toward the Sun. A governing differential equation is derived using Mushtari-Donnel-Vlasov simplifications, and a solution is presented which makes it possible to determine the principal deformation characteristics.
Loads and Pressures on Axisymmetric Bodies with Cruciform Fins
NASA Technical Reports Server (NTRS)
Dillenius, M. F. E.; Smith, C. A.
1983-01-01
NSWCDM computer program calculates aerodynamic loading and pressure distributions on supersonic configurations consisting of axisymmetric bodies with cruciform or planar canard and tail fins. Versatile program allows for configuration pitched and rolled, and fins deflected. Tail fins are interdigitated with respect to forward fins.
Stability of a compound sessile drop at the axisymmetric configuration.
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.
Decay of passive scalar fluctuations in axisymmetric turbulence
NASA Astrophysics Data System (ADS)
Yoshimatsu, Katsunori; Davidson, Peter A.; Kaneda, Yukio
2016-11-01
Passive scalar fluctuations in axisymmetric Saffman turbulence are examined theoretically and numerically. Theoretical predictions are verified by direct numerical simulation (DNS). According to the DNS, self-similar decay of the turbulence and the persistency of the large-scale anisotropy are found for its fully developed turbulence. The DNS confirms the time-independence of the Corrsin integral.
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.
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
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.
Numerical Studies of Two-Fluid Axisymmetric Steady-States with Flow in Ohmic NSTX-like Plasmas
NASA Astrophysics Data System (ADS)
Ferraro, Nathaniel; Jardin, Stephen
2008-11-01
Axisymmetric steady-states of the resistive two-fluid equations, including flow and gyroviscosity, are obtained by evolving these nonlinear equations from an initial ideal MHD equilibrium using the code M3D-C^1 [1], which has now been extended to toroidal geometry. Steady-states for high-β, inductively driven discharges in diverted NSTX geometries are studied. Excellent agreement with theoretical predictions of cross-surface Pfirsch-Schlüter flows in the axisymmetric steady-states is found. The dependence of flow velocities with resistivity is explored. It is found that in the two-fluid model, the statistical steady-state may be a fixed point, a limit cycle, or chaotic, depending on the parameters. Two-fluid terms lead to a preferred direction of toroidal rotation. The inclusion of gyroviscosity is observed to alter the character of the steady-state. The three-dimensional linear stability of simple equilibria in this two-fluid model are also explored using M3D-C^1 [2]. [1] N. Ferraro, S. Jardin. Phys. Plasmas 13:092101 (2006). [2] S. Jardin, N. Ferraro, J. Breslau, J. Chen, and M. Chance. Initial results for linear 3D Toroidal Two-Fluid stability using M3D-C1. APS DPP Conference, Dallas, TX (2008).
Modeling MHD Equilibrium and Dynamics with Non-Axisymmetric Resistive Walls in LTX and HBT-EP
NASA Astrophysics Data System (ADS)
Hansen, C.; Levesque, J.; Bialek, J.; Boyle, D. P.; Schmitt, J.
2016-10-01
In experimental magnetized plasmas, currents in the first wall, vacuum vessel, and other conducting structures can have a strong influence on plasma shape and dynamics. These effects are complicated by the 3D nature of these structures, which dictate available current paths. Results from simulations to study the effect of external currents on plasmas in two different experiments will be presented: 1) The arbitrary geometry, 3D extended MHD code PSI-Tet is applied to study linear and non-linear plasma dynamics in the High Beta Tokamak (HBT-EP) focusing on toroidal asymmetries in the adjustable conducting wall. 2) Equilibrium reconstructions of the Lithium Tokamak eXperiment (LTX) in the presence of non-axisymmetric eddy currents. An axisymmetric model is used to reconstruct the plasma equilibrium, using the PSI-Tri code, along with a set of fixed eddy current distributions. Current distributions are generated using 3D time-dependent, thin-wall, eddy current simulations using VALEN or PSI-Tet. 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. Work supported by US DOE.
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…
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…
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.
Gong, Lindan; Jang, Yoon Jung; Kim, Jinheung; Kim, Seog K
2012-08-16
Zn(II) meso-tetrakis(N-methylpyridinium-4-yl)porphyrin (ZnTMPyP) produced a unique linear dichroism (LD) spectrum when forming a complex with Z-form poly[d(G-C)(2)]. The spectrum was characterized by a large positive wavelength-dependent LD signal in the Soret absorption region. The magnitudes of LD in both the DNA and Soret band increased as the [porphyrin]/[DNA base] ratio increased and were larger by 20-40 times compared to the negative LD of the ZnTMPyP bound to B-form poly[d(G-C)(2)] and poly[d(A-T)(2)]. The angles calculated from LD were respectively 49° and 42° for B(x) and B(y) transitions of the porphyrin with respect to the local helix axis of Z-form poly[d(G-C)(2)]. The appearance of the unique LD spectrum for the Z-form poly[d(G-C)(2)] complex was accompanied by a bisignate circular dichroism spectrum in the Soret region, whose magnitude was proportional to the square of the porphyrin concentration, suggesting a stacking interaction between Z-form poly[d(G-C)(2)]-bound ZnTMPyP with other bound ZnTMPyP. From these observations, a conceivable binding mode of ZnTMPyP to Z-form poly[d(G-C)(2)] complex was proposed, in which ZnTMPyP binds at the major groove or across the groove. In contrast with Z-form poly[d(G-C)(2)], ZnTMPyP binds to poly[d(A-T)(2)] in a monomeric manner with the angles of 57° and 59° for the two porphyrin's transition moments with respect to the local polynucleotide helix axis. The polarized spectral properties of ZnTMPyP bound to B-form poly[d(G-C)(2)] coincide with the intercalated nonmetallic TMPyP, namely, a negative CD signal in the Soret band and a negative wavelength-dependent reduced LD signal, with a magnitude larger than that in the DNA absorption region in spite of its axial ligands.
ERIC Educational Resources Information Center
Yilmaz, Gül Kaleli
2015-01-01
This study aims to investigate the effects of using Dynamic Geometry Software (DGS) Cabri II Plus and physical manipulatives on the transformational geometry achievement of candidate teachers. In this study, the semi-experimental method was used, consisting of two experimental and one control groups. The samples of this study were 117 students. A…
Axisymmetric Afterbody Test Case for CFD Validation
NASA Astrophysics Data System (ADS)
Disotell, Kevin; Rumsey, Christopher
2016-11-01
As simulation complexity increases, the corresponding need for systematic, high-fidelity validation data sets continues to be important to advance physics-based CFD models. To this end, a parametric body of revolution is proposed as an experimental platform to support a wide validation domain for turbulent boundary layers outside the current bounds of DNS. Recognizing the challenges of detailed flow exploration on complex 3-D geometries, an analytically-defined body of revolution is pursued as a tractable, state-of-the-art measurement case for complex turbulent flows having extra rates of strain. The central feature of the concept based upon work by Presz Jr. & Pitkin is an interchangeable afterbody which can be tailored to distort a turbulent boundary layer in various ways, with incoming properties controlled by the forebody. An introduction to the test case design and overview of recent progress focused on smooth-body, turbulent separation physics are presented. Supported by appointment to NASA Postdoctoral Program, administered by Universities Space Research Association.
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
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.
Axisymmetric Tandem Mirror Magnetic Fusion Energy Power Plant with Thick Liquid-Walls
Moir, R W; Rognlien, T D
2006-04-26
A fusion power plant is described that utilizes a new version of the tandem mirror device including spinning liquid walls. The magnetic configuration is evaluated with an axisymmetric equilibrium code predicting an average beta of 60%. The geometry allows a flowing molten salt, (flibe-Li{sub 2}BeF{sub 4}), which protects the walls and structures from damage arising from neutrons and plasma particles. The free surface between the liquid and the burning plasma is heated by bremsstrahlung radiation, line radiation, and by neutrons. The temperature of the free surface of the liquid is calculated, and then the evaporation rate is estimated from vapor-pressure data. The allowed impurity concentration in the burning plasma is taken as 1% fluorine, which gives a 17% reduction in the fusion power owing to D/T fuel dilution, with F line-radiation causing minor power degradation. The end leakage power density of 0.6 MW/m{sup 2} is readily handled by liquid jets. The tritium breeding is adequate with natural lithium. A number of problem areas are identified that need further study to make the design more self-consistent and workable; however, the simple geometry and the use of liquid walls promise the cost of power competitive with that from fission and coal.
NASA Astrophysics Data System (ADS)
Weisberg, D. B.; Paz-Soldan, C.; Lanctot, M. J.; Strait, E. J.; Evans, T. E.
2016-10-01
The plasma response to proposed 3D coil geometries in the DIII-D tokamak is investigated using the linear MHD plasma response code MARS-F. An extensive examination of low- and high-field side coil arrangements shows the potential to optimize the coupling between imposed non-axisymmetric magnetic perturbations and the total plasma response by varying the toroidal and poloidal spectral content of the applied field. Previous work has shown that n=2 and n=3 perturbations can suppress edge-localized modes (ELMs) in cases where the applied field's coupling to resonant surfaces is enhanced by amplifying marginally-stable kink modes. This research is extended to higher n-number configurations of 2 to 3 rows with up to 12 coils each in order to advance the physical understanding and optimization of both the resonant and non-resonant responses. Both in- and ex-vessel configurations are considered. The plasma braking torque is also analyzed, and coil geometries with favorable plasma coupling characteristics are discussed. Work supported by GA internal funds.
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.
The role of axisymmetric reconnection events in JET discharges with extreme shear reversal
NASA Astrophysics Data System (ADS)
Stratton, B. C.; Breslau, J. A.; Budny, R. V.; Jardin, S. C.; Park, W.; Strauss, H. R.; Zakharov, L. E.; Alper, B.; Drozdov, V.; Hawkes, N. C.; Reyes-Cortes, S.; EFDA-JET Workprogramme, contributors to the
2002-07-01
Injection of lower hybrid heating and current drive into the current ramp-up phase of 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 qmin>1. Te-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.
NASA Astrophysics Data System (ADS)
Gizon, Laurent; Barucq, Hélène; Duruflé, Marc; Hanson, Chris S.; Leguèbe, Michael; Birch, Aaron C.; Chabassier, Juliette; Fournier, Damien; Hohage, Thorsten; Papini, Emanuele
2017-04-01
Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims: Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods: We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results: We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions: The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.
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.
Numerical Investigation of Transitional and Turbulent Axisymmetric Wakes at Supersonic Speeds
2007-11-02
Therefore, it follows P1,m,-1 = Plm ,2 Plm ,-2 = Plm ,31 PVxlm,-l PVxlm,2 P1Jxlm,-2: = PVxlm,32 CHAPTER 3. NUMERICAL METHOD 38 PVrlm,-1 - PVrlm,2 PVrlm,-2...physical space in the same fashion as for the axisymmetric problem. This leads to the following boundary conditions at the azimuthal location 0 = hAO...1,0 = -- P_-Im,2,0 ;-;D,1m,-2,0 = - PVrim,3,0O Pfelm,-1,o = PeIm,2,o PeIm,-2,o = Pelm,3,o, (3.29d) while for k = 1 Plm ,l,1 = 0, PV{Imj,, = 0, PV"Ii
Krishnamoorthy, Paramasivam; Sathyadevi, Palanisamy; Butorac, Rachel R; Cowley, Alan H; Bhuvanesh, Nattamai S P; Dharmaraj, Nallasamy
2012-04-21
A new series of geometrically different complexes containing ferrocenyl hydrazone ligands were synthesised by reacting suitable precursor complex [MCl(2)(PPh(3))(2)] with the ligands HL(1) or HL(2) (where M = Cu(II) or Ni(II); HL(1) = [Cp(2)Fe(CH=N-NH-CO-C(6)H(5))] (1) and HL(2) = [Cp(2)Fe(CH=N-NH-CO-C(5)H(4)N)]) (2). The new complexes of the composition [Cu(L(1))(PPh(3))(2)], (3) [Cu(L(2))(PPh(3))(2)] (4), [Ni(L(1))(2)] (5) and [Ni(L(2))(2)] (6) were characterised by various spectral studies. Among them, complexes 3 and 5 characterised by single crystal X-ray diffraction showed a distorted tetrahedral structure for the former with 1:1 metal-ligand stoichiometry, but a distorted square planar geometry with 1:2 metal-ligand stoichiometry in the case of the latter. Systematic biological investigations like DNA binding, DNA cleavage, protein binding, free radical scavenging and cytotoxicity activities were carried out using all the synthesised compounds and the results obtained were explained on the basis of structure-activity relationships. The binding constant (K(b)) values of the synthesised compounds are found to be in the order of magnitude 10(3)-10(5) M(-1) and also they exhibit significant cleavage of supercoiled (SC) pUC19 DNA in the presence of H(2)O(2) as co-oxidant. The conformational changes of bovine serum albumin (BSA) upon binding with the above complexes were also studied. In addition, concentration dependent free radical scavenging potential of all the synthesised compounds (1-6) was also carried out under in vitro conditions. Assays on the cytotoxicity of the above complexes against HeLa and A431 tumor cells and NIH 3T3 normal cells were also carried out.
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.
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…
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…
Venkatakrishnan, Thengarai S; Sahoo, Shaon; Bréfuel, Nicolas; Duhayon, Carine; Paulsen, Carley; Barra, Anne-Laure; Ramasesha, S; Sutter, Jean-Pascal
2010-05-05
Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {Fe(II)Nb(IV)} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb(IV), Mo(IV), W(IV)). X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H(2)O)Fe(L(1))}{M(CN)(8)}{Fe(L(1))}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L(1))}(2+) and {M(CN)(8)}(4-) units (L(1) stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L(1))} unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L(1))(H(2)O)(2)]Cl(2) a negative zero field splitting parameter of D approximately = -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L(1))(H(2)O)(2)]Cl(2) are also reported.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
NASA Astrophysics Data System (ADS)
Dolan, Sam R.; Shipley, Jake O.
2016-08-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.
1612 MHz OH maser emission from axisymmetric circumstellar envelopes - Miras
NASA Technical Reports Server (NTRS)
Collison, Alan J.; Fix, John D.
1992-01-01
Radiative transfer calculations are performed using a modified form of the Sobolev approximation to determine the inversion of the 1612 MHz line of OH in axisymmetric circumstellar envelopes around Miras. The mass loss is assumed to be occurring in the form of a smooth wind. Line profiles and maps are presented for three models of varying degrees of asymmetry and for various orientations of the envelopes. It is concluded that the axisymmetric models can reproduce many of the features of observed profiles and maps which both the standard, spherically symmetric model and the discrete emission model cannot easily explain. The model profiles reproduce all of the general features seen in the line profiles of real sources.
Numerical experiments on the oscillations of a rotating, axisymmetric galaxy
NASA Technical Reports Server (NTRS)
Miller, R. H.; Vandervoort, Peter O.; Welty, Daniel E.; Smith, B. F.
1989-01-01
Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.
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.
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.
Stability of flow over axisymmetric bodies with porous suction strips
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Reed, H. L.
1982-01-01
Linear triple deck, closed form solutions for mean-flow quantities are developed for axisymmetric incompressible flow past a body with porous strips. The solutions account for upstream influence and are linear superpositions of the flow past the body without suction plus the perturbations due to the suction strips. Flow past the suctionless body is calculated using the Transition Analysis Program System, and a simple linear optimization scheme to determine number, spacing, and mass flow rate through the strips on an axisymmetric body is developed using the linear, triple-deck, closed-form solutions. The theory is demonstrated by predicting optimal strip distributions, and the effect of various adverse pressure-gradient situations on stability is studied.
On the stability of compressible flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Malik, M. R.; Spall, R. E.
1991-01-01
Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.
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.
The axisymmetric jet in a rotating reference frame
NASA Astrophysics Data System (ADS)
Lawrie, A. G. W.; Duran-Matute, M.; Scott, J. F.; Godeferd, F.; Flor, J.-B.; Cambon, C.; Danaila, L.
2011-12-01
The axisymmetric jet is a geometrically simple, statistically stationary example of inhomogenous turbulence. Considering conservation of volume and momentum, Morton et al. (1956) offered a prediction of jet development, characterised solely by an unknown, constant entrainment coefficient. The presence of background rotation complicates the kinematics of the entrainment, and without special treatment, the jet suffers a helical instability. Here, we present one technique which stabilises the axisymmetric jet, yet preserves its desirable turbulent properties. The jet offers a steady-state flow in which there is an axial variation of local Rossby number, and after decay along the axis to a critical value, cones of inertial waves emerge. In this paper, we demonstrate these features using our numerical software MOBILE, offer our solution to stabilise the jet, and explain the mechanisms involved.
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.
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.
Asymptotic solution of the problem for a thin axisymmetric cavern
NASA Technical Reports Server (NTRS)
Serebriakov, V. V.
1973-01-01
The boundary value problem which describes the axisymmetric separation of the flow around a body by a stationary infinite stream is considered. It is understood that the cavitation number varies over the length of the cavern. Using the asymptotic expansions for the potential of a thin body, the orders of magnitude of terms in the equations of the problem are estimated. Neglecting small quantities, a simplified boundary value problem is obtained.
Generalized Rayleigh criterion for non-axisymmetric centrifugal instabilities
NASA Astrophysics Data System (ADS)
Billant, Paul; Gallaire, François
2005-10-01
The well-known Rayleigh criterion is a necessary and sufficient condition for inviscid centrifugal instability of axisymmetric perturbations. We have generalized this criterion to disturbances of any azimuthal wavenumber m by means of large-axial-wavenumber WKB asymptotics. A sufficient condition for a free axisymmetric vortex with angular velocity Ω(r) to be unstable to a three-dimensional perturbation of azimuthal wavenumber m is that the real part of the growth rate [σ (r) =-imΩ(r)+√{-φ(r)}] is positive at the complex radius r{=}r_0 where ∂ σ (r)/∂ r=0, i.e. [φ'(r_0) =-2{i}mΩ'(r_0)√{-φ(r_0)},] where φ=(1/r^3)∂{r^4Ω^2}/∂ {r} is the Rayleigh discriminant, provided that some a posteriori checks are satisfied. The application of this new criterion to various classes of vortex profiles shows that the growth rate of non-axisymmetric disturbances decreases as m increases until a cutoff is reached. The criterion is in excellent agreement with numerical stability analyses of the Carton & McWilliams (1989) vortices and allows one to analyse the competition between the centrifugal instability and the shear instability. The generalized criterion is also valid for a vertical vortex in a stably stratified and rotating fluid, except that φ becomes φ=(1/r^3)∂{r^4(Ω+Ω_b)^2/∂r, where Ω_b is the background rotation about the vertical axis. The stratification is found to have no effect. For the Taylor Couette flow between two coaxial cylinders, the same criterion applies except that r_0 is real and equal to the inner cylinder radius. In sharp contrast, the maximum growth rate of non-axisymmetric disturbances is then independent of m.
The Effect of Flow Curvature on the Axisymmetric Wake
NASA Astrophysics Data System (ADS)
Holmes, Marlin; Naughton, Jonathan
2016-11-01
The swirling turbulent wake is a perturbation to the canonical axisymmetric turbulent wake. Past studies of the axisymmetric turbulent wake have increased understanding of wake Reynolds number influence on wake characteristics such as centerline wake velocity deficit and wake width. In comparison, the axisymmetric turbulent swirling wake has received little attention. Earlier work by our group has shown that the addition of swirl can change the characteristics of the wake. The goal of this current work is to examine how wake mean flow quantities are related to the wake Reynolds number and the swirl number, where the latter quantity is the ratio of the angular momentum flux to the axial momentum deficit flux. A custom designed swirling wake generator is used in a low turbulence intensity wind tunnel flow to study the turbulent swirling wake in isolation. Stereoscopic Particle Image Velocimetry is used to obtain three component velocity fields in the axial-radial plane. From this data, the wake Reynolds number, the swirl number, centerline velocity decay, wake width, and other relevant wake mean flow quantities are determined. Using these results, the impact of swirl on wake development is discussed. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award # DE-SC0012671.
Non-axisymmetric magnetic fields and toroidal plasma confinement
NASA Astrophysics Data System (ADS)
Boozer, Allen H.
2015-02-01
The physics of non-axisymmetry is a far more important topic in the theory of toroidal fusion plasmas than might be expected. (1) Even a small toroidal asymmetry in the magnetic field strength, δ ≡ ∂ln B/∂φ ˜ 10-4, can cause an unacceptable degradation in performance. (2) Nevertheless, asymmetries—even large asymmetries δ ˜ 1—can give beneficial plasma control and circumvent issues, such as magnetic-configuration maintenance and plasma disruptions, that make axisymmetric fusion devices problematic. Viewed from prospectives that are adequate for designing and studying axisymmetric plasmas, the physics of non-axisymmetric plasmas appears dauntingly difficult. Remarkably, Maxwell's equations provide such strong constraints on the physics of toroidal fusion plasmas that even a black-box model of a plasma answers many important questions. Kinetic theory and non-equilibrium thermodynamics provide further, but more nuanced, constraints. This paper is organized so these constraints can be used as a basis for the innovations and for the extrapolations that are required to go from existing experiments to fusion systems. Outlines are given of a number of calculations that would be of great importance to ITER and to the overall fusion program and that could be carried out now with limited resources.
Axisymmetric Simulations of the ITER Vertical Stability Coil
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.
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
Evolution of the Sun's non-axisymmetric toroidal field
NASA Astrophysics Data System (ADS)
Martin-Belda, D.; Cameron, R. H.
2017-07-01
Aims: We aim to infer the sub-surface distribution of the Sun's non-axisymmetric azimuthal magnetic flux from observable quantities, such as the surface magnetic field and the large scale plasma flows. Methods: We have built a kinematic flux transport model of the solar dynamo based on the Babcock-Leighton framework. We constructed the source term for the poloidal field using SOLIS magnetograms spanning three solar cycles. Based on this source we calculated the azimuthal flux below the surface. The flux transport model has two free parameters which we constrained using sunspot observations from cycle 22. We compared the model results with observations from cycle 23. Results: The structure of the azimuthal field is mainly axisymmetric. The departures from axisymmetry represent, on average, 3% of the total azimuthal flux. Owing to its relative weakness, the non-axisymmetric structure of the azimuthal field does not have a significant impact on the location in which the emergences appear or on the amount of flux contained in them. We find that the probability of emergence is a function of the ratio between the flux content of an active region and the underlying azimuthal flux.
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
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
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.
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.
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
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.
Self consistent MHD modeling of the solar wind from coronal holes with distinct geometries
NASA Technical Reports Server (NTRS)
Stewart, G. A.; Bravo, S.
1995-01-01
Utilizing an iterative scheme, a self-consistent axisymmetric MHD model for the solar wind has been developed. We use this model to evaluate the properties of the solar wind issuing from the open polar coronal hole regions of the Sun, during solar minimum. We explore the variation of solar wind parameters across the extent of the hole and we investigate how these variations are affected by the geometry of the hole and the strength of the field at the coronal base.
Self consistent MHD modeling of the solar wind from coronal holes with distinct geometries
NASA Technical Reports Server (NTRS)
Stewart, G. A.; Bravo, S.
1995-01-01
Utilizing an iterative scheme, a self-consistent axisymmetric MHD model for the solar wind has been developed. We use this model to evaluate the properties of the solar wind issuing from the open polar coronal hole regions of the Sun, during solar minimum. We explore the variation of solar wind parameters across the extent of the hole and we investigate how these variations are affected by the geometry of the hole and the strength of the field at the coronal base.
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.
Developments in special geometry
NASA Astrophysics Data System (ADS)
Mohaupt, Thomas; Vaughan, Owen
2012-02-01
We review the special geometry of Script N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we disucss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
NASA Astrophysics Data System (ADS)
McNair, S. Lauren; Tragesser, Steven
2017-03-01
A unique formulation of the solution to a spinning, nearly axisymmetric rigid-body is presented. Direct integration of the linearized equations of motion gives accurate results for nearly axisymmetric inertia ellipsoids while avoiding the complexity of more general formulations. The simplicity of the formulation lends itself to a better understanding of the system behavior. Specifically, the motion of the spin axis for this nearly axisymmetric case is described by an oblate epicycloid, providing an extension of the classic epicycloid solution for axisymmetric objects.
Non-axisymmetric shapes of a rotating drop in an immiscible system
NASA Technical Reports Server (NTRS)
Wang, T. G.; Tagg, R.; Cammack, L.; Croonquist, A. P.
1982-01-01
The nonaxisymmetric shapes of a rotating drop in an immiscible system were studied. Five basic families of shapes (axisymmetric, two-lobed, three-lobed, four-lobed, and toroidal) were observed. The sequence (axisymmetric to two-lobed to three-lobed to four-lobed to toroidal) seems to be linked to increasing spin-up velocity. For the axisymmetric case, direct comparisons of experiments with the theory of a free rotating drop were surprisingly good the equatorial area differs from theory by only 30%. Furthermore, the non-axisymmetric shapes are in good qualitative agreement with the theory, although the theory does not address the presence of an outer fluid.
NASA Technical Reports Server (NTRS)
Woollett, R. R.; Meleason, E. T.; Choby, D. A.
1974-01-01
An experimental investigation determined the drag and pressure performance of an axisymmetric supersonic inlet when operated in the transonic speed range. The inlet configuration was derived from a Mach 2.5 mixed compression inlet design with assumed variable geometry. At typical engine airflows the drag coefficient varied from 0.057 to 0.192 when the Mach number changed from 0.80 to 1.27. The presence of a wing simulator resulted in a sizable increase in total drag at Mach 1.2. This interference drag, which is roughly a 0.1 increase in drag coefficient, originates equally from an increase in both additive and cowl pressure drag.
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'…
Twistors to twisted geometries
Freidel, Laurent; Speziale, Simone
2010-10-15
In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.
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…
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…
Geometry of multihadron production
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.
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…
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.
Non-Axisymmetric Inflatable Pressure Structure (NAIPS) Full-Scale Pressure Test
NASA Technical Reports Server (NTRS)
Jones, Thomas C.; Doggett, William R.; Warren, Jerry E.; Watson, Judith J.; Shariff, Khadijah; Makino, Alberto; Yount, Bryan C.
2017-01-01
Inflatable space structures have the potential to significantly reduce the required launch volume for large pressure vessels required for exploration applications including habitats, airlocks and tankage. In addition, mass savings can be achieved via the use of high specific strength softgoods materials, and the reduced design penalty from launching the structure in a densely packaged state. Large inclusions however, such as hatches, induce a high mass penalty at the interfaces with the softgoods and in the added rigid structure while reducing the packaging efficiency. A novel, Non-Axisymmetric Inflatable Pressure Structure (NAIPS) was designed and recently tested at NASA Langley Research Center to demonstrate an elongated inflatable architecture that could provide areas of low stress along a principal axis in the surface. These low stress zones will allow the integration of a flexible linear seal that substantially reduces the added mass and volume of a heritage rigid hatch structure. This paper describes the test of the first full-scale engineering demonstration unit (EDU) of the NAIPS geometry and a comparison of the results to finite element analysis.
Effects of streamwise convergence in radius on the laminar forced convection in axisymmetric ducts
Lee, S.H.K.; Jaluria, Y.
1995-07-01
A systematic study has been carried out on the effects of streamwise convergence in radius on the laminar forced convection in an axisymmetric duct. This transport circumstance is relevant to many practical processes such as injection molding, glass molding, fiber drawing, and extrusion, where large variations in the radius may occur downstream and where the flow rates are generally small enough to yield a laminar flow. A fairly uncommon transformation technique was used to transform the pseudo-transient conservation equations for the stream function, vorticity, and energy, and several new numerical techniques were developed. These include a nonuniform grid scheme, a second-order-accurate vorticity condition for an arbitrary surface, and a nominally second-order-accurate vorticity condition for an arbitrary surface, and a nominally second-order-accurate approximation for the derivatives on a nonuniform grid. The three geometries studied were those of the straight, periodic, and converging ducts, where the results for the first two were obtained mainly for validation purposes. However, new results were also obtained for the periodic duct, showing the attainment of a sinusoidal steady state with the local Nusselt number varying from 1.0 to 6.0. For the converging duct, the local Nusselt number was found, for the first time, to increase with increasing convergence of the duct wall.
NASA Astrophysics Data System (ADS)
Zmijanovic, V.; Lago, V.; Sellam, M.; Chpoun, A.
2014-01-01
Transverse secondary gas injection into the supersonic flow of an axisymmetric convergent-divergent nozzle is investigated to describe the effects of the fluidic thrust vectoring within the framework of a small satellite launcher. Cold-flow dry-air experiments are performed in a supersonic wind tunnel using two identical supersonic conical nozzles with the different transverse injection port positions. The complex three-dimensional flow field generated by the supersonic cross-flows in these test nozzles was examined. Valuable experimental data were confronted and compared with the results obtained from the numerical simulations. Different nozzle models are numerically simulated under experimental conditions and then further investigated to determine which parameters significantly affect thrust vectoring. Effects which characterize the nozzle and thrust vectoring performances are established. The results indicate that with moderate secondary to primary mass flow rate ratios, ranging around 5 %, it is possible to achieve pertinent vector side forces. It is also revealed that injector positioning and geometry have a strong effect on the shock vector control system and nozzle performances.
Non-axisymmetric flows on hot Jupiters with oblique magnetic fields
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.
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.
Space reconstruction of the morphology and kinematics of axisymmetric radio sources
NASA Astrophysics Data System (ADS)
Diep, P. N.; Phuong, N. T.; Hoai, D. T.; Nhung, P. T.; Thao, N. T.; Tuan-Anh, P.; Darriulat, P.
2016-10-01
The unprecedented quality of the observations available from the Atacama Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making the best of them. Reconstructing in space the morphology and kinematics of radio sources is an underdetermined problem that requires imposing additional constraints for its solution. The hypothesis of rotational invariance, which is a good approximation to, or at least a good reference for the description of the gas envelopes of many evolved stars and protostars, is particularly efficient in this role. In the first part of the article, a systematic use of simulated observations allows us for identifying the main problems and for constructing quantities aimed at solving them. In particular the evaluation of the orientation of the star axis in space and the differentiation between expansion along the star axis and rotation about it are given special attention. The use of polar rather than Cartesian sky coordinates to display the results of the analysis is shown to often better match the morphology and kinematics of actual stars. The radial dependence of the gas density and temperature and the possible presence of velocity gradients are briefly considered. In the second part, these results are applied to a few stars taken as examples with the aim of evaluating their usefulness when applied to concrete cases. A third part takes stock of what precedes and formulates some guidelines for modelling the radio emission of axisymmetric radio sources, limited however to the mathematics and geometry of the problem, physics considerations being generally ignored.
Passive control of base pressure on an axisymmetric blunt body using a perimetric slit
NASA Astrophysics Data System (ADS)
García de la Cruz, Juan Marcos; Oxlade, Anthony R.; Morrison, Jonathan F.
2017-04-01
The effect on the base pressure of a thin slit located at the base edge of a blunt axisymmetric body, communicating an internal cavity with the external flow, is investigated. A parametric study is performed of the effect on base pressure of changes in slit size and cavity depth. The base pressure increases initially with increasing cavity depth, but saturates at a depth which depends on the slit size. The base pressure increases monotonically up to 5 % with increasing slit size for the geometries tested. An upper limit of base pressure recovery of 20 % is extrapolated from the data. It is observed that the main effect of the slit is to reduce the instantaneous pressure asymmetry, which is linked to the total base pressure in a similar fashion for all the slit sizes. As a second-order effect, for highly asymmetric pressure distributions, the slit produces a base pressure increase not associated with the base pressure asymmetry. The results suggest a global effect of the slit on the wake due to a diametrical flow within the cavity driven by the pressure differences across the slit and regulated by the largest of the pressure drops between the slit and cavity. The slit also reduces the periodic base pressure fluctuations, corresponding mainly to the vortex shedding, and increases the rotational speed of the wake.
Filoux, Erwan; Callé, Samuel; Lou-Moeller, Rasmus; Lethiecq, Marc; Levassort, Franck
2010-05-01
The transient analysis of piezoelectric transducers is often performed using finite-element or finite-difference time-domain methods, which efficiently calculate the vibration of the structure but whose numerical dispersion prevents the modeling of waves propagating over large distances. A second analytical or numerical simulation is therefore often required to calculate the pressure field in the propagating medium (typically water) to deduce many important characteristics of the transducer, such as spatial resolutions and side lobe levels. This is why a hybrid algorithm was developed, combining finite- difference and pseudo-spectral methods in the case of 2-D configurations to simulate accurately both the generation of acoustic waves by the piezoelectric transducer and their propagation in the surrounding media using a single model. The algorithm was redefined in this study to take all three dimensions into account and to model single-element transducers, which usually present axisymmetrical geometry. This method was validated through comparison of its results with those of finite-element software, and was used to simulate the behavior of planar and lens-focused transducers. A high-frequency (30 MHz) transducer based on a screen-printed piezoelectric thick film was fabricated and characterized. The numerical results of the hybrid algorithm were found to be in good agreement with the experimental measurements of displacements at the surface of the transducer and of pressure radiated in water in front of the transducer.
Global modelling of non-axisymmetric disruptions and halo currents in tokamaks
NASA Astrophysics Data System (ADS)
McCarrick, James F.
1997-12-01
As tokamak plasmas become more robust with the development of increasingly advanced operating regimes, the occurrence of plasma disruptions places a greater demand on the tokamak structure. In particular, the flow of halo currents, large currents which appear in tokamak vacuum vessels as a result of direct contact with bulk plasma, has become a matter of increasing concern. Experimental measurements have confirmed the existence of large, toroidally asymmetric currents which flow poloidally in the wall, exerting strong localized forces on the wall as they interact with the toroidal magnetic field. A new model has been developed to study this phenomenon, based on the use of nested sheet currents to represent a disrupting plasma. This model contains the minimum number of degrees of freedom which permit the flow of continuous, non-axisymmetric poloidal and toroidal currents; furthermore, the model can be put into a compact integral formulation which allows rapid numerical solution even in the presence of complicated tokamak geometries. A fast code called TSPS-3D has been written to solve the sheet current model; the code has been matched against experimental data and used to examine basic scaling relationships of halo currents and the resulting J x B loads with plasma parameters. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253- 1690.)
Linear stability analysis of axisymmetric flow over a sudden expansion in an annular pipe
NASA Astrophysics Data System (ADS)
Beladi, Behnaz; Kuhlmann, Hendrik Christoph
2016-11-01
A global temporal linear stability analysis is performed of the fully-developed axisymmetric incompressible Newtonian flow in an annular pipe with a sudden radially-inward expansion. The geometry is characterized by the radial expansion ratio (radial step height to the outlet gap width) and the outlet radius ratio (inner-to-outer radius). Stability boundaries have been calculated with finite volumes for an outlet radius ratio of 0 . 1 and expansion ratios from 0 . 25 to 0 . 75 . For expansion ratios less than 0 . 55 the most dangerous mode has an azimuthal wave number m = 3 , whereas m = 2 for larger expansion ratios. An a posteriori analysis of the kinetic energy transferred between the basic state and the critical mode allows to check the energy conservation and to identify the physical instability mechanism. For all expansion ratios considered the basic flow arises as an annular jet between two separation zones which are located immediately after the step. The jet gradually widens downstream before reattaching to the cylinders. The deceleration of the flow associated with the widening of the jet is found to be the primary source of energy for the critical modes.
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).
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
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.
A simple, analytical, axisymmetric microburst model for downdraft estimation
NASA Technical Reports Server (NTRS)
Vicroy, Dan D.
1991-01-01
A simple analytical microburst model was developed for use in estimating vertical winds from horizontal wind measurements. It is an axisymmetric, steady state model that uses shaping functions to satisfy the mass continuity equation and simulate boundary layer effects. The model is defined through four model variables: the radius and altitude of the maximum horizontal wind, a shaping function variable, and a scale factor. The model closely agrees with a high fidelity analytical model and measured data, particularily in the radial direction and at lower altitudes. At higher altitudes, the model tends to overestimate the wind magnitude relative to the measured data.
Area-angular-momentum inequality for axisymmetric black holes.
Dain, Sergio; Reiris, Martin
2011-07-29
We prove the local inequality A≥8π|J|, where A and J are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes. Hence, we prove the validity of this inequality for all dynamical (not necessarily near equilibrium) axially symmetric black holes.
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.
Planetoid string solutions in 3+1 axisymmetric spacetimes
de Vega, H.J.; Egusquiza, I.L.
1996-12-01
The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid ansatz. This is a straight nonoscillating string, radially disposed which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass{sup 2}) (Regge) relation for the planetoids, which turns out to be nonlinear. {copyright} {ital 1996 The American Physical Society.}
A simplified analytic form for generation of axisymmetric plasma boundaries
NASA Astrophysics Data System (ADS)
Luce, T. C.
2017-04-01
An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. Examples of generation of boundaries, including tests with an equilibrium solver, are given.
An axisymmetric PFEM formulation for bottle forming simulation
NASA Astrophysics Data System (ADS)
Ryzhakov, Pavel B.
2017-01-01
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.
Optimal shapes of axisymmetric bodies penetrating into soil
NASA Astrophysics Data System (ADS)
Kotov, V. L.; Linnik, E. Yu.; Tarasova, A. A.
2016-09-01
This paper presents the results of a study of the shapes of axisymmetric bodies with minimum drag and maximum depth of penetration into the plastic soils. Optimal shapes of bodies of revolution of given length and cross-sectional radius with generatrices represented by line segments are obtained by a modified method of local variations. The problem is solved using a binomial quadratic model of local interaction, including inertial and strength terms containing constant and Coulomb frictions. The drag forces and the penetration depth of cones and the obtained bodies of optimal shape are determined at different penetration velocities.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
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)
Explosive loading of deformable gas-permeable axisymmetric structural elements
NASA Astrophysics Data System (ADS)
Glazova, E. G.; Konstantinov, A. Yu.; Kochetkov, A. V.; Krylov, S. V.
2016-09-01
A mathematical model is proposed which describes the interrelated processes of unsteady elastoplastic deformation of stacks of woven metal wire mesh and wave processes in pore gas in a two-dimensional axisymmetric approximation. The nonlinear equations of the dynamics of two interpenetrating continua are solved numerically using a modified Godunov's scheme. The problem of explosive loading of a multilayer shell with an internal permeable deformable layer is solved. The results of numerical solutions are compared with experimental data. The influence of the gas-permeable layer on shell deformation is determined.
Acoustic Bessel-like beam formation by an axisymmetric grating
NASA Astrophysics Data System (ADS)
Jiménez, N.; Romero-García, V.; Picó, R.; Cebrecos, A.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.; Staliunas, K.
2014-04-01
We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves.
MHD instabilities in accretion mounds - I. 2D axisymmetric simulations
NASA Astrophysics Data System (ADS)
Mukherjee, Dipanjan; Bhattacharya, Dipankar; Mignone, Andrea
2013-04-01
We have performed stability analysis of axisymmetric accretion mounds on neutron stars in high-mass X-ray binaries by 2D magnetohydrodynamic (MHD) simulations with the PLUTO MHD code. We find that the mounds are stable with respect to interchange instabilities, but the addition of excess mass destabilizes the equilibria. Our simulations confirm that accretion mounds are unstable with respect to MHD instabilities beyond a threshold mass. We investigate both filled and hollow mounds and for the latter also compute the expected profile of cyclotron resonance scattering features (CRSF). In comparison to the CRSF from filled mounds reported in our earlier work, hollow mounds display wider and more complex line profiles.
Coherent optical non-reciprocity in axisymmetric resonators.
Lenferink, Erik J; Wei, Guohua; Stern, Nathaniel P
2014-06-30
We describe an approach to optical non-reciprocity that exploits the local helicity of evanescent electric fields in axisymmetric resonators. By interfacing an optical cavity to helicity-sensitive transitions, such as Zeeman levels in a quantum dot, light transmission through a waveguide becomes direction-dependent when the state degeneracy is lifted. Using a linearized quantum master equation, we analyze the configurations that exhibit non-reciprocity, and we show that reasonable parameters from existing cavity QED experiments are sufficient to demonstrate a coherent non-reciprocal optical isolator operating at the level of a single photon.
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).
Vortex motion in axisymmetric piston-cylinder configurations
Shih, T.I.P.; Smith, G.E.; Springer, G.S.
1982-09-01
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.
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.
Initial condition effect on pressure waves in an axisymmetric jet
NASA Technical Reports Server (NTRS)
Miles, Jeffrey H.; Raman, Ganesh
1988-01-01
A pair of microphones (separated axially by 5.08 cm and laterally by 1.3 cm) are placed on either side of the jet centerline to investigate coherent pressure fluctuations in an axisymmetric jet at Strouhal numbers less than unity. Auto-spectra, transfer-function, and coherence measurements are made for a tripped and untripped boundary layer initial condition. It was found that coherent acoustic pressure waves originating in the upstream plenum chamber propagate a greater distance downstream for the tripped initial condition than for the untripped initial condition. In addition, for the untripped initial condition the development of the coherent hydrodynamic pressure waves shifts downstream.
On the attitude propagation of an axisymmetric satellite
NASA Astrophysics Data System (ADS)
Pizarro-Rubio, A.; Pelaez, J.
2008-12-01
This paper describes the method developed in the Group of Tether Dynamics of the UPM to gain accuracy in the numerical propagation of the attitude dynamics of a rigid axisymmetric spacecraft. We use a perturbation method which takes as unperturbed problem the Euler-Poinsot case (torque free). The perturbed problem provides the motion forced by non-vanishing external torques. Some numerical comparisons have been carried out to check the kindness of the procedure taking as forced motion some particular case of the Lagrange top, whose analytical solution permits an easy determination of the errors made in the numerical description of the motion.
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.
Axisymmetric vibrations of laminated composite conical shells with varying thickness
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.
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.
On the granular stress-geometry equation
NASA Astrophysics Data System (ADS)
DeGiuli, Eric; Schoof, Christian
2014-01-01
Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that i) the equation imposes that the voids cannot carry stress, ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and iii) the packing fabric plays an essential role.
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.
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.
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
Dynamo Models for Saturn's Axisymmetric Magnetic Field: Finding the Non-axisymmetry
NASA Astrophysics Data System (ADS)
Stanley, S.; Tajdaran, K.
2013-12-01
Magnetic field measurements by the Cassini mission have confirmed the earlier Pioneer 11 and Voyager missions' results that Saturn's observed magnetic field is extremely axisymmetric. For example, Saturn's dipole tilt is less than 0.06 degrees. The near-perfect axisymmetry of Saturn's dipole is troubling because of Cowling's Theorem which states that an axisymmetric magnetic field cannot be maintained by a dynamo. However, Cowling's Theorem applies to the magnetic field generated inside the dynamo source region and we can avert any contradiction with the theorem if we can find reason for a non-axisymmetric field generated inside the dynamo region to have an axisymmetric potential field observed at satellite altitude. Stevenson (1980) proposed that the Helium Insolubility Layer (HIL), which forms at the top of the metallic hydrogen layer in Saturn, could provide such a mechanism. This layer is stably stratified and electrically conducting. Differential rotation in this layer, which surrounds the dynamo source region, could act to attenuate the non-axisymmetric features and hence produce an axisymmetric observed magnetic field. In previous work, we used three-dimensional self-consistent numerical dynamo models to demonstrate that the HIL can produce a more axisymmetric field. We found that the morphology of the zonal flows in the layer is a crucial factor for magnetic field axisymmetry. Here we investigate the influence of the HIL's thickness, stability and thermal wind intensity on the axisymmetrization of the field. We find regions in parameter space for producing axisymmetric magnetic fields with similar spectral properties as Saturn's field. We also find that non-axisymmetric features exist at the surface at smaller wavelengths (i.e. higher multipoles) at high latitudes. This suggests that Cassini's final orbital passes of Saturn in 2017 may find non-axisymmetric features in Saturn's magnetic field for the first time.
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.
Omnidirectional Lamb waves by axisymmetrically-configured magnetostrictive patch transducer.
Lee, Joo Kyung; Kim, Hoe Woong; Kim, Yoon Young
2013-09-01
This work presents the generation of omnidirectional Lamb waves by a new magnetostrictive patch transducer (MPT) and investigates its generation mechanism. Although MPTs have been widely used for wave transduction in plates and pipes, no investigation reports the generation of omnidirectional Lamb waves in a plate by an MPT. For the generation, we propose an axisymmetrically-configured MPT that installs multiple axisymmetric turns of coil outside of a permanent cylindrical magnet located above the center of a circular magnetostrictive patch. After confirming the omnidirectivity of the proposed MPT experimentally, the mechanism of the Lamb wave generation and its frequency characteristics are investigated. It is also shown that the Lamb wave is most efficiently generated in a test plate when its wavelength is equal to two-thirds of the magnetostrictive patch diameter. If this wavelength¿patch diameter relation holds, the second radial extensional vibration mode of the patch of the proposed MPT is shown to be the mode responsible for generating the Lamb wave in a plate.
Axisymmetric structure of the long lasting summer Arctic cyclones
NASA Astrophysics Data System (ADS)
Aizawa, Takuro; Tanaka, H. L.
2016-09-01
Arctic cyclones are unique low pressure systems in the Arctic, which are different from the tropical cyclones and the mid-latitude cyclones. The axisymmetric structures of two major Arctic cyclones which appeared in June 2008 and August 2012 are examined based on the cylindrical coordinate system around the Arctic cyclone. The result demonstrates that the Arctic cyclone has a deep barotropic cyclonic circulation, a secondary circulation in the troposphere, a downdraft at the lower stratosphere, a coupling of a warm core at the lower stratosphere and a cold core in the troposphere, and a deep tropopause folding over the cyclone center. The horizontal scale of the Arctic cyclone reaches 5000 km in diameter which is one of the largest cyclones found on the Earth. Note that the cyclone of June 2008 appears showing axisymmetric cyclonic circulations at the surface level. The cyclone of 2012 is characterized by the structure change from the cold core to the warm core at the lower stratosphere, indicating a shift from the ordinary baroclinic cyclone to the typical Arctic cyclone. Although additional studies are needed, a schematic diagram of the Arctic cyclone is proposed in this study.
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.
Generalized energy principle for flute perturbations in axisymmetric mirror machines
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.
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.
THE ADVECTION OF SUPERGRANULES BY THE SUN'S AXISYMMETRIC FLOWS
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.
Interaction of two high Reynolds number axisymmetric turbulent wakes
NASA Astrophysics Data System (ADS)
Obligado, M.; Klein, S.; Vassilicos, J. C.
2015-11-01
With the recent discovery of non-equilibrium high Reynolds number scalings in the wake of axisymmetric plates (Nedic et al., PRL, 2013), it has become of importance to develop an experimental technique that permits to easily discriminate between different wake scalings. We propose an experimental setup that tests the presence of non-equilibrium turbulence using the streamwise variation of velocity fluctuations between two bluff bodies facing a flow. We have studied two different sets of plates (one with regular and another with irregular peripheries) with Hot-Wire Anemometry in a wind tunnel. By acquiring streamwise profiles for different plate separations and identifying the wake interaction length for each separation it is possible to estimate the streamwise evolution of the single wake width. From this evolution it is also possible to deduce the turbulence dissipation scalings. This work generalizes previous studies on the interaction of plane wakes (see Gomes-Fernandes et al., JFM, 2012) to include axisymmetric wakes. We find that the wake interaction length proposed in this cited work and a constant anisotropy assumption can be used to collapse the streamwise developments of the first three moments.
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.
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.
Two-soliton stationary axisymmetric sprouts from Weyl seeds
NASA Astrophysics Data System (ADS)
Zellerin, T.; Semerák, O.; Zellerin, T.
2000-12-01
The Belinskii-Zakharov inverse-scattering method is employed in its two-soliton version with a general Weyl seed, to obtain a stationary axisymmetric metric which in spheroidal coordinates of the Boyer-Lindquist type appears as a generalization of the Kerr-NUT solution. It contains several constants and two functions which can be found by integration from the seed potential (they can also be written as Legendre series). With a natural choice of parameters, the solution describes a reflectionally symmetric, asymptotically flat spacetime of a rotating black hole surrounded by a stationary axisymmetric source inherited from the seed. In a static limit, it goes over to a nonlinear superposition of the seed with a Schwarzschild black hole. A number of properties of the obtained class of solutions is given, in particular the characteristics of the horizon. For moderate angular momenta there seem to be no singularities on and outside the horizon. For a thin annular disc as the seed, the solution can represent a stationary thin annular disc around a rotating black hole.
NASA Astrophysics Data System (ADS)
Aiken, Brenda L.
The Commonwealth of Virginia requires high school students to receive a passing grade in core courses and a passing score on End-of-Course Standards of Learning (EOC SOL) tests to receive verified credits that lead to a Virginia high school diploma. These tests are believed to accurately reflect what students should know and be able to do in order to experience success in their endeavors beyond high school. For some students remediation is required to experience success on EOC SOL tests. This study sought to determine the effect of a County's public high school summer remediation program on student gains on EOC SOL tests in Algebra I, Biology, Chemistry, Geometry, and World History and Geography II. Specifically, the purpose of the study sought to determine the following: (a) If significant gains were made by students who attended the summer remediation program; (b) If significant gains were made by students who did not attend the summer remediation program; (c) If there were differences in gain scores of students who attended and those who did not attend the summer remediation program; and (d) If there were differences in gain scores among students who attended the summer remediation program related to school site, gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. The results of the study indicate that students who attended and those who did not attend the summer remediation program made significant gains. However, the gains for students who attended the summer remediation program were significantly greater than the gains made by students who did not attend. The study also found that there were no significant differences in gain scores among students who attended the summer remediation program related to gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. There were significant differences in Algebra I gain scores related to school site. Recommendations for
NASA Technical Reports Server (NTRS)
Robertshaw, H. H.; Reinholtz, C. F.
1989-01-01
Vibration control and kinematic control with variable-geometry trusses are covered. The analytical approach taken is to model each actuator with lumped masses and model a beam with finite elements, including in each model the generalized reaction forces from the beam on the actuator or vice versa. It is concluded that, from an operational standpoint, the variable-geometry truss actuator is more favorable than the inertia-type actuator. A spatial variable-geometry truss is used to test out rudimentary robotic tasks.
Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core.
Cooper, W A; Graves, J P; Pochelon, A; Sauter, O; Villard, L
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core
Cooper, W. A.; Graves, J. P.; Pochelon, A.; Sauter, O.; Villard, L.
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
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
New chemical-DSMC method in numerical simulation of axisymmetric rarefied reactive flow
NASA Astrophysics Data System (ADS)
Zakeri, Ramin; Kamali Moghadam, Ramin; Mani, Mahmoud
2017-04-01
The modified quantum kinetic (MQK) chemical reaction model introduced by Zakeri et al. is developed for applicable cases in axisymmetric reactive rarefied gas flows using the direct simulation Monte Carlo (DSMC) method. Although, the MQK chemical model uses some modifications in the quantum kinetic (QK) method, it also employs the general soft sphere collision model and Stockmayer potential function to properly select the collision pairs in the DSMC algorithm and capture both the attraction and repulsion intermolecular forces in rarefied gas flows. For assessment of the presented model in the simulation of more complex and applicable reacting flows, first, the air dissociation is studied in a single cell for equilibrium and non-equilibrium conditions. The MQK results agree well with the analytical and experimental data and they accurately predict the characteristics of the rarefied flowfield with chemical reaction. To investigate accuracy of the MQK chemical model in the simulation of the axisymmetric flow, air dissociation is also assessed in an axial hypersonic flow around two geometries, the sphere as a benchmark case and the blunt body (STS-2) as an applicable test case. The computed results including the transient, rotational and vibrational temperatures, species concentration in the stagnation line, and also the heat flux and pressure coefficient on the surface are compared with those of the other chemical methods like the QK and total collision energy (TCE) models and available analytical and experimental data. Generally, the MQK chemical model properly simulates the chemical reactions and predicts flowfield characteristics more accurate rather than the typical QK model. Although in some cases, results of the MQK approaches match with those of the TCE method, the main point is that the MQK does not need any experimental data or unrealistic assumption of specular boundary condition as used in the TCE method. Another advantage of the MQK model is the
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)
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)
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)
Flyby Geometry Optimization Tool
NASA Technical Reports Server (NTRS)
Karlgaard, Christopher D.
2007-01-01
The Flyby Geometry Optimization Tool is a computer program for computing trajectories and trajectory-altering impulsive maneuvers for spacecraft used in radio relay of scientific data to Earth from an exploratory airplane flying in the atmosphere of Mars.
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)
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)
Facilitating Understandings of Geometry.
ERIC Educational Resources Information Center
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
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)
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
NASA Astrophysics Data System (ADS)
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Tautges, Timothy J.
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 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 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.
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.
Asymptotic and numerical solutions of the axisymmetric moist Hadley circulation
NASA Astrophysics Data System (ADS)
Burns, Samuel P.
A simplified model of the moist axisymmetric Hadley circulation is examined in the asymptotic limit in which surface friction is strong and the meridional wind is weak compared to the zonal wind. This model consists of the Quasi-Equilibrium Tropical Circulation Model (QTCM) equations on an axisymmetric aquaplanet equatorial beta-plane. This model includes two vertical momentum modes, one baroclinic and one barotropic. Prior studies use either continuous stratification, or a shallow water system best viewed as representing the upper troposphere. The analysis here focuses on the interaction of the baroclinic and barotropic modes, and the way in which this interaction allows the constraints on the circulation known from the fully stratified case to be satisfied in an approximate way. The dry equations, with temperature forced by Newtonian relaxation towards a prescribed radiative equilibrium, are solved in chapter 4. At leading order, the resulting circulation has a zonal wind profile corresponding to uniform angular momentum at a level near the tropopause, and zero zonal surface wind, owing to the cancellation of the barotropic and baroclinic modes there. The weak surface winds are calculated from the first order corrections. The broad features of these solutions are similar to those obtained in previous studies of the dry Hadley circulation. The moist equations are solved in chapter 5, with a fixed sea surface temperature at the lower boundary and simple parameterizations of surface fluxes, deep convection, and radiative transfer. The solutions yield the structure of the barotropic and baroclinic winds, as well as the temperature and moisture fields. In addition, we derive expressions for the width and strength of the equatorial precipitating region (ITCZ) and the width of the entire Hadley circulation. The ITCZ width is on the order of a few degrees in the absence of any horizontal diffusion and is relatively insensitive to parameter variations. In chapter 6
Aeroacoustic data for high Reynolds number supersonic axisymmetric jets
NASA Astrophysics Data System (ADS)
Seiner, J. M.; Ponton, M. K.
1985-01-01
Both aerodynamic and near field acoustic behavior of several unheated axisymmetric shock free and shock containing high speed jet plumes are reported. The exit Mach number range for these data is from 0.9 to 2.5. The aerodynamic measurements include both mean and turbulence quantities for a shock free jet plume produced by a convergent divergent nozzle designed to have an exit Mach number of 2. The near field acoustic measurements presented include narrow band spectra, directivity and contour plots of select one third octave band data, and near field microphone correlations from a linear array. Shock noise results are also included as obtained by operating an underexpanded convergent nozzle at the design point of two supersonic exist Mach number convergent divergent nozzles.
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.
Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows
NASA Astrophysics Data System (ADS)
Gustavsson, K.; Einarsson, J.; Mehlig, B.
2014-01-01
We analyze the tumbling of small nonspherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of Lagrangian correlation functions. These capture preferential sampling of the fluid gradients, which in turn can give rise to differences in the tumbling rates of disks and rods. We show that this is a weak effect in Gaussian random flows. But in turbulent flows persistent regions of high vorticity cause disks to tumble much faster than rods, as observed in direct numerical simulations [S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Phys. Rev. Lett. 109, 134501 (2012), 10.1103/PhysRevLett.109.134501]. For larger particles (at finite Stokes numbers), rotational and translational inertia affects the tumbling rate and the angle at which particles collide, due to the formation of rotational caustics.
Meshless Petrov-Galerkin Method Applied to Axisymmetric Problems
NASA Technical Reports Server (NTRS)
Raju, I. S.; Chen, T.
2001-01-01
An axisymmetric Meshless Local Petrov-Galerkin (MLPG) algorithm is presented for the potential and elasticity problems. In this algorithm the trial and test functions are chosen from different spaces. By a judicious choice of these functions, the integrals involved in the weak form can be restricted to a local neighborhood. This makes the method truly meshless. The MLPG algorithm is used to study various potential and elasticity problems for which exact solutions are available. The sensitivity and effectiveness of the MLPG algorithm to various parameters such as the weight functions, basis functions and support domain radius, etc. was studied. The MLPG algorithm yielded accurate solutions for all weight functions, basis functions and support domain radii considered for all of the problems studied.
Confining individual DNA molecules in an axisymmetric entropy gradient
NASA Astrophysics Data System (ADS)
Peters, Robert D.; Dalnoki-Veress, Kari
2010-03-01
Many asymmetric and discontinuous confining environments have been used to study the properties of confined DNA. We have developed a unique method for studying DNA in micropipettes, resulting in a confining environment that is axisymmetric with a continuously changing entropy gradient. An applied electric field forces the chain into sub-micron confinement and fluorescence microscopy is used to track the effect of confinement on the entropy of individual DNA chains. Releasing the electric field, we probe the dynamics of the DNA chain in a continuously changing confinement, yielding a comprehensive study of the entropic force. This technique provides a novel method for studying the effect of polymer chain architecture on entropy. These architectures include knots in polymer chains, cyclic chains, or the presence of histones amongst DNA molecules.
Particle collector scoops for improved exhaust in ''axisymmetric'' devices
Conn, R.W.; Wolf, G.H.
1987-11-01
Application of particle collector scoops in front of the pumping ducts of axisymmetric divertor/magnetic limiter configurations is proposed. These scoops should enclose a significant fraction of the recycling particles. The resulting increase in natural particle pressure in front of the pumping ducts leads to an improved exhaust efficiency. This can permit an extension of the operational margin for density control. Alternatively, aiming at a prescribed exhaust flow in reactor-type devices such as INTOR, the pumping ducts could be reduced in aperture, leaving valuable space for other components. The lay-out of the proposed scheme depends on the heat load on the leading edge in front of the scoop and on the deflector in front of the pumping ducts. 14 refs., 5 figs.
Stabilized plane and axisymmetric Lobatto finite element models
NASA Astrophysics Data System (ADS)
Hu, Y. C.; Sze, K. Y.; Zhou, Y. X.
2015-11-01
High order elements are renowned for their high accuracy and convergence. Among them, Lobatto spectral finite elements are commonly used in explicit dynamic analyses as their mass matrices when evaluated by the Lobatto integration rule are diagonal. While there are numerous advanced first and second order elements, advanced high order elements are rarely seen. In this paper, generic stabilization schemes are devised for the reduced integrated plane and axisymmetric elements. Static and explicit dynamic tests are considered for evaluating the relatively merits of the stabilized and conventional elements. The displacement errors of the stabilized elements are less than those of the conventional Lobatto elements. When the material is nearly incompressible, the stabilized elements are also more accurate in terms of the energy error norm. This advantage is of practical importance for bio-tissue and hydrated soil analyses.
Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach
Gourgoulhon, Eric; Markakis, Charalampos; Uryu, Koji; Eriguchi, Yoshiharu
2011-05-15
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.
Time and 'angular' dependent backgrounds from stationary axisymmetric solutions
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.
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.
Full numerical simulation of coflowing, axisymmetric jet diffusion flames
NASA Technical Reports Server (NTRS)
Mahalingam, S.; Cantwell, B. J.; Ferziger, J. H.
1990-01-01
The near field of a non-premixed flame in a low speed, coflowing axisymmetric jet is investigated numerically using full simulation. The time-dependent governing equations are solved by a second-order, explicit finite difference scheme and a single-step, finite rate model is used to represent the chemistry. Steady laminar flame results show the correct dependence of flame height on Peclet number and reaction zone thickness on Damkoehler number. Forced simulations reveal a large difference in the instantaneous structure of scalar dissipation fields between nonbuoyant and buoyant cases. In the former, the scalar dissipation marks intense reaction zones, supporting the flamelet concept; however, results suggest that flamelet modeling assumptions need to be reexamined. In the latter, this correspondence breaks down, suggesting that modifications to the flamelet modeling approach are needed in buoyant turbulent diffusion flames.
Large elastic deformation of nonlinear axisymmetric membranes: a variational approach
Nielan, P.E.
1982-10-01
Variational equations for determining the deformed configuration of a pressurized axisymmetric membrane undergoing constant acceleration are derived. The general formulation is similar to that of Tielking and Feng. A Mooney-Rivlin material model is used for the membrane and large deformations and strains are accounted for. A Ritz procedure reduces the governing equations to a nonlinear algebraic form. Tensile instabilities are discussed in the context of the analytical solution available for a sphere. In a forthcoming report a computer program written to solve these equations will be described. The analysis and software will be verified by comparison with existing finite elasticity solutions. Solutions to new problems will be given. Ongoing work considering the coupling between structural deformation and the thermodynamics of inflation will be described and the effects of the acceleration on the pressure loads due to the gas will be discussed.
LAMINAR TRANSITIONAL AND TURBULENT BOUNDARY LAYERS FOR COMPRESSIBLE AXISYMMETRIC FLOW
NASA Technical Reports Server (NTRS)
Albers, J. A.
1994-01-01
This is a finite-difference program for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to a fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain factors of arbitrary Reynolds number, free-stream Mach number, free stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile. This program has been implemented on the IBM 7094/7044 Direct Couple System. This program is written in FORTRAN IV and was developed in 1974.
An analysis of turbulent diffusion flame in axisymmetric jet
NASA Technical Reports Server (NTRS)
Chung, P. M.; Im, K. H.
1980-01-01
The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.
Modular Coils and Plasma Configurations for Quasi-axisymmetric Stellarators
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.
Axisymmetric turbulent wakes with new non-equilibrium similarity scalings
NASA Astrophysics Data System (ADS)
Vassilicos, John Christos; Nedic, Jovan; Ganapathisubramani, Bharathram; TMFC, Imperial College London Team
2013-11-01
The recently discovered non-equilibrium turbulence dissipation law (Seoud & Vassilicos PoF 19, 2007, Mazellier & Vassilicos PoF 22, 2010, Valente & Vassilicos JFM 687, 2011, Valente & Vassilicos PRL 108, 2012, Gomes-Fernandes et al. JFM 711, 2012) 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 behaviour 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 fractal-like edges placed normal to an incoming free stream. EPSRC.
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.
Process modeling and development for three axisymmetric net shape forgings
El-Gizawy, A.S. . Dept. of Mechanical Aerospace Engineering)
1992-03-01
The results of dynamic material modeling experiments are reported on aluminum alloys 6061 and 7050, and steel alloy 4340. This information was used to accurately describe the variables in the various constitutive equations used in computer modeling programs. A description of the experimental equipment used to deform the specimens and gather data was given. Previously reported work regarding computer modeling of interface friction and the forging process was reviewed. Using dynamic flow models, three different axisymmetric parts were analyzed for their potential for being produced by net shape or near net shape forging processes. Two aluminum alloy parts were recommended as potential candidates while the steel part was not a potential candidate. Recommendations for processing conditions were also given. 18 refs.
Low frequency axisymmetric longitudinal guided waves in eccentric annular cylinders.
Pattanayak, Roson Kumar; Manogharan, Prabhakaran; Balasubramaniam, Krishnan; Rajagopal, Prabhu
2015-06-01
This paper studies the effect of axially uniform eccentricity on the modal structures and velocities of the lower order axisymmetric guided wave mode L(0,2) in circular tubes or pipes. The semi-analytical finite element method is mainly used, supported by fully three-dimensional finite element models and validated using experiments. The studies show that even a small eccentricity in the pipe can cause a loss in the L(0,2) mode axisymmetry, leading to its confinement in the thinned side of the pipe cross-section and also a reduction in mode velocities. The physics of this phenomenon is related to the feature-guiding and mode confinement effects noted in recent years in the literature, particularly studies on waveguides with local cross-section variations and curvature.
Tissue surface tension measurement by rigorous axisymmetric drop shape analysis.
David, Robert; Ninomiya, Hiromasa; Winklbauer, Rudolf; Neumann, A Wilhelm
2009-09-01
Certain behaviours of embryonic cell aggregates can be modelled by ascribing to them a tissue surface tension, with each cell analogous to a liquid molecule. Under normal gravity, aggregates are nearly spherical, but they can be partially flattened in a centrifuge. This allows measurement of their tissue surface tensions by a drop shape method such as axisymmetric drop shape analysis (ADSA). We study ectodermal embryonic cells from the frog Xenopus laevis subjected to centrifugation at 100 x g and 200 x g. We show that ADSA can be applied to irregular aggregate profiles and compare results with those from a previous, simpler version called ADSA-IP. With a modification in the experimental method, the two algorithms give similar results and the aggregate profiles more closely follow Laplacian curves. The ADSA fitting error allows an estimate of the relative uncertainty in the results.
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.
LAMINAR TRANSITIONAL AND TURBULENT BOUNDARY LAYERS FOR COMPRESSIBLE AXISYMMETRIC FLOW
NASA Technical Reports Server (NTRS)
Albers, J. A.
1994-01-01
This is a finite-difference program for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to a fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain factors of arbitrary Reynolds number, free-stream Mach number, free stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile. This program has been implemented on the IBM 7094/7044 Direct Couple System. This program is written in FORTRAN IV and was developed in 1974.
Theoretical study of multiple equilibria in simple axisymmetric tropical circulations
NASA Technical Reports Server (NTRS)
Goswami, B. N.
1983-01-01
The possibility that the asymmetric part of the atmospheric circulation can possess multiple equilibrium states is examined using a two-layer axisymmetric model involving balance equations on an equatorial beta plane. Mountains are excluded from consideration and a Newtonian cooling formulation represents thermal forcing. A temperature maximum at 25 deg N is selected to simulate summer conditions in the Northern Hemisphere. Steady-state solutions obtained are investigated for stability with regard to first and second y-mode perturbations. A single stable mode is found, together with two other quasi-stable states. Attention is given to numerically modeling multiple equilibria in symmetric circulations, and one steady-state is determined for the two-layer model. A model employing primitive equations with the Boussinesq approximation is also examined, and it also furnishes only one steady state. The reasons for the lack of multiple steady-states as derived by the models are discussed.
Drop trapping in axisymmetric constrictions with arbitrary contact angle
NASA Astrophysics Data System (ADS)
Ratcliffe, Thomas; Davis, Robert H.
2012-06-01
The differential Young-Laplace equations are solved numerically with an iterative solution using the method of steepest descent to determine the shape of a drop trapped under gravity in an axisymmetric ring constriction. Prior work for non-wetting drops with a contact angle of π is extended to arbitrary values of the contact angle at the three-phase contact lines. The critical Bond number, representing a dimensionless ratio of gravitational and interfacial forces, and separating static trapping at lower Bond numbers from dynamic squeezing at higher Bond numbers, decreases with decreasing contact angle, indicating that drop squeezing occurs more easily at smaller contact angle. Indeed, a critical contact angle, which depends only on the drop-to-hole and ring-cross-section-to-hole size ratios, is found, below which all drops squeeze through the hole.
A simplified analytic form for generation of axisymmetric plasma boundaries
Luce, Timothy C.
2017-02-23
An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less
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.
Axisymmetric nonlinear waves and structures in Hall plasmas
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.
Neutron tomography of axisymmetric flow fields in porous media
NASA Astrophysics Data System (ADS)
Gilbert, A. J.; Deinert, M. R.
2013-04-01
A significant problem in the study of fluid transport in porous media is the ability to visualize the structure of the flow field when moisture contents vary rapidly in space and time. Here we present a method for determining the radial and vertical saturation profiles within axisymmetric preferential flow fields using neutron radiography. Flow fields such as these are surprisingly common in nature and determining the three-dimensional structure of their wetting front region has proven difficult. In this work, the moisture profiles are determined using a simple algorithm for algebraic computed tomography, which gives the three-dimensional structure of the moisture profile with a temporal resolution that is limited only by the desired noise level. The algorithm presented can be translated to radiography done using X-rays or light and is applicable to any rotationally symmetric object.
Prediction of pressurant mass requirements for axisymmetric liquid hydrogen tanks
NASA Technical Reports Server (NTRS)
Vandresar, N. T.
1995-01-01
Experimental data from several test series are compared to an existing correlation that predicts the amount of pressurant gas mass required to expel liquid hydrogen from axisymmetric tanks. It was necessary to use an alternate definition of the tank equivalent diameter to accommodate thermal mass in the tank wall that is initially warm and to accommodate liquid residuals in the tank after expulsion is stopped. With this modification, the existing correlation predicted mass requirements to within 14 percent of experimental results. Revision of the correlation constants using a nonlinear least-squares fit of the current experimental data has a minor effect, thus supporting the validity of the original correlation's form, its fitted constants, and the alternate definition of the tank equivalent diameter.
Axisymmetric guided wave scattering by cracks in welded steel pipes
Zhuang, W.; Shah, A.H.; Datta, S.K.
1997-11-01
Scattering of axisymmetric guided waves by cracks and weldments of anisotropic bonding material in welded steel pipes is investigated in this paper by a hybrid method employing finite element and modal representation techniques. The study is motivated by the need to develop a quantitative ultrasonic technique to distinguish flaws and bonding materials in welded cylindrical structures. Numerical results for reflection coefficients are presented for a steel pipe with cracks and V-shaped weldments with and without cracks at the interface between the weldment and the steel pipe. It is shown that as the frequency increases, the coefficients of reflection exhibit resonant peaks at the cutoff frequencies of higher guided modes. These peaks become increasingly pronounced as the slope and the length of the crack increase. Numerical results presented have important applications in quantitative nondestructive evaluation.
Integrable Background Geometries
NASA Astrophysics Data System (ADS)
Calderbank, David M. J.
2014-03-01
This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric structure, governed by a nonlinear integrable differential equation, and each solution of this equation determines a background geometry on which, for any Lie group G, an integrable gauge theory is defined. In four dimensions, the geometry is selfdual conformal geometry and the gauge theory is selfdual Yang-Mills theory, while the lower-dimensional structures are nondegenerate (i.e., non-null) reductions of this. Any solution of the gauge theory on a k-dimensional geometry, such that the gauge group H acts transitively on an ℓ-manifold, determines a (k+ℓ)-dimensional geometry (k+ℓ≤4) fibering over the k-dimensional geometry with H as a structure group. In the case of an ℓ-dimensional group H acting on itself by the regular representation, all (k+ℓ)-dimensional geometries with symmetry group H are locally obtained in this way. This framework unifies and extends known results about dimensional reductions of selfdual conformal geometry and the selfdual Yang-Mills equation, and provides a rich supply of constructive methods. In one dimension, generalized Nahm equations provide a uniform description of four pole isomonodromic deformation problems, and may be related to the {SU}(∞) Toda and dKP equations via a hodograph transformation. In two dimensions, the {Diff}(S^1) Hitchin equation is shown to be equivalent to the hyperCR Einstein-Weyl equation, while the {SDiff}(Σ^2) Hitchin equation leads to a Euclidean analogue of Plebanski's heavenly equations. In three and four dimensions, the constructions of this paper help to organize the huge range of examples of Einstein-Weyl and selfdual spaces in the literature, as well as providing some new ! ones. The nondegenerate reductions have a long ancestry. More ! recently
NASA Astrophysics Data System (ADS)
Vassiliou, Peter J.
2009-10-01
Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equivariant method of Fels and Olver. Next, the contact geometry of curves in general Riemannian manifolds (M,g) is described. For the special case in which the isometries of (M,g) act transitively, it is shown that the contact geometry provides an explicit algorithmic construction of the differential invariants for curves in M. The inputs required for the construction consist only of the metric g and a parametrisation of structure group SO(n); the group action is not required and no integration is involved. To illustrate the algorithm we explicitly construct complete sets of differential invariants for curves in the Poincaré half-space H3 and in a family of constant curvature 3-metrics. It is conjectured that similar results are possible in other Cartan geometries.
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
A fast solver for systems of axisymmetric ring vortices
Strickland, J.H.; Amos, D.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{sup {minus}5} and 3 {times} 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities up to about 1 {times} 10{sup {minus}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% 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. 8 refs., 26 figs.
Topics in two-dimensional and axisymmetric vortex dynamics
NASA Astrophysics Data System (ADS)
Luithardt, Harry Hermann
1997-09-01
This work is composed of two independent parts whose common theme is the analysis of complex hydrodynamic phenomenon through the development of discrete vortex models. The first part investigates a new chaotic scattering phenomenon in two dimensions arising from the interaction of a thin vortex tube with a moving bluff body. Possible relevance to real hydrodynamic systems is established through development and implementation of a mixed finite difference-spectral algorithm applied to the direct simulation of Navier-Stokes equation around a cylindrical body for both inviscid and viscous boundary conditions. Small scale near boundary dynamics are resolved through employment of a radial stretching induced by a logarithmic coordinate transformation. Resulting simulations yielded an unexpectedly strong agreement between a point vortex model and the evolution of an initially Gaussian vortex patch. Completely new dynamics resulted only from initial conditions for large vortex patches which exhibit complex spatiotemporal dynamics. A new point vortex model was developed to explain this robustness of vortex patches. Pairs of point vortices were chosen. The guiding center of a pair corresponds to the previous single vortex, and the relative dynamics models internal degrees of freedom of a vortex patch. Resulting perturbation analysis and numerics reveals probable theoretical explanations of behavior observed in the CFD study. Further important parameters related to initial distribution of vorticity in patches are identified. Additional work done pertains to coherent structure formation in axisymmetric starting jets. A vortex sheet model for an impulsively started jet was decomposed into discrete, singular ideal vortex rings whose dynamical equations were derived from a Hamiltonian formalism. This motivated introduction of a novel symplectic integration scheme to avoid numerical stiffness. Detailed numerical studies show that simulations do not require artificial smoothing
Numerical Experiments of the Diurnal Cycle of Axisymmetric Tropical Cyclones
NASA Astrophysics Data System (ADS)
Navarro, E. L.; Hakim, G. J.
2015-12-01
Recent observational and modeling studies have shown that the diurnal cycle of radiation may be fundamentally linked to structural changes in the lifetime of a tropical cyclone. While these studies suggest that an underlying mechanism within the storm may exist, the dynamics for this response are still largely unexplained. Previous modeling studies were limited due to model configuration (e.g., initial and boundary conditions) as well as to radiative parameterization schemes. In this presentation, two new investigations are discussed to reexamine the role of the daily cycle of radiation on axisymmetric hurricane structure. In the first study, a tropical cyclone lasting 324 days is generated in Cloud Model 1 (CM1, see Bryan and Rotunno 2009) to quantify a tropical cyclone diurnal signal. A coherent response is observed in the temperature, wind, and cloud ice fields that accounts for up to a third of the overall variance. Composite analysis of each hour of the day shows a diurnal cycle in the storm intensity that, relative to the mean, intensifies in the early hours of the morning and is consistent with observational studies. Examination of the radial and vertical wind suggests two distinct circulations forced by the diurnal cycle: (1) a radiatively-driven circulation in the outflow layer due to absorption of solar radiation, and (2) a convectively-driven circulation within the storm due to latent heating. These responses are coupled and are periodic with respect to the diurnal cycle. In the second study, following the method of Pendergrass and Willoughby (2009) and Willoughby (2009), hypothesis tests using various prescribed, periodic heating distributions are performed to examine the dynamical response of the storm to radiation. Results reveal significant changes to the secondary-circulation structure of the storm, as well as to the intensification of the primary vortex. Sensitivity to the chosen heating distribution as well as to the initial vortex are discussed
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.
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…
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…
Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity
NASA Astrophysics Data System (ADS)
Tsuchida, T.; Watanabe, K.
1999-01-01
We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.
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.
Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses
NASA Astrophysics Data System (ADS)
Romero-García, V.; Cebrecos, A.; Picó, R.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.
2013-12-01
The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.
NASA Astrophysics Data System (ADS)
Maouche, B.; Feliachi, M.; Khenfer, N.
2006-01-01
We present the calculation of the impedance variation using a half-analytical formulation based on coupled electromagnetic variables. Such a formulation concerns an axisymmetrical device constituted with a voltage supplied solenoïdal inductor and a conducting workpiece. In this field of modelling, authors have already developed a method [Maouche and Feliachi, J. Phys. III France 10, 1967 (1997)] that determines the current distribution inside inductor coil loops in the case of weak skin depth and a low number of these coil loops. In the proposed development, the number of loops is relatively large and the skin effect in these loops is negligible. This formulation uses a voltage excitation, which makes the source field depending on induced currents and permits to consider the real geometry of the inductor. The model is applied to study an eddy current non destructive testing (ECNDT) device. The variation of the system impedance is calculated in the case of an axisymmetrical device. The obtained modelling results are validated by comparison to measurements and finite element computations [Rémy, Ph.D. thesis, University of Compiègne, France, 1997; La et al., Rev. Prog. Quant. Non-Destructive Eval. 16A, 295 (1997)]. Once validated, the proposed model is applied to determine geometrical and physical characteristics of an ECNDT device. To assemble this interest, we visualise the evolution of the impedance variation according respectively to the air-gap, to the thickness of the workpiece and its electric conductivity. The model is implemented within a software tool (CECM: Coupling Electromagnetic Circuits Method) developed in Matlab environment.
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).]).
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)]).
NASA Astrophysics Data System (ADS)
Lyons, B. C.; Jardin, S. C.; Ramos, J. J.
2012-08-01
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 ψ defines a flux surface, θ is the poloidal angle, v is the magnitude of the 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 cosχ, where χ is the pitch angle, Fourier series in cosθ, 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, 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., Comput. Sci. Discovery 5, 014002 (2012)]).
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.
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.
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.
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.
Sliding vane geometry turbines
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.
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…
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…
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.
ERIC Educational Resources Information Center
Hirata, Li Ann
Core Geometry is a course offered in the Option Y sequence of the high school mathematics program described by the Hawaii State Department of Education's guidelines. The emphasis of this course is on the general awareness and use of the relationships among points, lines, and figures in planes and space. This sample course is based on the…
Emergent Hyperbolic Network Geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Emergent Hyperbolic Network Geometry.
Bianconi, Ginestra; Rahmede, Christoph
2017-02-07
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
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)
ERIC Educational Resources Information Center
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
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)
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-01-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry. PMID:28167818
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)
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…
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
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
ERIC Educational Resources Information Center
Fielker, David
2007-01-01
Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…
ERIC Educational Resources Information Center
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
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)
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)
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
ERIC Educational Resources Information Center
Fielker, David
2007-01-01
Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…
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)
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
NASA Astrophysics Data System (ADS)
Galland, O.; Scheibert, J.
2013-03-01
In this paper, we develop a new axisymmetric analytic model of surface uplift upon sills and laccoliths, based on the formulation of a thin bending plate lying on an elastic foundation. In contrast to most former models also based on thin bending plate formulation, our model accounts for (i) axi-symmetrical uplift, (ii) both upon and outside the intrusion. The model accounts for shallow intrusions, i.e. the ratio a/h > 5 where a and h are the radius and depth of the intrusion, respectively. The main parameter of the model is the elastic length l, which is a function of the elastic properties of the bending plate and of the elastic foundation. The model exhibits two regimes depending on the ratio a/l. When a/l < 5, the uplift spreads over a substantial domain compared to that of the intrusion. In contrast, when a/l > 5, the uplift is mostly restricted upon the intrusion. When the elastic foundation is very stiff, our model converges towards that of a clamped plate. We provide, as supplementary material, a Matlab function that calculates the surface uplift from the set of system and control parameters. We discuss three possible applications of our model: (i) The model can be used to describe sill propagation by introducing a propagation criterion. For realistic values, our model reproduces well the behavior of horizontal intrusions simulated in experiments; (ii) The model can also be used to compute the critical size of saucer-shaped sills. It shows, for instance, that a soft elastic foundation favors the horizontal spreading of sills before they form inclined sheets; (iii) We show that the classical Mogi point source model cannot be used to constrain sill properties from the surface uplift. We thus propose that our model can be used as a valuable alternative to both simple analytical models like Mogi's and more complex numerical models used to analyze ground deformation resulting from sill intrusions in active volcanoes.
Experiences with the use of axisymmetric elements in cosmic NASTRAN for static analysis
NASA Technical Reports Server (NTRS)
Cooper, Michael J.; Walton, William C.
1991-01-01
Discussed here are some recent finite element modeling experiences using the axisymmetric elements CONEAX, TRAPAX, and TRIAAX, from the COSMIC NASTRAN element library. These experiences were gained in the practical application of these elements to the static analysis of helicopter rotor force measuring systems for two design projects for the NASA Ames Research Center. These design projects were the Rotor Test Apparatus and the Large Rotor Test Apparatus, which are dedicated to basic helicopter research. Here, a genetic axisymmetric model is generated for illustrative purposes. Modeling considerations are discussed, and the advantages and disadvantages of using axisymmetric elements are presented. Asymmetric mechanical and thermal loads are applied to the structure, and single and multi-point constraints are addressed. An example that couples the axisymmetric model to a non-axisymmtric model is demonstrated, complete with DMAP alters. Recommendations for improving the elements and making them easier to use are offered.
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.
MODELING MID-INFRARED VARIABILITY OF CIRCUMSTELLAR DISKS WITH NON-AXISYMMETRIC STRUCTURE
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.
Control of an axisymmetric turbulent jet by multi-modal excitation
NASA Technical Reports Server (NTRS)
Raman, Ganesh; Rice, Edward J.; Reshotko, Eli
1991-01-01
Experimental measurements of naturally occurring instability modes in the axisymmetric shear layer of high Reynolds number turbulent jet are presented. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes dominated only downstream of the potential core region. The energy content of the higher order modes (m is greater than 1) was significantly lower than that of the axisymmetric and m = + or - 1 modes. Under optimum conditions, two-frequency excitation (both at m = 0) was more effective than single frequency excitation (at m = 0) for jet spreading enhancement. An extended region of the jet was controlled by forcing combinations of both axisymmetric (m = 0) and helical modes (m = + or - 1). Higher spreading rates were obtained when multi-modal forcing was applied.
Control of an axisymmetric turbulent jet by multi-modal excitation
NASA Technical Reports Server (NTRS)
Raman, Ganesh; Rice, Edward J.; Reshotko, Eli
1991-01-01
Experimental measurements of naturally occurring instability modes in the axisymmetric shear layer of high Reynolds number turbulent jet are presented. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes dominated only downstream of the potential core region. The energy content of the higher order modes (m is greater than 1) was significantly lower than that of the axisymmetric and m = + or - 1 modes. Under optimum conditions, two-frequency excitation (both at m = 0) was more effective than single frequency excitation (at m = 0) for jet spreading enhancement. An extended region of the jet was controlled by forcing combinations of both axisymmetric (m = 0) and helical modes (m = + or - 1). Higher spreading rates were obtained when multi-modal forcing was applied.
Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
Lyons, Brendan Carrick
2014-11-01
Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literature
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
Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
NASA Astrophysics Data System (ADS)
Lyons, Brendan Carrick
Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literatureAB that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of fNM . We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered
Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical geometry
NASA Astrophysics Data System (ADS)
Zhang, J.; Wang, L. F.; Ye, W. H.; Wu, J. F.; Guo, H. Y.; Zhang, W. Y.; He, X. T.
2017-06-01
In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P 2 n and P 3 n , which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0- P 3 n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of three-dimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles.
Navier Stokes simulations of supersonic jets from axisymmetric and rectangular nozzles
NASA Astrophysics Data System (ADS)
Ying, S. X.; Krothapalli, A.; Wishart, D.
1992-07-01
A mass-weighted time-averaged Navier-Stokes approach is used to solve a 3D flow of supersonic jets. An algebraic eddy viscosity model is presented which accounts for the turbulence of the compressible mixing layer. Particular attention is given to Mach 2 jets from an axisymmetric nozzle and a rectangular nozzle of aspect ratio 4:1. Good agreement is found between measurements and the Navier-Stokes simulations for supersonic jets from both axisymmetric and rectangular nozzles.
NASA Technical Reports Server (NTRS)
Hamilton, H. H., II
1980-01-01
A theoretical method was developed for computing approximate laminar heating rates on three dimensional configurations at angle of attack. The method is based on the axisymmetric analogue which is used to reduce the three dimensional boundary layer equations along surface streamlines to an equivalent axisymmetric form by using the metric coefficient which describes streamline divergence (or convergence). The method was coupled with a three dimensional inviscid flow field program for computing surface streamline paths, metric coefficients, and boundary layer edge conditions.
EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO
Pipin, V. V.; Kosovichev, A. G.
2015-11-10
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{sub ⊙} 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 R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} 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.
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.
2014-12-01
CORRESPONDENCE Comments on ‘‘How Does the Boundary Layer Contribute to Eyewall Replacement Cycles in Axisymmetric Tropical Cyclones?’’ MICHAEL T...Axisymmetric Tropical Cyclones?’ 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f...hypothesis using observational data and choose instead tests using two independent cloud-representing numerical solu- tions of a mature tropical cyclone
General criteria for determining rotation or oscillation in a two-dimensional axisymmetric system
NASA Astrophysics Data System (ADS)
Koyano, Yuki; Yoshinaga, Natsuhiko; Kitahata, Hiroyuki
2015-07-01
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.
Geometry of thermodynamic control.
Zulkowski, Patrick R; Sivak, David A; Crooks, Gavin E; DeWeese, Michael R
2012-10-01
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one-dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first-order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory.
Cylindrical geometry hall thruster
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.
NASA Astrophysics Data System (ADS)
Cederwall, Martin; Rosabal, J. A.
2015-07-01
We investigate exceptional generalised diffeomorphisms based on E 8(8) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL( n + 1) is sketched. Some related issues are discussed.
Emergent geometry, emergent forces
NASA Astrophysics Data System (ADS)
Selesnick, S. A.
2017-10-01
We give a brief account of some aspects of Finkelstein’s quantum relativity, namely an extension of it that derives elements of macroscopic geometry and the Lagrangians of the standard model including gravity from a presumed quantum version of spacetime. These emerge as collective effects in this quantal substrate. Our treatment, which is largely self-contained, differs mathematically from that originally given by Finkelstein. Dedicated to the memory of David Ritz Finkelstein
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.
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.
Integral geometry and holography
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 AdS_{3}/CFT_{2} 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 AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Noncommutative geometry and arithmetics
NASA Astrophysics Data System (ADS)
Almeida, P.
2009-09-01
We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.
NASA Astrophysics Data System (ADS)
Beggs, Edwin J.; Majid, Shahn
2017-04-01
We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter λ, using a functorial approach. This leads us to field equations of 'Poisson-Riemannian geometry' between the classical metric, the Poisson bracket and a certain Poisson-compatible connection needed as initial data for the quantisation of the differential structure. We use such data to define a functor Q to O(λ2) from the monoidal category of all classical vector bundles equipped with connections to the monoidal category of bimodules equipped with bimodule connections over the quantised algebra. This is used to 'semiquantise' the wedge product of the exterior algebra and in the Riemannian case, the metric and the Levi-Civita connection in the sense of constructing a noncommutative geometry to O(λ2) . We solve our field equations for the Schwarzschild black-hole metric under the assumption of spherical symmetry and classical dimension, finding a unique solution and the necessity of nonassociativity at order λ2, which is similar to previous results for quantum groups. The paper also includes a nonassociative hyperboloid, nonassociative fuzzy sphere and our previously algebraic bicrossproduct model.
Emergent Complex Network Geometry
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